Title : Feasible Performance Evaluations of Digitally-Controlled Auxiliary Resonant Commutation Snubber-Assisted Three Phase Vo
Optimization of Controller Parameters
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- Bu səhifədəki naviqasiya:
- Simulation And Performance Analysis
- 5. Artificial bee colony algorithm (ABCA)
- Optimization Procedure Of ABC Algorithm
- 6. Experimental Results
- 7. Results and Discussions
4.1Optimization of Controller Parameters The steps that are used for optimizing the PID controller parameters are,
Let  This is done in order to record the best position for each bacteria which yields a lower value of ��. Find the position and velocity of each bacterium and update the position of each bacterium by performing swim and tumble. The position co-ordinates of each bacterium give the PID controller parameters.
Tumble: Generate a random vector  and  is the co-ordinate of the vector which is random number in the range [-1, 1] where . Then move (tumble) the bacterium using equation (2). The value of equation (2) which represents the velocity of each bacterium is changed for easy convergence. Then compute the objective function value which is the error for these co-ordinates of the vector. This gives the new .
Swim:  , then let , take another step in the same direction and compute the new. This swim makes the bacteria to take one step and to fetch a new value of ��. Here represents the local best position of each bacterium.
Compute the best (lower) error obtained
The PID controller parameters are being optimized using the BFOA algorithm. The variables used in BFOA are assigned the values given below. It is then simulated in MatLab environment.
By applying BFOA for optimization of PID control parameters Kp, Ki and Kd are obtained as Kp =10.0967, Ki=4.7640and Kd=13.2698. The simulation results of the controller with these controller parameters are shown. 
Fig. 8 Output response of the BFOA tuned PID controlled Buck Converter  Fig. 9 BFOA Error Plot
Figure 8 shows the output response of the PID controlled Buck Converter which is optimized using BFOA. The output response has a peak overshoot of 1.62V which is 13.5% of its final steady state value and settles at 11.328 μs. Figure 9 shows the ISE, IAE and ITAE error plot. It can be inferred that the errors are minimized very shortly. 
Fig. 10 Dynamic response of the BFOA-PID controlled Buck Converter for a step input change from 24V to 18V Figure 10 and Figure 11 show the dynamic response of the BFOA – PID controller for a dc-dc converter while subjecting it to a line voltage change from 24V to 18 V and 18V to 24V respectively. It can be observed that the output settles to the steady state value within 5μs.
Fig. 11 Dynamic response of the BFOA-PID controlled Buck Converter for a step input change from 18V to 24V 
Fig.12 Output response of a BFOA-PID controlled Buck Converter for a load change from 6Ω to 25Ω Figure 12 and Figure 13 shows how the BFOA-PID controlled Buck Converter operates, when the load change from 6Ω to 25 Ω and from 25Ω to 6Ω is applied suddenly at 30μs. The performance of the converter in these transient conditions shows that it regains its normal working status very shortly which demonstrates its robustness to load disturbances.
Fig.13 Output response of a BFOA-PID controlled Buck Converter for a load change from 25Ω to 6Ω 5. Artificial bee colony algorithm (ABCA) A real honey bee colony is one of the natural societies with the most specialized social divisions. A colony of honey bees are capable of performing complex tasks such as, optimizing multi-objective problems using relatively simple rules of individual bees’ behaviour. The Artificial Bee Colony Algorithm introduced by Pham et. al. [27] and further developed by Karboga and Basturk [28] in 2005 is a population-based stochastic optimization technique which is proved to be very robust and is well adapted to the optimization of nonlinear functions in multidimensional space.
