A Variable Pressure Multi-Pressure Rail System Design for Agricultural Applications

Abstract

This paper presents a solution for reducing energy loss in the hydraulic control system of agricultural tractors and their implements. The solution is referred to as a multi-pressure rail (MPR) and provides power to the hydraulic functions following a pressure control logic, as opposed to the traditional flow control logic typical of hydraulic systems used in off-road vehicles. The proposed hydraulic control system allows for elimination of redundant flow control valves in the state-of-the-art system, which cause excessive throttling losses leading to poor overall energy efficiency. Related work on MPR technology targets construction vehicles, where the MPR solution can allow energy recovery during overrunning loads and better engine management. This paper alternatively addresses the case of agricultural applications where functions mostly operate under resistive load conditions with slow dynamics, which offers an opportunity to target throttle losses. For this purpose, the paper introduces a variable pressure control strategy to handle the instantaneous pressure at each rail. To develop both the controller and the hydraulic system architecture, a stationary test rig is conceived and used to validate a numerical simulation model of the MPR system and its control strategy. Particular focus is given to the dynamic behavior of the system during the switches of a function between different pressure rails, which needs to ensure reduced oscillations of the flow provided to each hydraulic function. Once validated, the simulation model is used to predict the energy savings of the MPR solution in an actual application: a 435 hp hydraulic tractor powering a 16-row planter, for which operating features during typical drive cycles were available to the authors. The results show up to 59% total power reduction at the pump shaft, corresponding to 89.8% system efficiency gain.

1. Introduction

In recent years, global warming and climate change have gained enormous attention and motivated many technological advancements. One key parameter is fossil fuel usage leading to greenhouse gas emission. In that regard, off-road mobile machineries, which include agriculture equipment, construction equipment, etc., play an important role [1]. However, the state-of-the-art hydraulic architectures for agricultural applications result in low system efficiency (20% on average [2]) and are unsuited for the efficiency requirements of the coming years. As a result, this study will focus on agricultural machine systems.

The typical usage of an agricultural tractor includes performing a certain function on a field, such as a planter, seeder, bailer, etc. Such implements have their own actuators which are typically powered by the high-pressure hydraulic system of the tractor through so-called hydraulic remote connections. The most common configuration of the overall hydraulic circuit can be represented with the simplified schematic of Figure 1 below. The tractor is equipped with a load-sensing (LS) hydraulic circuit, comprised of a variable displacement pump with a differential flow limiter (or LS regulator) and a load-sensing valve (referred to as an electro-hydraulic remote valve, EHR). Such a circuit is among the most energy efficient solutions for controlling multiple actuators [3]; the pump delivery pressure settles to the maximum actuator pressure (plus a pump margin $p_{mar}$), thus minimizing excessive system pressurization.

The implement hydraulic control system includes the actuators performing the agricultural functions and a local flow control valve at each actuator to regulate its velocity. Such an arrangement allows the placement of multiple actuators on a single remote line in the tractor, as shown in Figure 1 (left) and makes the control performance of the implement independent of the tractor brand or technology level.

Unfortunately, this arrangement voids the principle of operation of the LS system because the commanded flow rate at the remote valve is not satisfied by the LS pump, which instead must meet the demand of the implement valves. This is achieved by commanding the maximum flow at the EHR and letting the pressure compensators (PCs) of the implement reach the maximum pressure of the pump $p^{*}$. Therefore, the pump is in pressure saturation conditions no matter the actual load at the actuators. This typically leads to a very low energy efficiency of the hydraulic control system, as represented in the power plot of Figure 1 right, where the orange area represents energy loss due to throttling. If the system functioned as an LS system, the pump pressure would be at $p_{LS}$, the maximum actuator load $p_{Ac{t}_{max}}$, plus the pump margin $p_{mar}$ to ensure correct functionality of the control valve, instead of $p_{max}$.

Due to the popularity of LS systems, the literature reports several methods for improve their energy efficiency. Bedotti et al. [4] attempted to reduce throttling losses by reducing the LS margin of the system. Reducing the margin risks compromising system performance, however, so ref. [4] settles on a safe margin reduction of 23%, yielding power savings of approximately 4%. Tian et al. [5] expanded on this and proposed a method of dynamically varying the LS margin of a pump, reducing throttling losses without risking system performance, but without addressing losses due to widely varied loads. Siebert et al. [6] put forward a system of reducing throttling losses by elevating the outlet pressure of actuators, thus lessening the losses while maintaining a constant pressure drop across the actuator. This solution saw a 44% reduction in throttling losses in a simulation. Another relevant technology is that of independent metering, wherein the inlet and outlet control orifice are decoupled and independently controlled [7], allowing for more flexible control and power optimization with precise dynamics [8].

None of the above solutions, however, solve the issue of the previously outlined control conflict among flow control valves, which is at the core of the inefficient tractor–implement operation due to pressure saturation of the supply pump. This pressure saturation could be avoided by sensing the load pressure at the actuator ($p_a$, $p_b$, or $p_c$, Figure 1 right), rather than at the EHR outlet ($p_U$). However, such a solution is normally not used because it does not achieve proper dynamic behavior (pump flow variation is not fast enough to cope with the actuator load variations), and it would make the tractor and planter technologies dependent on one another.

Therefore, to achieve higher energy efficiency in hydraulic control systems, alternative layout architectures should be considered. The literature usually reports on the displacement control actuation as one of the most efficient methods to control a function, as it eliminates throttling losses entirely [3,9]. However, this technology requires a dedicated flow supply (i.e., hydraulic pump) for each function, and therefore it is too costly and impractical for a tractor–implement system which must consider a multitude of functions. Successful application of displacement control technology was, however, possible in construction equipment [10,11,12,13,14]. A method for reducing the number of pumps was also proposed by Busquets et al. [15], where a control sharing protocol for the pump flow was designed based on typical excavator cycles, making it possible to control all excavator functions with four pumps. However, such a strategy is much more difficult to implement in agricultural systems as they can connect to implements with unknown drive cycles.

An alternative hydraulic actuation technology, not yet common in the field of off-road vehicles, are pressure-controlled flow supplies [3]. In such systems, the supply pump is not set to match a commanded flow, as in the system of Figure 1 (left), but rather to establish a commanded pressure. The simplest implementation of this design is the constant pressure (CP) system, in which the supply pump sets the pressure in a common pressure rail that connects the pump with the actuator, with control valves that control the flow from this rail [16]. The CP system decouples the actuators from the prime mover, allowing for power management strategies to be implemented at the prime mover. The CP system also achieves higher control bandwidth, as the actuator response usually functions on the control valve that is receiving flow from the rail and is independent of the supply pump. However, a basic CP system with one pressure rail suffers from excessive throttling losses, as the rail pressure must exceed the maximum load pressure, and flow from the rail to all other actuators at a lower pressure is throttled down. As described in [17], advanced CP systems address this problem in two possible ways: by controlling the displacement of the actuator directly, and thus the speed and torque, or by using hydraulic transformers to reduce the pressure delivered by the rail without throttling. The first strategy has been implemented successfully by Volvo [18] on a 30-ton excavator. This design utilized a novel variable-area cylinder and showed 34–50% gains in fuel efficiency. Several hydraulic transformer designs have been put forward, as seen in [19,20] but these systems have yet to see widespread adoption, due to the complexity, cost, and unproven reliability of the component.

