Design of PI Controller for Voltage Controller of Four-Phase Interleaved Boost Converter Using Particle Swarm Optimization

+is article introduces voltage feedback controlling using the PI controller tuned gains by metaheuristic optimizations for a fourphase interleaved boost converter.+emetaheuristic optimizations, particle swarm optimization (PSO), genetic algorithm (GA), and Tabu search (TS) are applied to find the optimal gains for the proposed control system. In experiment, the designed control system is implemented on the DSP board TMS320F28335 with MATLAB/Simulink. In this paper, there are two conditions of the control system in the test, without load and with load.+e response result of the proposed control system tuned gains by PSO is no overshoot and approaches to the steady state better than GA and TS methods. Moreover, it is able to maintain the output voltage feedback at a constant level according to the control signal both without load andwith load conditions. As a result, the four-phase interleaved boost converter is regulated by the PI controller tuned gains with PSO which could efficiently maintain the voltage of both levels.


Introduction
Currently, the need for energy is increasing. It is necessary to find energy from other possible resources, for example, solar energy, wind energy, and fuel energy. In general, to bring alternative energies to use, it is necessary to increase or reduce the voltage level before the actual use.
is is to make it conform with certain equipment. For increasing the voltage, a power electronic circuit is required. e boost converter is one of the circuits used for increasing voltage. e boost converter circuit is a circuit that uses less equipment and can raise the voltage. For this reason, it is one of the popular circuits used to increase the voltage for further applications [1,2].
Due to the increasing need for energies, at present the use of a single energy transforming set is not enough for serving the purpose. us, devices that work together in parallel are used to serve an increasing need for energies, and using only one boost converter which requires high energy might not be possible. So, it is necessary to have devices that work together in parallel in order to share the burden of increasing need for energies. However, when the boost converter works in parallel, it will create a high ripple of input and output voltage. For this reason, the operation of each set of the boost converter connected in parallel is set for working at appropriate degrees. is is to reduce the ripple of input and output current, and as a consequence, the output voltage has less ripple. e boost converter in parallel has been applied to various works like the use of power factor correction (PFC) in experiment rooms, the application for solar energy, fuel cell, and DC-DC switched-mode power converters (SMPC) [3][4][5][6][7][8].
However, though the voltage has less ripple, with no system to control the voltage output size to be constant when brought into actual use could possibly affect the stability of the system, for example, change from lower load to higher load.
is will cause the reduction of output voltage to become smaller than the required size. e same applies to changing from higher to lower load, and this will cause output voltage higher than that required. Because of this, it is very important to have a system to control output voltage in order to keep the output voltage constant, though there is a change in output or input load. For certain types of work, having only one PI controller is sufficient for controlling the process to be stable, and its result of controlling using the PI controller is acceptable.
ere are various ways to adjust the value of the Proportional-Integral (PI) controller, and currently, artificial intelligence plays an important role in searching suitable values. Examples are Tabu search (TS), genetic search (GS), and particle swarm optimization (PSO). e PSO, in particular, is a method to give a suitable value and has been used with many systems of PSO such as the DC motor control system, the one without carbon brush, the DC-to-DC converter circuit system, the test on the electric motor drive, and the multilevel inverter. e applications on the abovementioned systems gave a very satisfactory result, and using the search values with the test system also provided a satisfactory response [9][10][11][12][13][14].
As mentioned previously, the PSO is widely applied to the PI controller for simulation system and real-world system. However, it is usually employed in one-phase and two-phase interleaved boost converter circuits. ere are a few studies considering the gained value PI controller for real system of the four-phase interleaved boost converter circuit. is research introduces a design of the PI controller using PSO search for controlling the voltage of the four-phase interleaved boost converter in order to control output voltage at constant size throughout the use. e technique used was by PSO to control output voltage to have constant size according to the set voltage both when the load is constant and while the load is changed. e circuit keeps reducing the input and output voltage ripple as usual, so that it is possible to be used for further work related to increasing voltage level.

