Design and Implementation of a Linear Induction Launcher with a New Excitation System Utilizing Multi-Stage Inverters

Abstract

Linear induction launchers (LILs) are a specific subtype of linear motors. However, LILs are air-core machines that consistently operate in a transient rather than a steady state. Moreover, their operating currents and voltages exceed those of traditional machines. The execution time of LILs often remains within a few milliseconds, and it is essential to manage extremely high-power levels quickly. The control methods for LILs differ from those used for regular machines due to the differences from conventional linear motors. In this respect, there are still challenges to be overcome in power systems designed for LILs in the literature. This study has developed a novel power energization system to address these challenges, particularly in terms of inadequate V/f control and the unnecessary energization of regions along the barrel where no projectile is present. It focuses on the system’s design using multi-stage H-bridge inverters to produce a sinusoidal current for section-by-section polyphase excitation. An FPGA-based electronics control system generates bipolar PWM fiber-optical signals for IGBT switches for scalar V/f control of the inverters. Distributed multi-inverters power each stage of the launcher’s barrel and are controlled by the FPGA to create the travelling electromagnetic wave package. Three-dimensional FEM analysis is used for observation of the trigger timing to ensure positive force along the barrel. By driving each inverter independently, the coils on the barrel are excited sequentially based on the position of the projectile. This study also explains the implementation of a laboratory-scale barrel prototype, a 40 mm aluminum projectile, its power electronics, and the control part of the multi-stage inverters. In this study, 3300 V–1200 A IGBTs and 8.8 mF–2000 V DC-Link capacitors were used in the H-bridge inverter modules. Experimental studies have been conducted on the launcher, and the results obtained, including achieving a velocity of 30 m/s, are consistent with the electromagnetic simulations. It has been observed that the launcher, powered by the proposed system, is approximately 57.14% more efficient compared to the version energized by a single inverter.

1. Introduction

In the history of mankind, it has always been a significant objective to propel an object to hyper-velocity. Every century, new generations have been part of this effort with bigger dreams. One of these efforts has been launchers, which are systems that have a short flight time and are used to accelerate an object with high energy using mechanical, chemical, and electrical propulsion. These systems find applications in various industries, including defense, space exploration, and transportation [1].

Electromagnetic launchers, one of these launcher types, are systems that generate electromagnetic forces with electrical energy and convert it into kinetic energy on an object. They operate based on the principle known as the Lorentz force: applying force F to a charge q moving with speed v in a magnetic field B [2].

Linear induction launchers (LILs) are a special case of this type of launcher and create a traveling electromagnetic wave package, allowing the movement of a projectile. They are similar to linear induction motors in terms of the principle of operation. Here, a projectile can be a bullet from a weapon, as well as a satellite or payload to be launched into space [3].

Linear induction launchers consist of two main parts: a barrel and a projectile. Creating a traveling wave on the drive coils placed inside the barrel accelerates and launches the non-magnetic projectile. The barrel can consist of a single section or multi-sections. The muzzle velocity of a single-section launcher can be limited, whereas a multi-section launcher can reach very high (theoretically infinite) velocities [4].

The launcher utilizes closely arranged drive coils fed by a multiphase power supply to create a continuous traveling magnetic wave that propels a projectile forward due to eddy currents. The launcher can either increase the frequency of the excitation power supply or adjust the polar spacing between the drive coils to accelerate the speed of the traveling wave along the launcher. Since increasing the polar distance is impractical, increasing the frequency along the barrel is more feasible, resulting in different excitation frequencies for each section [5].

Various methods are used to energize these coils, which directly affect the launcher’s muzzle velocity, efficiency, and performance. The first power conditioner for a linear induction launcher in the literature was obtained from the resonance between high-voltage capacitors and drive coil inductance. It operates by sequentially exciting a series of coils in the gun barrel through a multi-stage power conditioner using thyristors. A multiphase system operating at a constant frequency powers each section of the gun barrel, which is divided into sections of different lengths. This design enables a smooth acceleration to launch the projectile without establishing synchronization between the projectile and the traveling magnetic wave and without any contact with the projectile. Furthermore, studies have demonstrated that the projectile and launcher surface experience high levitation stability due to the radial forces, effectively eliminating friction-related issues [6].