The multi-pressure rail (MPR) system considered in this paper does not fall into either of the previously outlined categories for advanced CP systems, and instead proposes the use of more than one pressure rail. The idea was initially somewhat outlined by Lumkes et al. [21] who designed a general form of the MPR system and tested its feasibility on a backhoe test rig. The results proved functionality, but the work did not address specific controller design or power-saving potential. Dengler et al. in [22,23] proposed the addition of a fixed pressure medium pressure rail, calculating a theoretical increase of 20% efficiency over a state-of-the-art LS system in a simulation.

The most relevant prior work to the MPR system considered in this paper is the STEAM excavator developed by the IFAS team at RWTH Aachen, [24,25] and the hybrid hydraulic architecture (HHEA) by Li et al. [26]. Both systems used variations of MPR architectures for construction equipment. The STEAM excavator system makes extensive use of engine management strategies and energy recovered from overrunning loads where possible. Published measurements show a 30% reduction in fuel consumption. Although not demonstrated in an actual vehicle, the HHEA system conceptualizes the use of additional hydraulic and electric machines (one per each actuator) to essentially replicate the function of hydraulic transformers and reduce the throttle loss. This system should allow energy consumption to be reduced by 40% according to the simulation. Neither of these architectures vary the level of the instantaneous pressure in the rails, mostly due to the high dynamic features of the drive cycles typical of construction equipment. Opgenoorth et al. in [27] proposed an MPR architecture for an electrified excavator which included variable rail pressures, showing a 29% efficiency gain over a standard LS system in a simulation. However, no controller design or experimental validation were presented. Bertolin and Vacca in [28] provided a parametric study that evaluates how different cylinder areas affect the efficiency of the proposed system. It also considers different number of rails in the system and how to optimize their pressure levels to maximize system efficiency.

Finally, the authors of this paper previously put forward several options for the architecture and control of a variable pressure rail MPR system in [29]. This work used a physical test rig to prove the basic controllability of the system, and also to compare the relative effectiveness of one pump, two accumulators, and two pumps, no accumulator systems for such a system. The work was successful in identifying that while the variable pressure system was controllable with both supply systems, the two-pump system without accumulators had far better dynamic behaviors due to the absence of the additional capacitance from the accumulators.

The purpose of this paper is to formulate, design, and experimentally prove a variable pressure MPR system specific to an agricultural-implement system, which are characterized by a high number of actuators with low dynamic requirements and limited chances of energy recovery. The goal of the paper is to address the hydraulic system design as well as quantifying the energy savings that can be achieved considering an actual application.

This paper first presents the MPR system design considering the unique system characteristics in Section 2. In Section 3, the multi-level controller is introduced in detail. Following this, a test rig is designed, modeled, built, and tested to validate the stability and performance of the proposed MPR controller in Section 4. Moreover, Section 5 shows the two reference vehicles (a tractor and an implement) that are very popular in the field. Finally, a lumped parameter complete system model, including the reference tractor, planter, and the proposed MPR components, is built, validated, and used to predict the power saving and efficiency gain at the machine’s representative working condition in Section 6. The results show up to 59% total power reduction at the pump shaft, corresponding to 89.8% system efficiency gain.

2. MPR System Description

Figure 2 shows the design of the MPR system with a generic number of pressure rails as considered in this work. It includes a supply system, pressure rails, pressure select and control valve sets (PSCV), and actuators. The supply system controls the pressure level in each rail. The rails connect the supply system to each PSCV. Then, the PSCVs connect the most appropriate rails to the inlet and outlet of each actuator to minimize throttling loss. The PSCVs also control the flow rate to match the commanded velocity.

Figure 3 and Figure 4 show an example of how the three-rail MPR system works for both hydraulic motors and cylinders with PSCV. First, the PSCV pressure selection stage (V1–V6) will be opened or closed to connect the line $A1$ and $B1$ to the pressure rails according to the command from the supervisory controller. Then, the metering stage control valve (VA and VB) will control the actuator speed tracking with the actuator controller. Using different combinations of inlet/outlet pressure levels, the MPR makes available to each actuator multiple output torque and force ranges. For example, considering an MPR system with three rails, a hydraulic motor can operate under six possible modes: high pressure at the inlet with low pressure at the outlet (HP-LP), HP-MP, MP-LP, LP-MP, LP-HP, and MP-HP. There are also three idle modes: LP-LP, MP-MP, and HP-HP. Due to the pressure losses in the lines and selection and metering valves, the pressure margin $p_{mar}$ needs to be considered to leave enough pressure drop for proper functioning of the actuator. As a result, the torque range for each working mode is shown in

Table 1. Working Mode Torque Range for Three-Rail MPR System.

Load Condition	Mode	Lower Limit (Nm)	Upper Limit (Nm)
Resistive	MP-LP	0	$\frac{{\mathrm{V}}_{\mathrm{m}}\left({\mathrm{p}}_{\mathrm{MP}}-{\mathrm{p}}_{\mathrm{LP}}-{\mathrm{p}}_{\mathrm{mar}}\right)}{2\mathsf{\pi }}$
	HP-MP	$\frac{{\mathrm{V}}_{\mathrm{m}}\left({\mathrm{p}}_{\mathrm{MP}}-{\mathrm{p}}_{\mathrm{LP}}-{\mathrm{p}}_{\mathrm{mar}}\right)}{2\mathsf{\pi }}$	$\frac{{\mathrm{V}}_{\mathrm{m}}\left({\mathrm{p}}_{\mathrm{HP}}-{\mathrm{p}}_{\mathrm{MP}}-{\mathrm{p}}_{\mathrm{mar}}\right)}{2\mathsf{\pi }}$
	HP-LP	$\frac{{\mathrm{V}}_{\mathrm{m}}\left({\mathrm{p}}_{\mathrm{HP}}-{\mathrm{p}}_{\mathrm{MP}}-{\mathrm{p}}_{\mathrm{mar}}\right)}{2\mathsf{\pi }}$	$\frac{{\mathrm{V}}_{\mathrm{m}}\left({\mathrm{p}}_{\mathrm{HP}}-{\mathrm{p}}_{\mathrm{LP}}-{\mathrm{p}}_{\mathrm{mar}}\right)}{2\mathsf{\pi }}$
Overrunning	LP-LP/MP-MP/HP-HP	$\frac{{\mathrm{V}}_{\mathrm{m}}\left({\mathrm{p}}_{\mathrm{LP}}-{\mathrm{p}}_{\mathrm{MP}}+{\mathrm{p}}_{\mathrm{mar}}\right)}{2\mathsf{\pi }}$	0
	LP-MP	$\frac{{\mathrm{V}}_{\mathrm{m}}\left({\mathrm{p}}_{\mathrm{MP}}-{\mathrm{p}}_{\mathrm{HP}}+{\mathrm{p}}_{\mathrm{mar}}\right)}{2\mathsf{\pi }}$	$\frac{{\mathrm{V}}_{\mathrm{m}}\left({\mathrm{p}}_{\mathrm{LP}}-{\mathrm{p}}_{\mathrm{MP}}+{\mathrm{p}}_{\mathrm{mar}}\right)}{2\mathsf{\pi }}$
	MP-HP	$\frac{{\mathrm{V}}_{\mathrm{m}}\left({\mathrm{p}}_{\mathrm{LP}}-{\mathrm{p}}_{\mathrm{HP}}+{\mathrm{p}}_{\mathrm{mar}}\right)}{2\mathsf{\pi }}$	$\frac{{\mathrm{V}}_{\mathrm{m}}\left({\mathrm{p}}_{\mathrm{MP}}-{\mathrm{p}}_{\mathrm{HP}}+{\mathrm{p}}_{\mathrm{mar}}\right)}{2\mathsf{\pi }}$
	LP-HP	Maximum System Torque	$\frac{{\mathrm{V}}_{\mathrm{m}}\left({\mathrm{p}}_{\mathrm{LP}}-{\mathrm{p}}_{\mathrm{HP}}+{\mathrm{p}}_{\mathrm{mar}}\right)}{2\mathsf{\pi }}$

.