Theory of Boost Converter
e boost converter circuit is a power converter circuit that works to increase output voltage to be higher than that of the input. e structure of the circuit is shown in Figure 1.

eory of Four-Phase Interleaved Boost Converter Circuit.
e four-phase interleaved boost converter is a circuit designed based on the original boost converter. e original boost converter is designed to work in parallel while the circuit operation is interleaved. e interleave depends on the number of the parallel boost converters while the fourphase interleaved boost converter helps to solve the problem of overload burden the original boost converter has. As the circuit load increases, it is necessary to design larger equipment as a result. Also, switch operation will get a higher load as a result. Four-phase interleaved boost converter can solve this problem. is also helped in reducing the ripple of input and output. e four-phase interleaved boost converter circuit [15][16][17][18] is shown in Figure 2.
where D is duty cycle, V input is voltage input, and V output is voltage output. e equation for designing inductance value can be derived using the following equation: where L is inductor, ΔI L is induction ripple current, and f S is switching frequency. e equation for designing capacitor value can be derived form the following equation: where C is capacitor, R is resistor load, and ΔV output is a ripple factor of the output voltage. For designing the angle of the boost converter in each phase, the switching angle of the boost converter in each phase can be designed to form the following equation: where θ is angle of switching and N is number of phases of the boost converter circuit.

Algorithm of PSO
e origin of searching the most suitable value of PSO was developed by Reynolds in 1987 [19,20]. He got inspiration from the patterns of herd movement such as flock of birds, school of fish, and insect swarm as shown in Figure 7. e movement is based on three main principles: confrontation avoidance of swarm, same speed control within the swarm,

Journal of Control Science and Engineering
Algorithm of PSO has the same feature of evolutionary calculation, i.e., there will be a creation of population called particle which will move around the search space. Each particle has a speed vector and a memory unit to be used for storing previous good answers. p best is set as good answer in the current search while g best is set as global solution. All particles will move in a similar manner, and the ones closest to the target are the strongest. With the particle swarm movement principle, the rest of the particles will be adjusted to have a similar movement direction as that of those strongest ones. is makes it possible for the whole particle swarm to move to the target effectively.
Consider that the search-space is d-dimensional and at particle i-th in the swarm. It can be defined as . , x id ) and the velocity can be represented by another d-dimensional vector as V i � (v i1 , v i2 , . . . , v id ) and the best previously visited position of this particle be denoted by P i � (p i1 , p i2 , ..., p id ). e adjustment of particle movement direction and the answers found are shown in equations (6) and (7) accordingly [22]. Where x is a particle or answer, v is speed vector showing adjusted direction, w is inertia weight, c 1 is cognitive acceleration, c 2 is social acceleration, and r 1 and r 2 are random numbers uniformly distributed in the range [0,1].
In case of 2D space, the movement of particles should be adjusted as shown in Figure 8.
e inertial weight w can be calculated from the relation as in equation (8), where w max is the maximum weight, w min is the minimum weight, k max is the number of the highest search round set, and k is the current search round. e best value suitable for use is the number of current search round, and the most suitable value of work application is c 1 and c 2 which should be in-between 1 and 2 while w min and w max should be equal to 0.4 and 0.9 accordingly [23]. Algorithm of PSO has the following details: e steps of designing PSO are as follows: Step 1: setting initial values which are search space, number of particles, and maximum number of search rounds.
Step 2: creating particles with normal sampling distribution according to the number set.
Step 3: evaluating the strength of each particle using objective function.
Step 4: adjusting the movement direction in accordance with the strongest particle using equations (6) and (8).
Step 5: calculating the particle of the current search round using equation (7).
Step 6: checking the ending condition. If it is correlated, this means that the best search is obtained.
en, stop the search or perform step 3 to further the next search.

Theory PI
e PI controller is a combination between the proportional controller, P, and integral controller, I. e system for controlling PI is shown as a block diagram in Figure 9. PI controlling system is composed of error signal, E(s), control signal, U(s), output response signal, C(s), reference signal, R(s), disturbing signal, D(s), and transferring signal of the system G p (s) and G c (s). e theoretical function of the PI controller is stated in the following equation: e PI controlling system is shown in Figure 9. e four-phase interleaved boost converter system has a fast output response but lacks stability. e PI controller has the advantage of faster response times and less stable errors. erefore, it is very appropriate to choose a PI controller for this system.
To obtain the value of the PI controller for the four-phase interleaved boost converter circuit, the design of the PI controller uses PSO search to control four-phase interleaved boost converter voltage as shown in Figure 10.