Frequency and voltage control are difficult in launchers driven with pulsed power supplies using capacitor banks. Instead, researchers have proposed using permanent-magnet flywheel motor/generator sets as an energy source. This system charges by rotating the permanent-magnet synchronous motors to their maximum speed. After reaching full speed, the motors disconnect from their power sources and operate as generators. The flywheel then releases this stored kinetic energy into the electromagnetic launcher. Thus, the launcher is divided into multiple sections, and each section is driven at the desired frequency with high efficiency [7].

With the widespread use of high-voltage and high-current semiconductor power devices such as IGBTs, modern inverter topologies have also started to be used in launchers. In this method, all coils in the launcher are energized at the same time by using a single three-phase inverter, and a waveform with a constant voltage/frequency ratio is obtained. Thus, the projectile’s movement is provided by an adjustable-frequency power supply. However, this system’s drawback is low efficiency since the sections where the projectile is not present are also energized [8,9].

When evaluating the energization methods of linear induction launchers in the literature, two significant drawbacks become apparent:

(i)

The impracticality of adjusting frequency and current by altering the values of circuit elements or changing the speed of the generator;

(ii)

The low efficiency resulting from energizing regions on the barrel where no projectile is present.

This article introduces a novel coil energization method to overcome these drawbacks in existing power conditioner systems. The linear induction launcher is divided into sections, with coil pairs in each section driven by an independent high-power H-bridge inverter with the sinusoidal PWM method. An FPGA-based centralized controller generates the necessary PWM signals for the independent inverter modules. These signals generate a traveling magnetic wave with a frequency that incrementally increases section by section based on the projectile’s position. Induced currents in the projectile cause it to follow slightly behind this wave. The algorithm in the FPGA is optimized according to the physical characteristics of the projectile and the desired muzzle velocity with the aid of 3-D FEM analysis. This way, there is no need to energize the coils in places where there is no projectile in the barrel, contributing significantly to the launcher’s efficiency, as shown in Figure 1. In addition, the high current and frequency changes required to implement the VVVF method in the launcher are performed based on a pure software algorithm without using a physical method (such as changing capacitor values or the speed of a generator). The objectives of this paper are as follows:

(i)

To present a modular and highly efficient launcher system, analyze and simulate inverter power circuits, and develop an FPGA-based central control unit hardware and VVVF algorithms to control the inverters;

(ii)

To implement a laboratory-scale linear induction launcher prototype, including high-power IGBT H-bridge modules, FPGA-controlled fiber-optic transceivers, a high-voltage capacitor charger circuit, and a laser position detection system;

(iii)

To optimize the continuity of the traveling magnetic wave in order to minimize thrust fluctuation using 3-D FEM analysis;

(iv)

To verify the proper operation of IGBT switches and drivers for each H-bridge module using the double pulse testing method;

(v)

To demonstrate the projectile’s acceleration to the intended velocity with high efficiency using current, voltage, and speed measurement results.

2. System Design

A linear induction launcher (LIL) is an air-cored system operating on the same principle as the induction motor. Multiphase excitation generates a packet of electromagnetic waves that travel at increasing frequency along the launcher until the projectile completely leaves the launcher. The projectile consists of a simple hollow cylinder made of aluminum with a thickness capable of withstanding heat caused by intense magnetic fields. It always lags behind the traveling magnetic wave, resulting in a slip. This phenomenon induces azimuthal currents on the projectile and creates thrust and centering forces through its interaction with the magnetic field. In the proposed system, the drive coils of the barrel are divided into sections and grouped into three phases: A, B, and C. Each phase in each section is energized using H-bridge inverters with a phase delay. The delay between phases is a critical issue for the launcher’s performance. The primary objective is to generate the traveling magnetic wave as rapidly as possible, making a 60-degree phase delay the optimal choice. Researchers have observed that phase delays above and below 60 degrees, such as 120 degrees, diminish the launcher’s performance [10]. A sequence of A, −C, and B is applied along the barrel to achieve a delay of 60 degrees between phases A, B, and C, as shown in Figure 2.

The oroposed arrangement to create the polyphase system with a phase shift is illustrated in Figure 3 and consists of three main structures:

• Launcher: including barrel, coil, projectile, and optical speed sensors;
• Power stage: including IGBT power switches and their drivers, high-voltage capacitors, and chargers;
• FPGA Control Unit: implementation of a launcher algorithm, generation of fiber-optic PWM signals for H-bridge inverters, projectile position control, and GUI communication.