If the motor load is at the value T1 as shown in Figure 3, the system should work under mode MP-LP (the red line in the figure) to minimize the throttling loss to $\mathsf{\Delta }{p}_1$. Clearly, this is a great advantage in comparison with the baseline system of Figure 1 (left) which puts all the actuators under the maximum pressure differential. In case of an overrunning load, such as $T_2$, the MPR has the potential to recover energy by connecting the motor inlet to LP and the outlet to MP. This allows the motor to work in pumping mode, thus inputting energy back to the system, under a minimal throttling loss $\mathsf{\Delta }{p}_2$.

The hydraulic cylinder, illustrated in Figure 4 (pressure margin lines are omitted), works under a similar principle. The only difference is for cylinders with differential areas, the idle modes for hydraulic motors can also output force, such as force levels $A\left(p_{HP}-\alpha p_{HP}\right)$, $A\left(p_{MP}-\alpha p_{MP}\right)$, and $A\left(p_{LP}-\alpha p_{LP}\right)$. As a result, there are nine force lines in total compared to the six torque lines of a symmetric actuator. When the cylinder has a resistive load, such as $F_1$ in Figure 4 (right), the best working mode is MP-LP (the red line in the figure) with the throttling loss $\mathsf{\Delta }{p}_3$. With overrunning load $F_2$, the system prefers working in the same mode to recover energy to the MP rail with throttling loss $\mathsf{\Delta }{p}_4$.

The case of unidirectional motors with no overrunning loads is further considered in this section to present general design considerations for the MPR system. This case is particularly relevant for agricultural tractor–implement systems, and in particular for the reference tractor–planter as it will be described in Section 4.

2.1. Number of Rails

The number of rails is a critical parameter in an MPR system, as it directly determines the number of modes available for the actuator connections. A two-rail system has only one mode, as each actuator can be connected only with the HP line and the LP line. In a three-pressure MPR, there are three modes: supply from medium pressure (MP) to LP rail (MP-LP), from HP to MP rail (HP-MP), and from HP to LP rail (HP-LP). The number of modes $\left(n_{md}\right)$ is determined by the number of rails $\left(n_R\right)$ as seen in Equation (1) with a unidirectional motor as the actuator.

$$n_{md}=\frac{n_R\left(n_R-1\right)}{2}$$

(1)

Intuitively, the more rails there are in the system, the less throttling losses will occur. However, a high number of rails can be impractical, as it implies a high number of components (detrimental for costs and spatial requirements) and added control complexity. Therefore, the optimal number of rails comes from a compromise between energy loss and technical-economic feasibility. Considering all the benefits and costs of adding rails, the three-rail MPR system is the most suited choice for the reference system which will be introduced in Section 4. As a result, the MPR system design in this study will continue with three pressure rails. The simulation results that drove this decision can be seen in Section 6.

2.2. Supply System

Based on the analysis and experimental work in [29], to achieve the target of unidirectional, resistive load conditions present in most agricultural implements, the supply system shown in Figure 5 is most suitable due to its fast response in rail pressure control. This system uses one pump per pressure rail, allowing for a fast control response for both pressures independently. Most of the time this is the operating mode in which the system will run. Should a user require a higher flow than one pump can provide, however, a merging valve is included which connects both pumps to one rail. This setup allows for the pumps to be downsized somewhat, in turn causing them to typically run at higher displacements and efficiencies. Finally, the MP pump must be able to go over center in order to handle any cases in which flow coming from the HP rail to the MP rail exceeds the flow from the MP to LP rails.

To size the pumps, there are two options. For the first option, both pumps should be sized large enough to supply the full flow required by the users to eliminate any possibility of pump flow saturation for both rails. This sizing option will ensure the system always remains in normal MPR mode and no merging of flow is needed. However, the pumps will suffer from lower efficiency due to working at a lower displacement. For the second option, owing to the merging valve, the total flow from both pumps needs to satisfy the maximum required flow rate as shown in Equation (2). This provides design freedom on how to size HP and MP pumps and an optimization method is proposed in this work to determine the best size for both pumps.

$$V_{p_{HP}}+V_{p_{MP}}\ge \frac{q_{max}}{{\omega }_p}$$

(2)

To find the best size for both pumps, a cost function $J$ is defined in Equation (3). This cost function evaluates only the average power loss during the reference machine’s normal working condition, which represents the bulk of the machine’s operating time throughout its lifetime. The first half of the cost function represents the summation of volumetric $q_{s_{p_k}}$ and hydromechanical losses $T_{s_{p_k}}$ for the pump $k$ at corresponding working pressure $p_{pk}-p_{LP}$, and rotational speed ${\omega }_{p_k}$. The second half calculates the throttling loss in the control valves for all $n_{act}$ actuators at their flow rate $q_j$, and pressure drop across their control valve $p_{in}-\mathsf{\Delta }{p}_i-p_{out}$. $p_{in}$ and $p_{out}$ are the inlet and outlet rail pressures that are selected by the pressure selection stage valve in Figure 4, and they are either HP, MP, or LP. The actuator load pressure $\mathsf{\Delta }{p}_i$ is the pressure drop across the actuator suction side and deliver side. With the cost Function (3) and Constrain (2), the best pump size that could satisfy the flow requirements and minimize the system loss could be found for the selected target machine.

$$J={\displaystyle \sum }_{k=1}^2\left(q_{s_{pk}}\left(p_{pk}-p_{LP}\right)+T_s{}_{pk}{\omega }_{p_k}\right)+{\displaystyle \sum }_{j=1}^{n_{act}}{q}_j\left(p_{in}-\mathsf{\Delta }{p}_i-p_{out}\right)$$

(3)

Due to limited resources, this study will use the same size of units as the reference machine (45 cc), which follows the first sizing option, and all the controller design and simulation results are with respect to that size.

2.3. Pressure Select and Control Valve Set

There are many ways to achieve these two functions. The most generic design is shown in Figure 6 (left). It includes six on/off valves (V1–V6) as the pressure select valves and two proportional valves (VA and VB) as the actuator control valves. Two pressure relief valves and check valve sets are used to protect the circuit from overpressure or cavitation. In this setup, the actuator can operate in both directions (A to B, or B to A) in both resistive and overrunning loading conditions, as both the inlet and return of the actuator could be connected to any rail. Moreover, both metering-in and metering-out control strategies are possible. This design is very flexible but also expensive, as it uses many solenoid-operated valves.