The ABC algorithm simulates the intelligent foraging behaviour of a swarm of honey bees. It combines local search methods, carried out by employed and onlooker bees with global search methods, managed by onlookers and scouts, attempting to balance both the exploration and exploitation processes. In this ABC algorithm, a part of the honey bee population consists of employed bees and the remaining part consists of onlooker bees. For each food source, an employer bee is being recruited. The Employed Bee stays on a food source and provides the neighborhood of the source in its memory. The employer bee whose food source has been exhausted becomes a scout. The position of the food source represents a possible solution to the optimization problem. The nectar amount of the food source represents the quality of the food source, which is actually the fitness of the associated solution of the optimization problem. Onlooker bees are recruited to that food source depending on the quality of the food source which is being done by a probability based greedy selection process. If the nectar amount (fitness) of that food source (possible solution) increases, then the probability value of that food source being preferred by the onlookers also increases. Step 1: Initialization The size of the bee colony NP (employed bees + onlooker bees); the number of food sources (FS) (possible solutions); the maximum number of trials made by its employed bees (limit); the maximum number of cycles for foraging which is the stopping criteria (maxcycle). The objective function is the cost function which is to be optimized. The number of parameters of the problem (D) to be optimized is also initialized. The upper bounds and lower bounds of the parameters are given as
The algorithm can be run many times in order to check its robustness. All the food sources are initialized. Step 2: Selection of Objective Function A food source is randomly selected and it’s objective value is found out. Then, the fitness of that objective value is calculated. The food source which produces the minimum objective value is memorized. This cycle is repeated until the stopping criterion is met. At the end of this step, the food source which produces the minimum objective value is considered to be the best food source and its objective vale is assigned as the global minimum. The food sources which produce this global minimum are considered as the global parameters. In this PID controller optimization problem in which the ABC algorithm has been applied, the food sources refers to the various values that can be assigned for the PID controller parameters (KP, Ki and Kd), the objective function refers to the minimization of errors and the objective values refers to the error values. Step 3: Employed Bee Phase The number of employed bees NE is found out using the formula  (20)
Where Step 4: Calculate Probabilities A food source is chosen with a probability which is proportional to its quality. Probability values can be calculated by using the fitness values and normalizing it by dividing with the maximum fitness value.  (21)
Step 4: Onlooker Bee Phase Onlookers are assigned to every food source in order to exploit the neighbourhood of the food sources according to the probability calculated in equation (5.4). Hence, the number of onlookers Where These onlooker bees also exploit the neighbourhood of their own food source as given by equation (20). They follow the same greedy selection procedure as that followed by the employed bees and the trial is made for Step 5: Scout Bee Phase For some food sources, the employed bees and the onlooker bees may not be able to find out the optimum position, even though the trial counter exceeds the ‘limit’ value. In such case, those bees become scout bees and enter into the Scout Bee Phase. In this phase, one scout is allowed to occur in one cycle. The Scout bee carries out an exploration step to discover new parameter values with a new optimized objective value. This exploration is carried out based on the equation (23).
Where The steps (2) to (6) are repeated until the stopping criterion is met.
The ABC algorithm is used for optimizing the controller parameters of the PID controller of a Buck Converter. The values assigned for the control parameters of the ABC algorithm are:
By applying ABCA, the PID control parameters are optimized and the control parameters Kp, Ki and Kd are obtained as Kp=79.2547, Ki=1.7399 and Kd=35.8917. The MatLab simulation results of the controller with these controller parameters are shown. 
Fig. 14 Output response of the ABCA tuned PID controlled Buck Converter The output voltage settles in 1.9x10 -6s with negligible overshoot. This is clear from Figure 14.
Fig. 15 ABCA error plot Figure 15 shows the ISE, IAE and ITAE error plot. It can be inferred that the errors are minimized very shortly when compared with the BFO algorithm.
Fig. 16 Dynamic response of the ABCA tuned PID controlled Buck Converter for a step input change from 24V to 18V Figures 16 and 17 shows the dynamic response of the ABCA tuned PID controlled Buck converter for a step input change from 24V to 18V and from 18V to 24V respectively. It can be inferred that the controller output takes about 0.23μs to settle at its reference value. 
Fig. 17 Dynamic response of the ABCA tuned PID controlled Buck Converter for a step input change from 18V to 24V 
Fig. 18 Dynamic response of ABCA tuned PID controlled Buck Converter for a load change from 25Ω to 6Ω  Fig.19 Dynamic response of ABCA tuned PID controlled Buck Converter for a load change from 6Ω to 25Ω
Figure 18 and Figure 19 shows the dynamic response of an ABCA tuned PID controlled Buck Converter for a step load change from 25Ω to 6Ω and 6Ω to 25Ω at 40μs. It can be inferred that the controller regains its steady state within 0.4μs and 0.38μs respectively thus proving its effectiveness in overcoming the load disturbances. The Kp, Ki and Kd values for the various PID controller designed are given in Table 1. TABLE 1
PID controller parameter value of various controllers
6. Experimental Results The PID control algorithm was implemented in a PIC microcontroller to drive the actual circuit of the Buck converter with Experimental investigations have been performed for various input voltages and load conditions on the Buck converter with a PID controller implemented using the PIC microcontroller. The results are given below. The input voltage is given a step change from 24 to 15 volts and the performance of the Buck converter is analysed. The desired output voltage of the Buck converter is set to 12V. Figure 20 shows the output voltage waveform of the converter when the input voltage is varied from 24V to 15V. The peak overshoot voltage at the time of input voltage variation is 4.16% and the settling time is 0.82μs. Figure 21 shows the output voltage waveform of the converter for a step input change from 15V to 22V. The peak overshoot voltage at the time of input voltage variation is 9% and the settling time is 0.45μs. 