The FPGA control unit controls each section to maintain a constant V/f ratio over a specified range of increasing frequencies. To keep this ratio constant throughout the barrel, it also adjusts the section transitions according to the position of the projectile and the current waveforms of the previous section. The independent H-bridge inverters generate all phase currents, as shown in the system block diagram. The sinusoidal PWM method applied in the FPGA generates these currents, resulting in a smooth force profile along the launcher. Furthermore, as not all the coils in the system are energized at the same time, energy in the capacitors is saved, leading to inherent high efficiency. Switching a high-power and high-frequency semiconductor transistor is challenging due to the intense magnetic fields in the electromagnetic launcher. Therefore, we connect the PWM signals from the FPGA to the H-bridge inverters optically instead of electrically. This method prevents the long switching lines between the FPGA controller and the modules from being affected by the noisy environment.

The structure, consisting of three H-bridge modules and driver coils, results in a modular section. In this way, up to N modular sections can be created to reach higher speeds and are controlled by the FPGA controller algorithm. The traveling wave analysis created with this structure is quite complex. When developing the power stage, initiating the process with a simplified model would be a more practical approach [11].

A magnetically coupled projectile with a single drive coil is defined as the simplest component of the launcher and its equivalent circuit is shown in Figure 4.

The equations of the circuit model are obtained as follows:

$${\mathrm{v}=\mathrm{R}}_1{\mathrm{i}}_1+\frac{{\mathrm{d}\mathsf{\psi }}_1}{\mathrm{dx}}, {\mathsf{\psi }}_1={\mathrm{L}}_1{\mathrm{i}}_1+\mathrm{M}{\mathrm{i}}_2 (\mathrm{coil}\text{-}1 \mathrm{flux} \mathrm{linkages}),$$

(1)

$${0=\mathrm{R}}_2{\mathrm{i}}_2+\frac{{\mathrm{d}\mathsf{\psi }}_2}{\mathrm{dx}}, {\mathsf{\psi }}_2={\mathrm{L}}_2{\mathrm{i}}_2+\mathrm{M}{\mathrm{i}}_1 (\mathrm{coil}\text{-}2 \mathrm{flux} \mathrm{linkages}),$$

(2)

$${\mathrm{v}=\mathrm{R}}_1{\mathrm{i}}_1+\frac{\mathrm{d}}{\mathrm{dt}}({\mathrm{L}}_1{\mathrm{i}}_1+\mathrm{M}{\mathrm{i}}_2),$$

(3)

$${0=\mathrm{R}}_2{\mathrm{i}}_2+\frac{\mathrm{d}}{\mathrm{dt}}({\mathrm{L}}_2{\mathrm{i}}_2+\mathrm{M}{\mathrm{i}}_1),$$

(4)

where M represents the mutual inductance of the drive coil and short-circuited projectile. Neglecting the resistance of the projectile (R₂) and the initial flux (ψ₂(0), the equation becomes the following:

$${\mathrm{v}=\mathrm{R}}_1{\mathrm{i}}_1+\frac{\mathrm{d}}{\mathrm{dt}}({(\mathrm{L}}_1-\frac{{\mathrm{M}}^2}{{\mathrm{L}}_2}{)\mathrm{i}}_1),$$

(5)

and the equivalent circuit in Figure 5 is obtained.

The power supplied to the equivalent circuit by the power source is

$${\mathrm{p}=\mathrm{R}}_1{{\mathrm{i}}_1}^2+\frac{\mathrm{d}{\mathrm{W}}_{\mathrm{m}}}{\mathrm{dt}}-\frac{1}{2}\frac{{{\mathrm{i}}_1}^2}{{\mathrm{L}}_2}\frac{\mathrm{d}{\mathrm{M}}^2}{\mathrm{dt}},$$

(6)

${\mathrm{R}}_1{{\mathrm{i}}_1}^2$: ohmic losses;

$\frac{\mathrm{d}{\mathrm{W}}_{\mathrm{m}}}{\mathrm{dt}}$: magnetic field in the system;

$\frac{{{\mathrm{i}}_1}^2}{{\mathrm{L}}_2}\frac{\mathrm{d}{\mathrm{M}}^2}{\mathrm{dt}}$: kinetic energy input.

The force applied to a projectile can be calculated from kinetic energy input part of Equation (6):

$$\mathrm{F} =-\frac{1}{2}\frac{{{\mathrm{i}}_1}^2}{{\mathrm{L}}_2}\frac{\mathrm{d}{\mathrm{M}}^2}{\mathrm{dx}},$$

(7)

Although this force description is useful for designing and analyzing inverter power circuits, more is needed for a linear induction launcher based on the traveling magnetic wave principle. The slip concept, as previously defined and commonly used in induction machines, becomes significant at this point.