Digital Signal Processor Set
is part will focus on the digital signal processor or Digital Signal Processor (DSP) board TMS320F28335 of Texas Instruments company [24] as shown in Figure 11 for analyzing real-time controlling. e Texas Instrument TMS320F28335 consisting of a 32-bit CPU and a single-precision 32-bit floating-point. e CPU speed is controlled by a clock signal with the frequency of 150 MHz working with MATLAB/ Simulink [25]. It produces pulse width modulation (PWM) signal for driving the four-phase interleaved boost converter circuit switch of 25 kHz frequency as shown in Figure 12.

Design of Four-Phase Interleaved Boost
Converter Circuit e parameter value of the four-phase interleaved boost converter obtained from equations (1)-(5) is shown in Table 1.
For the design of a four-phase interleaved boost converter circuit to simplify circuit design, the four-phase interleaved boost converter has parallel circuits.
erefore, considering only one model of the circuit to make it easier to design. e transferring function of the boost converter circuit uses the impedance method where the analysis makes use of switching operation while the switch is off. is can be shown as follows [26]. All of the impedance value (Z total ) is shown in the following equation: Z 1 (s) is the condition of the switch when the circuit is open, and Z 2 (s) is the condition of the switch when the Journal of Control Science and Engineering circuit is closed. e value of Z 1 (s) is shown in the following equation and the value of Z 2 (s) is shown in equation (12).
and the transferring function of the system is shown in the following equation: Where the value with parameter from Table 1 is replaced and the transfer function of the system is obtained, and it is shown in the following equation: G p (s) � 2 117.3 × 10 −9 s 2 + 586.5 × 10 −6 s + 2 .
As mentioned in equation (14), the term 117.3 × 10 −9 s 2 is a very small value considered close to zero.
is system, therefore, became first order, called Type 0 system. us, it is suitable for the PI controller.
In designing the value of PI for the four-phase interleaved boost converter circuit using particle swarm search based on Figure 8, PSO search was used for designing a PI controller for the four-phase interleaved boost converter circuit system where PSO algorithm was made by MAT-LAB, working with Intel(R) Core (TM) i5-3210M @2.5 GHz. e number of particle sets is 100 where c 1 � c 2 is 2.0, r 1 and r 2 are random numbers uniformly distributed in the range [0, 1], w min is 0.4, w max is 0.9, and k max is 1,000, i.e., maximum iteration set as the termination criteria for each trial.
Based on comparing GA and TS, the design was done using a PI controller for the four-phase interleaved boost converter circuit. GA and TS parameter search is designed as original. Both GA and TS will be canceled when processing the construction or making a repletion of up to 1,000 times. GA and TS will not be discussed. But they show more details of GA in [27,28] and TS in [29][30][31] accordingly. e algorithm of the two searches mentioned works by using MATLAB.
For designing the PI controller, its parameter PI is set for searching the following spaces: K p ranges [0, 10] and K i ranges [50, 100]. e processing designed for 50 experiment    Journal of Control Science and Engineering searches starts with different search points to find the best value. After the search processing stops, the parameter value of the PI controller is obtained using GA, TS, and PSO methods as shown in equations (15)- (17) accordingly. e result of the simulation of the controller system is shown in Figure 13.
Based on Figure 11, the response of four-phase interleaved boost converter circuit simulation and time for searching can be seen in Table 2 where T r is the rise time, M p is the maximum percent overshoot, T s is the settling time, and e ss is the steady state error. Based on Table 2, PSO is able to search the PI parameter value for the four-phase interleaved boost converter with minimum time. Moreover, the    control system of the four-phase interleaved boost converter also gives a quick response when rise time and settling time have the best value and show the result of convergence to the answer of PI search value using PSO as shown in Figure 14.