To better fit the valve set design to the actuator, the load characteristic (mentioned at the end of the state-of-the-art section) should be considered. Based on these characteristics, the architecture of Figure 6 (right) would be a more suitable design for this study. It only has two on/off valves (V1 and V2) with two check valves at the pressure select stage. The inlet side can connect to HP and MP pressure rails and the outlet can connect to MP and LP pressure rails. On top of that, it has only one metering valve (VA) on the A side for meter-in control. An anti-cavitation check valve is placed between the actuator work ports and two pressure relief and check valves are used to protect the circuit. This design can no longer achieve all working conditions as option 1 can, but is adequate for the previously discussed unidirectional actuators, without overrunning loads, and greatly reduces the number of solenoids, and thus cost and control complexity.

3. MPR Controller Design

The control structure for the proposed MPR system has two levels: the actuator level controllers and the supervisory level controller. The actuator level controllers include the actuator speed controller, the rail pressure controller, and the pump displacement controller. The supervisory controller is the online optimization controller that sets the HP and MP rail pressure to minimize total power loss due to fluid throttling.

The basic control structure is shown in Figure 7. The mechanical and hydraulic components of the tractor and its implement are in red and orange boxes, and the controllers are in green boxes. When the actuator command comes in, the supervisory controller records it and passes it on to the actuator speed controller. Following this, the actuator speed controller controls the metering valve of the actuator to track the actuator command. In the meantime, the actuator load pressure is measured and sent back to the supervisory controller, along with the actuator command, for use in the rail pressure online optimization. Next, the supervisory controller sends the optimized HP and MP rail pressure commands and the optimal working mode for each actuator to the rail pressure controller and the actuator selection valves. In addition, a feedforward displacement command is generated from the actuator speed and rail pressure commands and is then sent to the pump displacement controller. The rail pressure controller causes the rail pressure to follow the optimized command by sending the pressure feedback displacement command to the pump displacement controller. Finally, the pump displacement controller maneuvers the displacement of the HP and MP pumps.

The detailed controller design is shown in the following sections.

3.1. Supervisory Controller

The supervisory controller will give the best HP and MP rail pressures and the corresponding mode for each actuator to minimize the throttling loss in the MPR system.

$$p_{HP}=\max \left(\mathsf{\Delta }{p}_1,\mathsf{\Delta }{p}_2,\dots ,\mathsf{\Delta }{p}_n\right)+p_{mar}$$

(4)

To determine the HP rail pressure Equation (4) is used. The HP rail pressure is equal to the highest load pressure in the system plus a pressure margin of $p_{mar}$ to overcome any losses in the line and the losses associated with the pressure drop necessary for the control valve to properly function.

As the HP rail pressure is easily determined, the only independent variable is the MP rail pressure $\left(p_{MP}\right)$. To this end, an optimization method is used based on the cost function defined in Equation (5). This variable is constrained by Equations (7) and (8) which will be introduced later to maintain the pressure margin for proper actuator functionality. The three summations in the cost function represent the throttling loss for each actuator at all three modes. For example, when actuator$i$ is working in mode MP-LP, its throttling loss is the product between its flow rate $q_i$ and the pressure drops across the control valve, $p_{MP}-\mathsf{\Delta }{p}_i-p_{LP}$. The last part of the cost function accounts for the power loss of the HP and MP supply pumps.

$$\begin{gathered} P\left(p_{MP}\right)={\displaystyle \sum }_{i=1}^{MP-LP}{q}_i\left(p_{MP}-\mathsf{\Delta }{p}_i-p_{LP}\right)+{\displaystyle \sum }_{j=1}^{HP-MP}{q}_j\left(p_{HP}-\mathsf{\Delta }{p}_j-p_{MP}\right) \\ +{\displaystyle \sum }_{k=1}^{HP-LP}{q}_k\left(p_{HP}-\mathsf{\Delta }{p}_k-p_{LP}\right)+q_{p_{HP}}\left(p_{HP}-p_{LP}\right)\left(1-{\eta }_{p_{HP}}\right) \\ +q_{p_{MP}}\left(p_{MP}-p_{LP}\right)\left(1-{\eta }_{p_{MP}}\right) \end{gathered}$$

(5)

This cost function is discontinuous. When actuators work in a different combination of modes, Equation (5) has to be rearranged with different constraints for $p_{MP}$, which will lead to different local optimal choices of $p_{MP}$ for difference combinations. In order to find the global minimum of this cost function, all the possible combinations must be evaluated. With a system that has $n_R$ working rails and $n_{act}$ actuators, the total number of possible working mode combinations $n_{comb}$ is calculated in Equation (6).

$$n_{comb}={\left(\frac{n_R\left(n_R-1\right)}{2}\right)}^{n_{act}}$$

(6)

For a five-actuator system working with a three-pressure rail system, the $n_{comb}$ is 243, which means the cost function needs to be evaluated 243 times at every instant to insure a global minimum for the cost function. This makes the optimization quite impractical for an online implementation. An incomplete list of possible combinations is shown in

Table 2. Incomplete list of possible combinations for three-rail five-actuator MPR system.

Combi Nation	Actuators					Combi Nation	Actuators
	1	2	3	4	5		1	2	3	4	5
1	MP-LP	MP-LP	MP-LP	MP-LP	MP-LP	82	HP-MP	MP-LP	MP-LP	MP-LP	MP-LP
2	MP-LP	MP-LP	MP-LP	MP-LP	HP-MP	83	HP-MP	MP-LP	MP-LP	MP-LP	HP-MP
3	MP-LP	MP-LP	MP-LP	MP-LP	HP-LP	84	HP-MP	MP-LP	MP-LP	MP-LP	HP-LP
4	MP-LP	MP-LP	MP-LP	HP-MP	MP-LP	85	HP-MP	MP-LP	MP-LP	HP-MP	MP-LP
…						…

.

Fortunately, there are ways to reduce the list of combinations to be considered. First, organize actuators 1–5 with respect to their load pressure in decreasing order into actuators a–e. Following this, apply the rules below.

Rule 1: an actuator a should always work in mode HP-LP. After organizing the actuators, it is important to note that a-e is not necessarily in the same order as 1–5. From the organized list of load pressures, it is clear that actuator a, as the highest load pressure actuator, should always be working in mode HP-LP because the HP rail pressure is set based on this pressure. As a result, 162 combinations can be eliminated.

Rule 2: when an actuator moves to a lower mode, the actuators with a lower load pressure should never move to a higher mode. This is because there will always be a better combination to take its place. Figure 8 graphically describes this concept. In this setup, assuming the minimum pressure drop is guaranteed, the best combination is 229 (HP-LP, HP-LP, HP-MP, HP-MP, and MP-LP) with the optimized HP and MP pressure. The throttling loss for actuators d and e are $\mathsf{\Delta }{p}_{d_{HP-MP}}$ and $\mathsf{\Delta }{p}_{e_{MP-LP}}$, respectively. If actuators d or e were working in mode HP-LP instead of their current mode, this would result in combinations 231 (HP-LP, HP-LP, HP-MP, HP-MP, and HP-LP), 232 (HP-LP, HP-LP, HP-MP, HP-LP, and MP-LP), or 234 (HP-LP, HP-LP, HP-MP, HP-LP, and HP-LP) It is clear that from the plot, none of those combinations will result in lower throttling loss than combination 231, as the throttling losses of $\mathsf{\Delta }{p}_{d_{HP-LP}}$ and $\mathsf{\Delta }{p}_{e_{HP-LP}}$ are greater than $\mathsf{\Delta }{p}_{d_{HP-MP}}$ and $\mathsf{\Delta }{p}_{e_{MP-LP}}$. As a result, an additional 60 combinations are eliminated.