A magnetic field moves along the barrel with a synchronous speed given by

$${\mathrm{V}}_{\mathrm{s}}=2\mathsf{\tau }\mathrm{f},$$

(8)

where $\mathsf{\tau }$ is the pole pitch and f is the frequency of the current applied to the drive coils. To induce currents on the projectile, there must be a difference between the synchronous and actual projectile speeds (${\mathrm{V}}_{\mathrm{p}}$). This will cause the projectile to move slower than the travelling wave under normal operating conditions. The net force applied to the projectile is zero when the synchronous speed and the projectile speed are equal. The slip calculation (s) is obtained as follows:

$$\mathrm{s}=\frac{{\mathrm{V}}_{\mathrm{s}}-{\mathrm{V}}_{\mathrm{p}}}{{\mathrm{V}}_{\mathrm{s}}},$$

(9)

The force per coil generated by the interaction between the traveling magnetic wave package and the projectile is similar to the torque–slip equation of a classical induction machine:

$$\mathrm{F}=\frac{2{\mathrm{F}}_{\mathrm{c}\mathrm{m}}}{\frac{\mathrm{s}}{{\mathrm{s}}_{\mathrm{c}}}+\frac{{\mathrm{s}}_{\mathrm{c}}}{\mathrm{s}}},$$

(10)

where ${\mathrm{F}}_{\mathrm{c}\mathrm{m}}$ is the maximum force value and ${\mathrm{s}}_{\mathrm{c}}$ is the critical slip for which the force applied to the projectile is the maximum. ${\mathrm{F}}_{\mathrm{c}\mathrm{m}}$ is a function of various parameters such as the following:

• The axial length of a barrel coil;
• Non-dimensional functions that depend only on the pole pitch and the dimensions of the launcher;
• Voltage, current, and turns per coil.

The force–slip characteristic of the linear induction launcher (LIL), as defined in Equation (10), is depicted in Figure 6. A continuous positive force must be applied for the projectile to accelerate continuously and smoothly, as in the first quadrant. The third quadrant is when the projectile’s speed is faster than the traveling wave speed and causes negative forces. The FPGA control algorithm aims to prevent such undesirable situations by applying the currents in phase during section transitions.

3. Power Stage

A multiphase power stage with a phase difference is required in the proposed system to create a traveling wave packet. Furthermore, the launcher’s power system needs to be capable of varying the voltage and frequency of the drive coils. To achieve this, single-phase inverter structures are used with the FPGA control unit.

A single-phase inverter converts DC power to AC power at the desired output voltage and frequency. It is classified into two types: voltage source (VSI) and current source (CSI) inverters. A VSI is characterized by a DC source with negligible impedance, maintaining a constant voltage at the input terminals. On the other hand, a CSI is supplied with an adjustable current from a high-impedance DC source. Since VSI is well suited for highly dynamic applications, it is preferred in the launcher power stage. Another advantage is that it can be charged with a simple rectifier.

Pulse-width modulation is an efficient way to control single-phase inverters without external circuitry. While the input capacitor is fed with a constant voltage, the value of the AC voltage at the output is achieved by adjusting the on and off times of the inverter switches. When the switching frequencies to be generated in the launcher are observed, selecting switches in the 20 kHz frequency range and with a megawatt power rating would be most appropriate. As shown in the power switch technology scaling illustration in Figure 7, the insulated-gate bipolar transistor (IGBT) is the most suitable switch type for our application.

A single-phase inverter in the H-bridge topology consists of four IGBT switching devices, as shown in Figure 8 [13]. When switches S1, S3 and S2, S4 are alternately switched on and off at a frequency of fs, an alternating voltage waveform is produced across the drive coils in the launcher.

An H-bridge inverter is capable determining of the rms value and frequency of the output voltage fundamental component [14]. For this purpose, the sinusoidal pulse-width modulation (SPWM) method is one of the most widely used methods [15]. Although bipolar or unipolar switching is possible in the SPWM method, since the inductances of the launcher coils are generally very small, a bipolar control scheme is used in the launcher to control very high di/dt values. In this scheme, diagonal IGBT switches (S1–S3 and S2–S4) are turned on and turned off simultaneously by the relationship between reference (${\mathrm{V}}_{\mathrm{r}}$) and carrier (${\mathrm{V}}_{\mathrm{c}}$) signals. The output voltage is determined by comparing ${\mathrm{V}}_{\mathrm{r}}$ and ${\mathrm{V}}_{\mathrm{c}}$ using the FPGA algorithm.