Experiment Result
e test on the PI controller with the PSO search for controlling voltage of the four-phase interleaved boost converter uses 4 sets of original boost converter circuit working in parallel. e operation is done with 90-degree interface and has a voltage sensor sending electrical signals to the DSP board TMS320F28335 working with MATLAB/ Simulink of sampling time at 0.0001 second.
In this research, the voltage level was kept at 2 levels, i.e., 20 V and 24 V.
e result of the experiment shows the stability condition treatment of circuit voltage while changing load without the control system and voltage control of 20 V and 24 V while changing load accordingly. e data collection was done using digital storage scope GW Instek GDS-3000 Series 150 MHz 4 input channels.
Based on the experimental results of circuit voltage treatment while changing load without a control system with voltage control of 20 V and 24 V as shown in Figures 15 and  16, it was found that the output voltage of the circuit dropped significantly when the load was increased. e figure shows that the system was unstable to maintain the output voltage level to be constant.
From Figure 17, the inductor current phases 1 and 2 are indicated with switch signals S1 and S2, respectively. e signals S1 and S2 are determined to operate the inductor current in 90 degree of differentiation. It can be seen that when both switches are on, there will be increase in current in the load. On the other hand, when both switches are off, current will decrease. erefore, experiment results confirm the theoretical analysis. From Figure 18, the current of the four-phase interleaved boost converter is investigated for every 90-degree switch signal overlapping. It can be seen that all inductor currents still appear according to the switch signals S1 and S2, respectively.
For controlling PI controller voltage at 20 V, the gained values of the PI controller using three optimization algorithms of GA, TS, and PSO are applied to examine the response and the stability of the circuit voltage. e results are shown in Figures 19-24. Figures 19, 21, and 23 show the result of voltage response and current when the gained values of the PI controller are applied in GA, TS, and PSO, respectively. e initial voltage input is set at 13.8 V, and this study focused on the voltage  Signal S1 Signal S2 Inductor current phase1 Inductor current phase2 Inductor current phase1 Inductor current phase2 Inductor current phase3 Inductor current phase3 changing the load. It can be seen that the stability of voltage output from three algorithms still remains unchanged although load has changed. Table 3 shows the system response by the PI controller at 20 V.
In summary, the system response of voltage output from the PI controller at 20 V using GA, TS, and PSO can be concluded as in Table 3. Also, the PI control with PSO search had the quickest response to reference signal when compared to GA and TS. e PSO establishes the lowest rise time at 6 ms and the lowest time to steady state at 8 ms. erefore, the PSO is the best algorithm in controlling the voltage output at 20 V.
In order to control voltage output at 24 V, the same PI controller gained values as one for 20 V are applied in GA, TS, and PSO, respectively. It was found that GA, TS, and PSO had a quick response to reference signal and could enter the condition in less than 20 ms. Figures 25-27 show the result of voltage response and current when the gained values of the PI controller are applied in GA, TS, and PSO, respectively. e initial voltage input is set at 13.8 V. In the experiment case, the voltage output is controlled at 24 V. ree optimization algorithms can provide good response results and also can remain the steady state of voltage output similar to the case of 20 V controlling. Figures 28-30 show the results, when changing the load. It can be seen that the stability of voltage output from three algorithms still remains unchanged although load has changed. Table 4 shows the system response by the PI controller at 24 V.
As in Table 4, the system response of voltage output by the PI controller at 24 V using GA, TS, and PSO can be concluded. e GA performs at the lowest rise time of 7 ms, whereas GA needs 16 ms in converging to steady state. However, for PSO algorithm, rise time is 7.2 ms which is close to the GA algorithm while the time to go to the steady state is about 10 ms which is less than GA. e PSO, therefore, provides most suitable algorithm in controlling

Conclusion
In this paper, the four-phase interleaved boost converter circuit is controlled by the PI controller. In order to tune the gains of the PI controller, the PSO, GA, and TS and metaheuristic optimizations, are applied. In testing the control system, the response of the four-phase interleaved boost converter obtained by PSO has the rise time and setting time faster than the GA and TS methods. Additionally, it is found that the tracing and controlling response result of output voltage is extremely satisfactory when load condition is constant and while changing the load. It can be concluded that the four-phase interleaved boost converter circuit using the PI controller tuned gains by PSO is greatly effective for regulating the voltage in a real system.

Data Availability
No data were used to support this study.

Conflicts of Interest
e authors declare that they have no conflicts of interest.