Rule 3: at least one actuator should work in mode MP-LP. This rule is based on the recirculated excess flow in the MP rail. If no actuator is working in mode MP-LP, such as combination 203 (HP-LP, HP-MP, HP-MP, HP-MP, and HP-MP), there is no actuator taking flow from the MP rail, and all the flow coming from actuators working in mode HP-MP will need to be recirculated through the MP pump back to the shaft; this process generates losses. Therefore, it is certain that if the actuators working in mode HP-MP switch to mode MP-LP with correct MP pressure, such as combination 163 (HP-LP, MP-LP, MP-LP, MP-LP, and MP-LP), it will result in less losses for the system, as the pump loss due to recirculation is eliminated. As a result, five more combinations are eliminated.

To summarize, after applying the above rules, the final list of 16 available combinations is listed in

Table 3. List of final combinations.

Combi Nation	Actuators					Combi Nation	Actuators
	a	b	c	d	e		a	b	c	d	e
163	HP-LP	MP-LP	MP-LP	MP-LP	MP-LP	218	HP-LP	HP-LP	MP-LP	MP-LP	HP-MP
164	HP-LP	MP-LP	MP-LP	MP-LP	HP-MP	221	HP-LP	HP-LP	MP-LP	HP-MP	HP-MP
167	HP-LP	MP-LP	MP-LP	HP-MP	HP-MP	226	HP-LP	HP-LP	HP-MP	MP-LP	MP-LP
176	HP-LP	MP-LP	HP-MP	HP-MP	HP-MP	229	HP-LP	HP-LP	HP-MP	HP-MP	MP-LP
190	HP-LP	HP-MP	MP-LP	MP-LP	MP-LP	235	HP-LP	HP-LP	HP-LP	MP-LP	MP-LP
199	HP-LP	HP-MP	HP-MP	MP-LP	MP-LP	236	HP-LP	HP-LP	HP-LP	MP-LP	HP-MP
202	HP-LP	HP-MP	HP-MP	HP-MP	MP-LP	238	HP-LP	HP-LP	HP-LP	HP-MP	MP-LP
217	HP-LP	HP-LP	MP-LP	MP-LP	MP-LP	241	HP-LP	HP-LP	HP-LP	HP-LP	MP-LP

.

For each combination, the MP rail pressure must fall within the upper and lower constraints to ensure the combination works properly. The lower constraint is determined by Equation (7). The total pressure difference from the MP rail to the LP rail needs to be higher than the highest load working in mode MP-LP plus the pressure margin to ensure proper functioning of the control valve. The upper constraint is determined by Equation (8). The total pressure difference from the HP rail to the MP rail needs to be higher than the highest load pressure that is working in mode HP-MP plus the pressure margin. If the constraints for one combination are incompatible, then the combination is eliminated for that calculation. After rearranging the constraints, as shown in Equations (7) and (8),

Table 4. List of constrains for the final 16 combinations.

Combi Nation	Constraint *		Combi Nation	Constraint *		Combi Nation	Constraint *		Combi Nation	Constraint *
	Lower	Upper		Lower	Upper		Lower	Upper		Lower	Upper
163	$\mathsf{\Delta }{p}_b$	$inf$	190	$\mathsf{\Delta }{p}_c$	$-\mathsf{\Delta }{p}_b$	218	$\mathsf{\Delta }{p}_c$	$-\mathsf{\Delta }{p}_e$	235	$\mathsf{\Delta }{p}_d$	$inf$
164	$\mathsf{\Delta }{p}_b$	$-\mathsf{\Delta }{p}_e$	199	$\mathsf{\Delta }{p}_d$	$-\mathsf{\Delta }{p}_b$	221	$\mathsf{\Delta }{p}_c$	$-\mathsf{\Delta }{p}_d$	236	$\mathsf{\Delta }{p}_d$	$-\mathsf{\Delta }{p}_e$
167	$\mathsf{\Delta }{p}_b$	$-\mathsf{\Delta }{p}_d$	202	$\mathsf{\Delta }{p}_e$	$-\mathsf{\Delta }{p}_b$	226	$\mathsf{\Delta }{p}_d$	$-\mathsf{\Delta }{p}_c$	238	$\mathsf{\Delta }{p}_e$	$-\mathsf{\Delta }{p}_d$
176	$\mathsf{\Delta }{p}_b$	$-\mathsf{\Delta }{p}_c$	217	$\mathsf{\Delta }{p}_c$	$inf$	229	$\mathsf{\Delta }{p}_e$	$-\mathsf{\Delta }{p}_c$	241	$\mathsf{\Delta }{p}_e$	$inf$

* All lower constraints need to add $p_{mar}+p_{LP}$, and all upper constraints need to add $p_{HP}-p_{mar}$.

shows the complete list of all lower and upper constraints for all combinations.

$$p_{MP}-p_{LP}\ge \max \left(\mathsf{\Delta }{p}_{i_{MP-LP}}\right)+p_{mar}=>p_{MP}\ge \max \left(\mathsf{\Delta }{p}_{i_{MP-LP}}\right)+p_{mar}+p_{LP}$$

(7)

$$p_{HP}-p_{MP}\ge \max \left(\mathsf{\Delta }{p}_{i_{HP-MP}}\right)+p_{mar}=>p_{MP}\le -\max \left(\mathsf{\Delta }{p}_{i_{HP-MP}}\right)+p_{HP}-p_{mar}$$

(8)

Finally, with a closer look at the cost function (5), the value of the cost function is a linear function with the independent variable $p_{MP}$. This means if the derivative of the cost function with respect to $p_{MP}$ is positive, the minimum $p_{MP}$ should be used to achieve the lowest value of the cost function, which is at the lower constraint of $p_{MP}$, and vice versa. This further simplifies the optimization to just one evaluation of the sign of the derivative with respect to $p_{MP}$ and one evaluation of the cost function at the corresponding constraint for each combination.

3.2. Real-Time Implementation of Supervisory Controller

The supervisory control logic shown above is operated at a constant frequency on a central ECU, checking continuously to ensure that the system stays in the optimal operating condition. The speed at which the supervisory controller runs can be far lower than that at which the actuator level controls run, 10 Hz and 100 Hz, respectively, for example. This real-time implementation does, however, introduce two control challenges that need to be addressed to ensure the system can operate stably.

First, the control logic proposed above assumed that the system reached a steady state immediately after switching modes and stayed there until the next switch. However, during real drive cycles, small fluctuations of actuator pressures may lead to switches between optimal modes and cause excessive switching between combinations if the value of the cost function for multiple combinations get very close. This could potentially make the system unstable. To overcome this issue, a power loss margin $P_{mar}$ is added to the cost function comparison. The supervisory controller will allow a switch only if the new combination is outperforming the current combination in cost by $P_{mar}$. There is a possibility that the current combination will not work in the new time step. For example, the current combination at the new time step may have contradictory $p_{MP}$ upper and lower constraints, which lead to no possible $p_{MP}$ existing for the current combination. In this case, to ensure that the system functions correctly, the supervisory controller will force a switch to the new combination, regardless of $P_{mar}$. This way, switches will happen much less frequently at the cost to savings of $P_{mar}$, which is small compared to the total savings, and the benefits of system stability.