Asynchronous modulation is applied in the bipolar SPWM inverter due to software design difficulties and the fact that sub-harmonics do not have much effect on the efficiency of the system in the induction launcher.

Electrical simulation of the single power stage formed when the H-bridge inverter was connected as the power source to the launcher’s equivalent circuit obtained in the second section (Figure 5) was carried out as shown in Figure 9 [16].

It is seen in Figure 10 that the desired sine current wave (Iload) for the excitation of drive coils is obtained by selecting fixed ma = 0.6 (modulation index) and mf = 15 (frequency ratio) values. To simplify the analysis of the power circuit, the ratio of the mutual inductance and the short-circuited projectile in the equivalent circuit is neglected. Vref and Vcarrier signals are generated in the FPGA to obtain the PWM voltage to be applied to the driver coils. The capacitor at the inverter input is charged using a half-wave rectifier, thereby obviating the necessity for a sophisticated power supply in launcher systems.

3.1. Scalar V/f Control

The proposed power system in the launcher allows for changing the voltage and frequency values using a software algorithm, as described earlier. Increasing both voltage and frequency along the induction launcher facilitates obtaining a smooth force graph with a constant air gap flux value. This method [17] is based on the principle of keeping the voltage–frequency ratio constant in the linear region, as shown in Figure 11.

At 0-fc Hz, the drive coil resistance cannot be neglected due to the voltage drop across it. Therefore, the V/f profile is not linear, and the launcher does not operate in this range. At fc-frated Hz, it follows the constant V/f ratio linearly. This is achieved by adjusting the modulation index and frequency ratio values in the H-bridge inverter, ensuring operation in this region [18]. Since the flux is maintained constant along the barrel, the force only depends on the slip, as mentioned earlier in Equation (10).

In order to simulate the V/f control in the equivalent launcher circuit as shown in Figure 9 and Figure 10, it is necessary to define the reference voltage as a time-dependent mathematical function:

$${\mathrm{v}}_{\mathrm{ref}}=({\mathrm{V}}_{\mathrm{start}}+{\mathrm{k}}_1\mathrm{t}\left)\sin \right(2\mathsf{\pi }{(\mathrm{f}}_{\mathrm{start}}+{\mathrm{k}}_2\mathrm{t})\mathrm{t}+\mathrm{phasedelay}),$$

(11)

where ${\mathrm{k}}_1$ and ${\mathrm{k}}_2$ are the parameters that depend on the required V/f ratio according to the structure of the launcher.

When the FFT simulation results in Figure 12 and Figure 13 are evaluated, it is seen that by applying a signal with increasing frequency and voltage along the launcher, a constant and smooth force characteristic is obtained due to a current with constant amplitude and increasing frequency, as derived in Equation (7).

In the proposed system, this increasing frequency current characteristic, which is aimed to be obtained along the barrel, is generated by sequentially controlling the H-bridge inverters in each section using the FPGA controller, as shown in Figure 14.

The current graphs show that one section is energized while the other sections remain inactive. When the power consumed in a section during time T is denoted as P, the total energy consumption for the entire launcher is approximately 3 × P × T. If the sections without the projectile are energized while the projectile is in motion (e.g., Section-3 while moving through Section-1, Section-1 while moving through Section-2, and Sections-1 and -2 while moving through Section-3), the energy consumption would be 7 × P × T. Therefore, the proposed system consumes 57.1% less energy than the launchers, which energizes the entire system.

3.2. FPGA Implementation

The algorithms necessary for the launcher and communication via GUI were implemented on the Xilinx Spartan 3 series FPGA. The primary responsibility of the FPGA controller is to generate sinusoidal PWM signals connected to the H-bridge inverters. A modular and hierarchical design methodology was followed because the control of the inverters is independent and parallel. The necessary top-level modules were designed and then coded using the VHDL language. Before the design implementation steps (translate, map, and place&route) and testing in a real experimental environment, design verification was implemented using the ISIM/Modelsim test bench.

