1. Introduction
Conical tank systems have high applicability rates in industrial processes; they are mainly used in colloidal mills; in leach extraction in pharmaceutical industries, chemical industries, food processing industries, and oil industries; and in mixing tanks, biodiesel processing, reactors, cider production, alcohol production, vertical rainwater tanks, fertilizers, and chemical storage tanks. Their importance lies in the fact that conical tanks allow for benefits such as sedimentation and the drainage of impurities [
1].
Conical tank research is relevant in process control and involves analyzing several control theories after obtaining a mathematical model. Due to their high nonlinearity rates, the study, modeling, and control of conical tanks present a challenge. Due to their shape, they have different dynamics at the point of operation.
The level control of conical tanks is a process with nonlinear dynamics, where applying traditional or linear control strategies does not guarantee an efficient transient state at its level. In the specialized literature, the control of conical tanks has been reported with conventional techniques, such as PID controls, and variants, such as fractional order PID (FOPID), which differs from the traditional control method by the process of obtaining a fractional integrator and derivative and establishing parameters of the order that each one will have; despite this method having a complex structure and being difficult to tune, it, however, guarantees effective stability [
2]. On the other hand, advanced control strategies have also been reported in conical tanks, such as fuzzy control algorithms, where establishing a set of rules and relevant membership functions allows for obtaining better performance in tuning parameters such as a fast settling time and low impulses [
3], neural control [
4], and the use of the SMC rolling horizon control strategy, which consists of establishing the state of the system and extracting it to a sliding surface plane; this type of control strategy guarantees a high degree of robustness in its design, unlike traditional control strategies [
5].
Predictive control algorithms based on MPC models have been applied in many industrial processes with nonlinear characteristics—for example, in temperature and level control strategies [
6], combined-cycle thermal power plants, biphasic separators [
7], correlated temperature and level processes [
8], and industrial processes [
9]. On the other hand, for model predictive control, there are several methods to obtain the process model—for example, by using an echo state network (ESN), which uses the recursive least squares method applied to the level control strategy for a conical tank [
10]. The application of control algorithms in MIMO systems is complex due to the various dynamics of the process. Having a nonlinear process such as a conical tank control strategy requires advanced algorithms and the use of a dynamic matrix controller (DMC) for correction by using dynamic behavior to control the process [
11] with no lineal model—for example, in the case of fuzzy logic- and proportional–integral–derivative-based multi-objective optimization of the active suspension system of a 4 × 4 in-wheel, motor-driven electrical vehicle [
12], which uses an advanced control algorithm for the control of nonlinear plants.
A conical tank plant, due to its nonlinearity when controlling with a traditional control strategy, tends to have low performance, which is the reason why self-adjustments are performed—for example, the use of an interval type-2 fuzzy logic system with genetic self-adjustment of its membership functions [
13]. Another alternative is the use of mathematical modeling to represent a hybrid interactive two-tank system (IHTTS) by analyzing a multivariable system with nonlinearities [
14] or an analysis of traditional tuning parameters using the Ziegler–Nichols tuning (ZNT) method, root locus technique (RLT), and (IAE) through comparisons of server responses [
15]. Another alternative to improve control is the implementation of advanced control methods such as fuzzy control (FLC) and the use of the Kalman algorithm, which employs fuzzy logic rules to help reduce error in noisy environments [
16]. Another alternative is an RTDA controller (robustness, set point tracking, disturbance rejection, aggressiveness), whose main advantage is parameter tuning, thus improving the performance of the closed-loop system [
17], or the rolling horizon control strategy for improved robustness to disturbances [
18].
Advanced control strategies have demonstrated superiority in processes with nonlinear and multivariable dynamics [
5]. In conical tanks, predictive control based on MPC models has also been used, but, in the control process, they perform a model mismatch; that is, the design model does not coincide with the real process, and, within the structure, an estimator parallel to the process occurs. This type of control strategy is known as NMPC [
19], and it should be noted that within the literature investigated, it has been implemented in a conical tank plant, but the MPC applied to the same plant has not been developed. However, in one paper, the authors simulated the process, thus showing an idealistic model of a conical tank. Other examples of these are featured in similar research such as “Design and Comparison of Strategies for Level Control in a Nonlinear Tank” [
20] and “Real-Time Level Control of Conical Tank and Comparison of Fuzzy and Classical Pid Controller” [
21].
The controllers in these works have been validated by simulation, while in this research, control proposals are also implemented and validated experimentally. In addition, a model predictive control (MPC) strategy is proposed to protect actuators and, at the same time, provide good performance.
MPC is an advanced technique that provides a sophisticated way to control complex systems in real-time, considering multiple variables and constraints to achieve desired objectives efficiently and accurately. In this research, a model predictive control (MPC) strategy is designed and implemented for the level control of a conical tank on a laboratory scale. The evaluation performance of the controller is compared with a traditional integral (PI) controller, and the rise time, settling time, overshoot, and steady-state error are analyzed when subjected to different set points. In addition, an interactive interface is developed in LabVIEW software 2021 Sp1 so that students can directly experience how MPC works in real or simulated situations, which would provide them with a deeper and more practical understanding of this advanced technique.
The contributions of this research include (i) an approximate model of a conical tank plant on a laboratory scale; (ii) the design of an interactive interface that allows for the applications of automatic control and advanced control to a conical tank; (iii) and the design, implementation, and validation of an advanced MPC proposal that improves the performance of level control in a conical tank in comparison to classic PI controllers.
4. Conclusions
In this research, a conical tank was implemented for level control, obtained via design of an interactive learning interface. A comparison of two control algorithms, a traditional PI and an MPC, was performed in a real and simulated process, analyzing rise time (Tr), overshoot (OS), and settling time (Ts).
The efficient interaction of the interactive learning interface made in Lab-VIEW with the real plant was verified, showing similarities in the dynamics of the process both in the real-time animation of the tank level and in the activation of components, as well as the dynamic response of the level. The interface will have a direct impact on student learning since it allows multiple practices to be carried out in a nonlinear conical tank and can be used to investigate new advanced and advanced control methods, being able to put theoretical knowledge into practice.
The use of an advanced MPC algorithm improved the performance of the level control strategy used for the conical tank in terms of transient response and steady state compared to the experimental results, as well as to the traditional PI controller tuned by the HAALMAN method. Furthermore, it can be noted that the MPC presented better performance concerning the rise time, with a reduction of 527.5 [s] as compared to the value obtained for the traditional control strategy, causing the level signal to have a rapid establishment time; however, for this reason, a maximum overshoot of 0.9% was generated. When faced with disturbances, the establishment time of the MPC was less than 171 [s] than in the PI controller, in an MPC controller of 333 [s] and PI controller of 504 [s]. It can be concluded that when using an MPC, the rise and establishment time is faster than with a PI controller. Furthermore, when the set point changes, the control actions are more stable and less aggressive to the actuator.