Second, during transient condition, such as multi-actuator switching, the system pressure experiences a discontinuity that will impose actuator load pressure oscillation for a short time. An example is shown in Figure 9. A simple step change is demonstrated in a single actuator load (top), along with a sample of four of the cost functions (middle), and the actuator’s connection mode (bottom). The simulation used accounts for other actuators and cost functions, but only the relevant ones are shown. When the load change occurs, there are transient oscillations in the system that cause corresponding oscillations in the cost functions. The magnitude of these oscillations is instantaneously greater than $P_{mar}$, and if left unchecked, could lead to uncontrolled switching as seen in the figure. To resolve this, a brief cooldown time, $t_{cd}$, was added to the controller, forcing a minimum time (two seconds for the reference controller) between switches. As with the $P_{mar}$ logic, an exception was implemented allowing the system to switch modes immediately if its current operating condition is unable to satisfy the pressure margin constraints.

3.3. Actuator Level Controllers

The actuator controller is a simple closed-loop PI (proportional integral) controller for actuator speed (Figure 10). The actuator command comes from the supervisory controller and the actuator speed is fed back from a speed sensor to close the control loop.

The rail pressure controller and pump displacement controller form a cascaded PI controller (Figure 11). The outer loop is the rail pressure controller that takes rail pressure commands from the supervisory controller and outputs the reference pump displacement command to the inner loop. The rail pressure measurements are used to close the control loop. The inner loop is a feedback–feedforward controller. In addition to the command from the outer loop, the feedforward pump displacement command is sent from the supervisory controller, which is a displacement estimation from the actuator modes and flow needed. The measured pump displacement is used to close the control loop.

4. MPR Test Rig and Reference Machine

4.1. MPR Test Rig Design

A standalone test rig was designed to validate the effectiveness of the control scheme being used. The system was designed as shown in Figure 12. Key features in the design were variable load units, allowing the simulation of a wide variety of loading conditions, an unloading valve, enabling the switch between one and two pump supply systems, and a switching valve and accumulator system, enabling the function of the one pump system. The system also used the more general design for the valve set outlined above. This was done to ensure flexibility in future work with the system.

The test rig design shown above was designed to be able to operate as both a one pump and two pump MPR system, by using the unloading valve (ULV) to isolate the MP pump and using the switching valve (SWV) to switch the HP pump between the rails, as it was initially designed for use on [29]. For the purposes of this paper, however, the system is used in the two-pump configuration.

The system is controlled using an NI CRio controller, which in turn uses Bosch Rexroth’s BODAS pump controllers and pressure transducers to control the hydraulic components of the system. Figure 13 shows the completed test stand implementation.

4.2. Reference Machine

To show the power savings introduced by the proposed MPR system and controller design, two reference machines (a tractor and an implement) are selected and modeled. The reference machines have been instrumented and tested in the field under normal working conditions to gather baseline data for building and validating the hydraulic model. Finally, the actual power consumption by the hydraulic system on the reference machines for the baseline machine and the proposed MPR machine are compared.

The reference tractor is a T8.390 New Holland tractor. The tractor and its simplified hydraulic circuit are shown in Figure 14. It has two sets of centralized load-sensing hydraulic systems. The first system has the first HP pump as a flow source and steering system, using the power beyond function and remote valves one to three as users. The flow first goes through the steering priority valve to satisfy the steering needs, then continues to supply the rest of the functions. The second system is powered by the second HP pump with the hitch function and EHR valves four to six. The implement is connected to the hydraulic system through the tractor EHR. An LP pump is used to power all low-pressure functions, such as the brake, clutch, differential lock, etc. The LP system, which is also a low power system, is not included in this study.

The reference implement is a Case Early Riser 2150 16-row planter. The planter and its simplified hydraulic circuit are shown in Figure 15. The planter has two hydraulic circuits. Circuit one contains a bulk fill fan system, fertilizer system, and compressor system. Circuit two contains an alternator system, vacuum system, weight management cylinder system (WMC), and hydraulic down pressure cylinder system (HDPC). These functions, except the compressor system, are continuously working during normal planter working conditions. In addition to the motor actuators, the two-cylinder systems also appear in the system. The cylinder systems follow the terrain and maintain a commanded downward force to ensure planting quality.

5. System Modeling Methodology

This section presents the lumped parameter models used to estimate the effectiveness of the MPR solution in terms of controllability and energy savings. Specifically, the test rig model is used to validate the proposed MPR control performance. The tractor–planter model is instead used to predict the total power saving in realistic working conditions.

5.1. Test Rig Model

For easier understanding of the test rig modeling, the system is decomposed into individual components that could be modeled with a governing equation, such as hydraulic motor, pumps, valves, lines, etc. The exchange of information between the blocks is indicated in the block diagram in Figure 16. The inputs for the simulation are the actuator commanded speeds, commanded loads, and electric motor speed. They are directly fed into the MPR controller through the simulation. All other variables such as pressure, flow rate, torque, speed, and power are calculated internally in the simulation.

For simplicity, the electric motor in this model is assumed to be an ideal rotational speed source. The motor shaft speed ${\omega }_m$ is simulated using Equation (9). $I_{shaft}$ is motor shaft inertia. $T_L$ is the load torque on the motor shaft. $T_m$ are the torque outputs by the motor.

$$I_{shaft}\dot{{\omega }_m}=T_m-T_L$$

(9)

Following this, the hydraulic unit (HP and MP pumps, motor, and load pump), effective flowrate $q_{eff}$, and torque $T_{eff}$ are modeled using Equations (10) and (11). $V$ is the unit maximum displacement. The volumetric loss $q_s$ and hydromechanical loss $T_s$ are determined using empirical lookup tables. The losses are related to unit fractional displacement $\beta$, pressure drop across the unit $\mathsf{\Delta }p$, and unit speed $\omega$. A more detailed description on the setup of the hydraulic unit model can be found in [30].

$$q_{eff}=\pm \beta V\omega -q_s\left(\beta ,\mathsf{\Delta }p,\omega \right)$$

(10)

$$T_{eff}=\pm \frac{\beta V\mathsf{\Delta }p}{2\pi }-T_s\left(\beta ,\mathsf{\Delta }p,\omega \right)$$

(11)

Next, the pressure dynamics in each control volume (HP and MP rail, line A1, B1, A, B, and L) are modeled by the pressure build up Equation (12), where the $K$ is the bulk modulus, $Vol$ is the volume, $q_{in/out}$ is the flowrate that flows into or out of the control volume, and the $\frac{dV}{dt}$ is the control volume rate of change.

$$\dot{p}=\frac{K}{Vol}\left(q_{in}-q_{out}-\frac{dV}{dt}\right)$$

(12)

Finally, the flowrate $q_V$ through valves (V1–6, A, B, and L) are modeled using the orifice Equation (13). The maximum orifice area $A$ for each valve is different and it is calculated from the valve datasheet. The normalized opening of the valve $y_V$ depends on the type of valve. For a proportional valve, the control input, which is normalized between 0 to 1, serves as the valve opening. For check valves and electrical on/off valves, the opening is either 0 or 1 depending on the working logic. For valves with hydraulic pilot pressure, a force balance between solenoid force, hydraulic force, and spring force is applied to calculate the valve opening.

$$q_V={\alpha }_{D}A{y}_V\sqrt{\frac{2\mathsf{\Delta }p}{\rho }}$$

(13)

A summary of the components and parameters used in this simulation model is shown in

Table 5. Components and parameters used for test rig modeling.