Figure 15 shows the block diagram of the modules that generate the PWM signal. Firstly, reference and carrier signals were generated and then they were compared with each other. Lookup tables were used to generate the reference signal in sine form, while counter units were used to generate the carrier signal. A clock frequency of 25 MHz was used to generate these signals. As a result of the comparison, four PWM signals were created to drive the IGBT switches. Here, a dead time was added to the control scheme between the switching signals to prevent the upper and lower switches from turning on at the same time. To prevent a leg shoot-through and ensure proper operation of the H-bridge inverter, the dead time should be chosen carefully, keeping it as short as possible. The ideal dead time calculation is selected by taking into account the absolute values of the IGBT elements used:

$${\mathrm{t}}_{\mathrm{dead}}=\left[\right({\mathrm{t}}_{\mathrm{d}\text{\_}\mathrm{off}\text{\_}\max }-{\mathrm{t}}_{\mathrm{d}\text{\_}\mathrm{on}\text{\_}\min }{)+(\mathrm{t}}_{\mathrm{pdd}\text{\_}\max }-{\mathrm{t}}_{\mathrm{pdd}\text{\_}\min }) \times 1.2,$$

(12)

where ${\mathrm{t}}_{\mathrm{d}}$ is the delay time, ${\mathrm{t}}_{\mathrm{pdd}}$ is the propagation delay of the driver, and 1.2 is the safety margin.

It was necessary to use discrete PWM modules for the nine inverters in the system and their control was performed by the top module. In general, the top module is responsible for communication with the user interface (GUI), time and phase control of H-bridge inverters, and sending commands such as start–stop–reset to the PWM modules accordingly, as shown in Figure 16. As described in the previous section, the reference signal is modified in Figure 17 as necessary to achieve constant V/f control throughout the launcher.

4. Three-Dimensional FEM Analysis

In order to observe the behavior of the proposed power system, a launcher and its power system qwew first modeled in a simulation environment. The frequency and phase transitions and V/f characteristics of each section were obtained using 3-D FEM (Finite Element Method) analysis. With the results obtained from the simulation’s speed, force, and displacement graphs, the FPGA controller was designed and provided as input to the algorithm performed in the real environment.

The modeled linear induction launcher consists of 3 sections and 18 coils. According to [19], we observed the system parameters and performance of the modeled linear induction launcher. The physical properties of the modeled linear induction launcher are given in

Table 1. Main physical parameters of the LIL.

	Parameters	Value
Barrel	Barrel Length	0.75 m
	Number of Coils	18
	Number of Phases	3
	Number of Section	3
	Coil Axial Length	0.04 m
	Coil Inner Radial Width	0.04 m
	Coil Outer Radial Width	0.09 m
	Coil Inductance	20 uH
	Coil Number of Turns	2 × 10
Projectile	Length	0.24 m
	Inner Radial Width	0.0038 m
	Outer Radial Width	0.0039 m
	Material	Aluminum

.

The transient response magnetic field analysis was used to determine the thrust force at a specific translation location of the projectile in the linear induction launcher. The Finite Element Method (FEM) model, necessary for conducting field analysis, consists of a mesh model, material attributes, and analysis conditions [20].

A three-dimensional model was employed due to the launcher’s design and the three-dimensional nature of its magnetic field. Figure 18 shows a 3-D view of the launcher whose physical properties are given.

The mesh model in this study sets the size of the air region to be 1.05 times greater than the longest edge of the launcher. When including motion in the analysis, it is necessary to ensure that the mesh is consistent between the moving portions and the stationary sections. Generating a mesh that maintains consistency between moving and stationary pieces for each incremental motion is challenging. During the analysis process, the mesh was produced iteratively. Due to the time-varying nature of the magnetomotive force and the translational location of the projectile, we employed a transient response analysis. Furthermore, using a 3-D model necessitates selecting 3-D transient response analysis as the chosen analysis type.

For the most accurate operation of the 3-D model, voltage and current sources were created with external electrical circuits as shown in Figure 19.

The current and voltage waveforms generated for 250 Hz, 500 Hz, and 750 Hz are shown in Figure 20. The aim was to keep the V/f ratio constant while increasing the amplitude of the voltage as the frequency increases in the applied voltage. The launcher always intends to apply a positive force to the projectile along the barrel. With this aim, it is ensured that the currents are in the same phase at the section transitions and aimed at obtaining a smooth-traveling magnetic wave.