Oil Density	$\mathrm{ 850}\mathrm{kg}/{\mathrm{m}}^3$
Discharge Coef.	0.7
Bulk Modulus	$\mathrm{ 1.7}\mathrm{e}9\mathrm{Pa}$
El. Motor Speed	$\mathrm{ 1500}\mathrm{rpm}$
Supply Pumps	$\mathrm{ Bosch}\mathrm{Rexroth}\mathrm{A}10\mathrm{VO}(\mathrm{EOC}-\mathrm{P}),\max .\mathrm{displacement}45\mathrm{cc}/\mathrm{rev}$
Load Pump	Bosch Rexroth AZPV, 8 cc/rev, custom made
Load Motor	Bosch Rexroth AZMV, 8 cc/rev, custom made
Load Inertia	$\mathrm{ 0.001}·\mathrm{kg}·{\mathrm{m}}^2$
On/Off Valve	$\mathrm{ Bosch}\mathrm{Rexroth}\mathrm{VEI}-16-10\mathrm{A}-\mathrm{NC}(5\mathrm{bar} \mathsf{\Delta }p$$\mathrm{for}30\mathrm{lpm}\mathrm{q}$)
Proportional Valve	$\mathrm{ Bosch}\mathrm{Rexroth}\mathrm{KSVSR}2(14\mathrm{bar} \mathsf{\Delta }p$$\mathrm{for}75\mathrm{lpm}\mathrm{q}$)
Load Valve	$\mathrm{ Bosch}\mathrm{Rexroth}\mathrm{VEP}-5\mathrm{B}-2\mathrm{S}-\mathrm{P}(\max .\mathrm{cracking}\mathrm{pressure}220\mathrm{bar}$,$\mathrm{flow}\mathrm{rate}\mathrm{pressure}\mathrm{gradient}7.5\mathrm{L}/\min /\mathrm{bar}$

below.

5.2. Complete System Model

The complete tractor–planter model was built in the Simcenter Amesim environment. The model includes the tractor model and the planter model, in both the commercial solution and the proposed MPR component configuration. The simplified hydraulic circuit is shown in Figure 17. It is a 3-rail MPR system with 5 actuators. The 5 actuators are alternator motor, vacuum fan motor, bulk fill fan motor, fertilizer motor, and the cylinder systems.

The models for the tractor and planter were built following the same lumped parameter approach as the test rig model. Previous studies conducted by this team have presented the model development and its validation for the commercial tractor system [31,32] and tractor–implement system [33]. The baseline simulation results that will be presented in the next section are the straight output of these previously presented models. The relevant portions of the tractor model (engine, pumps, and control valves) and of the validated planter model (motors, cylinders, control valves, and corresponding load) will serve as the baseline for comparison with the MPR supply system and the MPR working actuator, respectively. The test rig model (HP and MP rails, PSCV, and MPR controllers) will serve as the MPR component models which transfer power in between the tractor and planter models.

One important note regarding the model used is to consider the downforce cylinder system of the planter. An accurate modeling of the cylinder system presents complexity in determining the correct force inputs from the ground, as well as including a proper dynamic model for the bodies connected to the cylinder. To simplify this portion of the model, and ensure a realistic simulation, a simplified load module was built to recreate the cylinder flow/pressure dynamic using experimental data from real measurements as shown in Figure 18. This module will enforce the flow rate needed from the cylinder systems (which was measured from experiments) and use the same pilot-operated, electric-controlled, 3/2 proportional pressure-reducing valves to track the measured working pressure (also measured from experiments) in the cylinders (CH). Therefore, this load module consumes the flow rate and outputs the controlled cylinder pressure as measured from the experiments.

6. Results and Discussion

This section firstly presents the simulation used to select a three-rail system, then discusses the validation of the test rig model, the planter model, and the power consumption prediction of the complete MPR tractor–implement model compared to the baseline solution.

6.1. Rail Number Analysis

A representative drive cycle was acquired for the selected reference machine, seen in

Table 6. Representative drive cycle for the rail number analysis.

Normalized Cmd	Time	Alternator	Bulk Fill Fan	Fertilizer	Vacuum Fan	Cylinders
Normal	5–38%	60%	60%	~40%	~63%	Dynamic

, which displays typical usage. It was run through a streamlined version of the model discussed above, with most transient dynamics removed to focus on steady state performance.

Averaged over time, the simulation results are shown in Figure 19, with each additional rail improving loss reduction; by far the most remarkable improvement occurred following the addition of two to three pressure rails. These results motivated the selection of a three-rail system for this application, as the relatively minor reduction in losses for rails above three was judged not to be worth the additional control complexity.

6.2. Test Rig Model Validation Result

A drive cycle was generated for the test rig using the output of the supervisory controller to select loading conditions and command speeds for the three actuators to force the system into a sequence of mode switches. These switches were selected specifically to test the controllability and stability of the system. This drive cycle is outlined in

Table 7. Validation drive cycle for MPR test rig.

Time	(A) 0–10 s		(B) 10–30 s		(C) 30–50 s		(D) 50–70 s
	Command	Mode	Command	Mode	Command	Mode	Command	Mode
${\omega }_{1_{cmd}} \left[\mathrm{rpm}\right]$	1200	3	1200	3	1200	3	600	2
$p_{1_L}$ [bar]	160		160		160		20
${\omega }_{2_{cmd}}$ [rpm]	800	1	800	1	800	3	800	1
$p_{2_L}$ [bar]	20		100		140		100
${\omega }_{3_{cmd}}$ [rpm]	600	1	600	2	600	1	1200	3
$p_{3_L} \left[\mathrm{bar}\right]$	20		20		20		160

.

The results from the test rig model are shown in Figure 20. The first row shows the switch from working condition B to C (started at 30 s) in the drive cycle of Table 7. The second row shows the last switch from working condition C to D (started at 50 s), which is the hardest switch. The plot on the left shows the actuators speed tracking, the middle plot shows the actuators load pressure and corresponding optimized rail pressures, and the right plot shows the actuators operating mode as determined by the supervisory controller.

Overall, the system behaves as expected and both the actuator level controller and supervisory controller perform correctly. The steady state command tracking is excellent, and the system is stable with a minimum number of mode switches. From the results, a speed peak for all actuators at the moment of the mode switch can be noticed. This occurs because when the switch happens, the local actuator speed controller, not being informed of the change in supply pressure, must react from its previous state. As a result, the sudden pressure change will create a flow spike and change the pressure drop across the motor. This aspect is accentuated in the test rig actuators because they have an extremely low mechanical inertia, being simply a pump directly connected to a hydraulic motor. Therefore, a short torque spike is reflected in a corresponding speed peak. The second reason is because the on/off valves have different opening and closing times. The on/off valves on the test rig have a closing time approximately three times longer than the opening time. When a switch happens, there will be a very short time during which the two rails are directly connected, causing the higher pressure rail flow to rush to the lower pressure rail, resulting in flow loss to the actuators and a subsequent drop followed by an overshoot in speed. A more sophisticated actuator-level control method could help alleviate some of these issues. The corresponding systems on the reference machine, however, are largely fan drives with very large inertias which will be much more robust against fluctuations in supply flow and pressure; as a result, the current level of control complexity is suitable for progressing to on-machine implementation.