Simulation Results

In this chapter, we examine the simulation results obtained by energizing the drive coils section by section. The V/f ratio was kept approximately constant by increasing the applied voltage in response to the increasing frequency along the barrel. With the power system obtained by external electrical circuits, the projectile’s movement was achieved, and the traveling wave visuals in the simulation are shown in Figure 21.

Figure 22a shows the force applied to the projectile. The minimization of the negative forces caused by the end effect when moving from one section to another is ensured by the currents in each section being almost in phase with the currents in the previous section.

When the projectile is completely inside the section where it is located, it is observed that the maximum force is obtained, while the force applied decreases as it passes to the other section. Figure 22b shows the projectile velocity graph along the launcher. As a result of the simulation, the maximum muzzle velocity reached was 35 m/s.

5. Experimental Study

5.1. Construction of LIL and Power Systems

A laboratory-scale linear induction launcher and power system were designed and manufactured, and experiments were carried out. The coupling of the coils to each other was achieved by threading a glass fiber tube through them, and their respective physical properties are detailed in Table 1. The barrel was mounted on a chassis mechanism with damper elements. An optical measurement system was installed at each section’s exit, and the projectile’s velocity was measured. High-power and high-voltage H-bridge inverters were used to verify the proposed power system. The inverter switches were controlled through a fiber-optic system rather than electrically to mitigate the risk of high electromagnetic noise interference.

H-bridge inverter units, one of the main components of the system, were designed modularly. The modules consist of 4 IGBT switches (MITSUBISHI CM1200HC-66H), their drivers (Power Integrations -1SD536F2), two capacitors, and bus bars forming the full bridge structure as shown in Figure 23. In order to provide kilo-ampere-level currents applied to the launcher system, 2000 VDC and 8.8 mF MKP capacitors that can deliver high currents were used in the H-bridge inverters.

Stand-alone module tests were conducted prior to integrating the H-bridge modules into the launcher power system. The double pulse test method was applied to each module to measure the switching parameters, observe the dynamic behavior of the IGBTs, and identify any manufacturing, insulation, or other potential issues in the modules [21]. In the H-bridge module, this test was executed by applying two pulse signals to the switch under test while the switch across was consistently turned on.

As seen in Figure 24, to test the S1 switch, the S3 switch was first turned on. During the duration of T1, the S1 switch was turned on. During the T2 period, it was turned off and then turned on again for the T3 period. The turn-off time at the end of the T1 period and the turn-on time at the end of the T2 period were observed.

Figure 25 shows the test results for the S1 IGBT switch. During T1 and T3, the current flows through path-1, while during T2, the current flows through path-2 via the reverse diodes in the switches. When the parameters obtained as a result of this test are used in Equation (12), a dead time of 10 μs is preferred to avoid unwanted shoot-through in the same arm.

The FPGA control unit is the equipment that controls the IGBT drivers in the inverters according to the algorithms on them, resets the operation of the system in case of errors, sends information to the computer interface via USB communication, and receives commands to start and stop the launcher operation.

A XILINX Spartan 3A series FPGA was used to implement the VHDL top module illustrated in Figure 16, as previously described. HFBR series fiber-optic receivers and transmitters with a wavelength of 660 nm were used to convert the TTL-level PWM signals at the FPGA output into fiber-optic signals, as depicted in Figure 26.

For proper operation, the backplane board establishes the connection between the unit containing the fiber-optic converter boards and the FPGA control board. All the cards were assembled using a 3U rack cabinet to achieve this. The FPGA was also connected to the speed measurement optical signals and IGBT driver status signals through this cabinet.

The driver coils used in the electromagnetic analyses and simulations are made of a copper strip with high current capacity. They were placed in a polyamide box for mounting on the barrel. The projectile is a hollow aluminum cylinder. These are shown in Figure 27.

All units and measurement equipment constituting the experimental setup were assembled as shown in Figure 28. The launcher system and the connected power system form a highly modular structure. Thus, it was possible to increase the number of sections without changing the structure.

The capacitors were charged using transformers with a conversion ratio of 1 to 40. A half-wave rectifier was connected to the transformer outputs, and the charging current was limited by the resistor. Including isolation in the charging circuits enhances the system’s safety. Additionally, it was feasible to charge the capacitors during the launch operation.

5.2. Experimental Results

Studies on the proposed power system were carried out with the experimental setup. The 1st section operated at 250 Hz, the 2nd section at 500 Hz, and the 3rd section at 750 Hz. The three-phase currents within each section and the current graphs during section transitions were analyzed.