The simulation drive cycle was then run on the physical test stand. The results were formatted using the simulation results and can be seen in Figure 21. The test stand results show good agreement with the simulated results, with the same speed peaks occurring due to low inertia and opening timing issues. One other clear discrepancy occurs during the difficult switch (bottom right panel from 50–54 s), due to factors not accounted for in the simulation. While the simulation shows the switch happening cleanly, in reality, additional dynamics result in the switch being divided into two separate switches for the test stand, with the first switch occurring immediately, and the second bringing the system to its optimal condition after the dynamic has settled out. This effect demonstrates the effectiveness of the anti-chatter logic, without which the system would have had numerous undesirable switches during this period.

6.3. Complete System Performance and Power Consumption Prediction Result

This section presents the simulation result for the proposed MPR system applied to the tractor and the planter. All controllers are running at a fixed speed of 10 Hz. First, the drive cycle will be introduced. Then, system tracking and mode switching results will be presented to demonstrate system functionality. Finally, the pump shaft power consumption comparison will be introduced to show the power saving and efficiency gains.

The drive cycle includes two working conditions: normal and high-speed conditions. The normal and high-speed conditions are representative of two commonly used operating modes for this implement, according to the manufacturer, and are run back-to-back for the simulation. In reality, they are not run together, but this is a simplification only to show the operating conditions of both systems, and to provide a command switch to display transient behavior. According to the machine manufacturer, most users operate the planter in normal working conditions when planting. Therefore, power saving is most important in normal conditions. The drive cycle is shown in

Table 8. Representative drive cycle for the complete system model.

Normalized Cmd	Time	Alternator	Bulk Fill Fan	Fertilizer	Vacuum Fan	Cylinders
Normal	5–38%	60%	60%	~40%	~63%	Dynamic
High-Speed	60–90%	80%	80%	~60%	~70%	Dynamic

. For confidentiality, all parameters are normalized. This drive cycle was executed in the field during the baseline tests. The command for the alternator and the bulk fill fan is a constant motor speed. Fertilizer and vacuum fan systems do not have a direct motor speed command, so the measured flow rate of these systems is used to back-calculate the actual motor speed as the modeled system speed command. The cylinder system uses measured pressure values and flow rates from actual system operation for the load module to recreate the load condition, as discussed in Section 5.

Figure 22 shows the results from the proposed three-rail MPR system for the reference machines. The vacuum and cylinder system has been chosen to show the system performance and controller activity. The left plot shows the results for the vacuum fan and the right plot shows the results for the cylinder systems from the same simulation. The top plot shows the actuator command tracking (left y-axis) and system mode (right y-axis), while the bottom plot shows the actuator load pressure with optimized rail pressures.

From the results, all sub-systems track their command closely, as demonstrated by the vacuum. At mode switching, very little speed disturbance could be observed in the motor actuators. The tracking results prove that the proposed MPR system achieves at least the same level of performance as the baseline systems. In addition, from the bottom plot, the HP rail pressure closely follows the highest actuator pressure (which is the cylinder system pressure), the MP rail pressure is continuously adjusting with respect to the actuators load pressures, and the corresponding mode for each actuator is switching to ensure the power loss due to throttling is minimized. This shows that the supervisory controller works as expected to minimize system power loss.

In this drive cycle, when active, the cylinder system is always the highest load actuator, dominating the HP rail pressure. The high dynamic pressure variation leads to rapid mode switching in other actuators. This is more severe in normal working conditions. At high-speed working conditions, the cylinder system load is less dynamic, and the system becomes more stable as fewer switches occur. The designed controller is robust enough to ensure all systems stay stable and maintain good tracking, despite this fast dynamic.

Finally, Figure 23 shows the pump shaft power consumption comparison between the baseline and the MPR system. There is no doubt that the MPR system generates great power savings compared to the baseline simulation. The MPR system demonstrates that some of the mode switches reduce the system power. This is due to the pressure transient in chambers $A_1$ and $B$ (Figure 6 right) at the moment of actuator mode switch. When it happens, for example when MP-LP switches to HP-LP, the pressure difference between the HP rail and the inlet chamber (which is currently at MP) creates a very short but large flow surge to charge the chamber pressure to the HP pressure. This flow peak, although it is short, shows its effect on the power consumption.

Table 9. Complete system model result on average power saving and efficiency gain for baseline and MPR system.

	Baseline		MPR System
	Normal	High-Speed	Normal	High-Speed
Total Power [%]	65.41	81.90	34.46	47.27
Reduction [%]	-	-	47.32	42.28
Efficiency [%]	20.19	27.89	38.32	48.32
Efficiency Gain [%]	-	-	89.80	73.25

summarizes the normalized total power, the efficiency for each simulation, and the corresponding power reduction and system efficiency gain as a percentage. As stated, the MPR system results in great power saving and efficiency gain.

7. Conclusions

This study applied the multi-pressure rail (MPR) hydraulic system to agricultural applications, such as tractors and towed implements, which normally run at long steady state conditions with unidirectional hydraulic motors as the main actuator. The detailed system design and controller designs were presented considering the application characteristic. The proposed MPR system could minimize the throttling loss at the actuator control valves by strategically choosing the pressures in HP and MP rails. This system represents a great alternative to the traditional centralized load sensing system for off-road agricultural machines.

The paper presented a complete MPR system design, including the number of rails, supply system, and pressure select and control valve set (PSCV). The optimal number of rails was first determined to be three, based on the tradeoff between power saving, system cost, and complexity for the chosen machine. The supply system was then selected to have two pumps to supply each rail independently. This design allowed for the elimination of the accumulators on the rails and enabled fast and accurate rail pressure control to help lower the throttling loss. Following this, two different PSCV designs were presented. A multi-level controller was designed to control the proposed MPR system. The supervisory controller controls the rail pressure for both rails and the actuator operation mode to minimize throttling loss, while the actuator controllers ensure the stability of the subsytems and command tracking. A detailed design was presented. One important note is that the proposed supervisory controller design follows the first sizing option for the supply system, meaning neither pump flow saturates. This condition holds true with the pump sizing and the actuator flow requirements of the reference vehicles. However, if the rails could suffer from flow saturation, i.e., insufficient pump flow, then the supervisory controller case elimination process and case selection logic would need to be modified, which is a great potential direction for future development.

To prove the stability and command tracking performance of the proposed MPR system, a test rig was designed to test the system design. After the test rig was designed, a lumped parameter model was built and a drive cycle that tested several critical mode switchings was constructed to predict the behavior of the test rig and aid in controller tuning. The test rig was then built and ran with the same drive cycle to validate the controller design. The results showed that the proposed MPR design and controller are stable, with exceptional performance during both steady state and transient conditions.

Finally, to predict the power saving and efficiency gain of the proposed MPR system compared to the baseline system, a high-fidelity lumped parameter model was built for the complete system, including the reference tractor, planter, and the proposed MPR system components. The model was fully validated, and a measured baseline drive cycle was used as a command input for each actuator in the complete system model. The results show that the proposed MPR system is not only able to provide the same level of performance, but also provides huge power savings and efficiency gains over the baseline system. For the most frequent normal working conditions, the MPR system achieved up to 59.4% total power reduction at the pump shaft, and 89.8% system efficiency gains.