As explained in the system design section, a 120-degree phase difference was provided between the A, B, and C phases in each section for optimum launch performance. Figure 29 shows some ripple in the sinusoidal currents due to the low inductance of the driver coil. With this phase difference, a traveling magnetic wave is created, the projectile follows this field, and the launch is provided.

Phase transitions within each section were measured by the phase-A current, as shown in Figure 30. The start and stop timing of the sections was set according to the projectile position obtained as a result of electromagnetic simulations. In order to keep the current constant while increasing the frequency for each section, the modulation index was increased in the FPGA to ensure a constant V/f ratio along the barrel.

The sections in the launcher were energized by separate inverters. In order not to apply negative force at the section transitions and to ensure that the traveling magnetic wave was smooth, phase control was performed at the section transitions. Figure 31 and Figure 32 illustrate the phase-A currents during the transition from Section-1 to Section-2 and Section-2 to Section-3, respectively. In the voltage source inverter structure, the coil currents were produced in the same phase while the frequency and voltage were increased.

An optical velocity sensor integrated into the launcher output measured the muzzle velocity using an oscilloscope. As shown in Figure 33, when the projectile leaves Section-3, the energy of Section-3 is not cut off, and the energization of the related coils continues. This prevents the phenomenon known as the end effect and eliminates the negative forces as the projectile leaves the launcher. Optical velocity measurements taken from the 24 cm long projectile passing through the muzzle revealed a duration of 8 ms, resulting in a muzzle velocity of 30 m/s.

6. Results

This article introduces a novel power system for linear induction launchers. Initially, the equivalent electrical circuit was derived for power system analysis. Transient simulations of the H-bridge inverter were conducted using scalar V/f control, yielding launcher currents and voltages. Control algorithms were developed using the Xilinx Spartan 3A FPGA and scrutinized through the ISE Simulator test bench. The impact of the currents applied to the driver coils on the induction launcher was analyzed using 3-D Finite Element Method (FEM) analysis. A comprehensive system model was created for this purpose, employing external electrical circuits to generate the required waveforms. These analyses optimized the frequency, phase, and current parameters in the actual system. The real experimental setup was created like the 3-D model, and launch experiments were performed.

The FPGA control unit drove the inverters sequentially, section by section, with fiber-optic connections and observed phase current values. With a 400 VDC bus voltage, currents of 1000 A with frequency values of 250 Hz in Section-1, 500 Hz in Section-2, and 750 Hz in Section-3 were applied. Negative forces were prevented by obtaining in-phase currents at section transitions. Experiments were carried out with the launcher system reaching a projectile speed of 30 m/s. With a muzzle velocity of approximately 35 m/s obtained by 3-D FEM analysis, the simulation and experimental results are similar.

7. Discussion

As a result of all these efforts, a more flexible, modular, and efficient power system has been obtained compared to other launcher power systems in the literature as shown in

Table 2. A comparison of parameters for the power systems of LIL.

Parameter	LC Resonance	Generator	Single Inverter	Proposed System
V/f control	X	X	√	√
Section-by-section energization	√	√	X	√

√: Applicable, X: Not Applicable.

.

In pulse generators [22] obtained by the resonance of inductances and capacitors, the frequency depends on the value of these elements. In generator-driven power systems [7], the voltage and frequency depend on the physical properties of the electrical machine and the operating speed. It is highly complicated to change these values for changing voltage, frequency, and phase; it is not flexible. In the proposed system, the adjustment of voltage and frequency relies on a software algorithm, allowing for easy modification based on the specific requirements of speed and the electrical and physical properties of any launcher.

Single-inverter power systems [8,9] suffer from efficiency problems when all drive coils in the launcher are energized at the same time because the coils where the projectile is not present are also energized. For an efficient launch operation, the section-by-section energization method is of great importance. At this point, while the proposed system applies the optimum current, voltage, and frequency values for the launcher using modern inverter methods, the aim is to achieve high efficiency by energizing each section separately in the proposed system. Compared to the launchers energizing the whole system, the proposed system consumes 57.1 percent less energy.

In future studies, the aim is to reach higher speeds by increasing the number of coils in the launcher. The plan is to reduce ripple effects and harmonics in the coil currents using vector control instead of scalar control and high-frequency switching using SiC technology. In addition, the effect of increasing the frequency in smaller steps along the barrel on the muzzle velocity will be observed.