Fig. 20 Output voltage response of ABCA optimized PID controlled Buck Converter for step input change from 24 V to 15V 
Fig. 21 Output voltage response of ABCA optimized PID controlled Buck Converter for step input change from 15V to 22V The Buck converter is also analyzed subjecting it to a step load variation. Figure 22 shows the output voltage waveform for a step load variation from 6Ω to 25Ω. It is found that the controller regains the constant output voltage of 12 volts within 0.5μs. Figure 23 shows the output voltage waveform for a step load variation from 25Ω to 6Ω. It is found that the controller acts very effectively and it settles at its steady state value within 0.48μs.
Fig. 22 Output voltage response of ABCA tuned PID controller for a Buck Converter for a step load change from 6Ω to 25Ω 
Fig. 23 Output voltage waveform of ABCA tuned PID controlled Buck Converter for a step load change from 25Ω to 6Ω 7. Results and Discussions Designing a control technique suitable for a dc-dc non-linear dynamical Buck converter which is now finding increasing applications in our day-to-day life is considered to be the main objective in this paper. The controller designed should cope with their intrinsic non-linearity and wide input voltage and load variations ensuring stability in any operating condition while providing fast transient response. The controller may be of either linear or non-linear type. The traditional linear PID controller is analyzed subjecting it to sudden line and load disturbances. It can be inferred that the PID controlled Buck converter when operated in CCM settles at 0.46ms with a peak overshoot of 6.525V which is about 54.375% of it’s reference value. But, the non-linear sliding mode controller designed for the same Buck converter as given in literature [2], shows that the controller settles at 0.184ms which is 3.29 times lesser than the former case and produces a maximum peak overshoot of 5.253V which is also less than the former case. But, it is evident that the design procedure is complicated and cumbersome. Hence, designing a controller with simple design procedure and which produces a much better output than the sliding mode controller is considered to be the main task. It will be better if the PID controller’s performance can be improved as the PID controller has become an inevitable control algorithm in industries because of its simple structure and control. The PID controller’s performance is decided by the proper selection of the control parameters. In order to improve the performance of the PID controller, nature inspired optimization algorithms such as BFOA and ABCA are used which are described elaborately in this paper. It is found that while tuning the PID controller parameters with these techniques, the performance of the converter improves considerably. Table 2
Performance parameters of various controllers
Table 3
Load and Line regulation property of various controllers
Performance evaluation comparisons of the output response produced by the traditional PID controller, the PID based Sliding Mode Controller [2], the BFOA tuned PID controller and the ABCA tuned PID controller are made. It can be noticed that the PID controller’s output settles at 463.5μs, the PID based SMC’s output settles at 184.4μs, the BFOA tuned PID controller’s output settles at 11.328μs and that of the ABCA tuned PID controller settles at 1.05μs. The settling time of this ABCA tuned PID controller is much less than that of the PID based Sliding Mode Controller. Moreover, in the ABCA tuned PID controller the peak overshoot is eliminated. Thus, it is evident that the PID controller when tuned using ABCA, its effectiveness is much improved than that of the non-linear PID based SMC. So, it can be concluded that the ABCA tuned PID controller is more efficient than that of the other controllers. These performance parameters are listed in Table 2. These controllers designed for Buck converter with resistive load is also checked for their robustness subjecting them to various line and load disturbances. The time taken for the controllers to settle down at its steady state value is given in table 3. Table 4
Comparison of simulation results with practical values
The simulation results of the ABCA tuned PID controlled Buck converter is compared with the practical results and is tabulated which is given in Table 4. This tabulation proves that the prototype works well and produces nearly the same results as that produced by simulation. Yüklə 120 Kb. Dostları ilə paylaş:
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. Then compute
, where 
represents the difference in error achieved between the current and the previous chemotactic steps. If
, where 
then end the chemotactic operations. The bacterium with the minimum cost (error) gives the optimal PID controller parameters. Otherwise goto step 4.
, then goto step 3.
and dispersing each bacterium in a new location for maintaining the number of bacteria constant. This process helps the dispersed bacterium to take entirely new parameter values. If 
then goto step 2.
(18)
(19)
, where 
is a random number between 0 and 1. This number decides the times for which this loop is to be executed. One of the parameters to be optimized is chosen randomly for further optimization. This randomly chosen parameter is used for producing a mutant parameter. The mutant parameter is found by using the formula
and
, 
represents the new mutant parameter value that the employed bee finds at the search step (n +1), 
represents the optimum value of the parameter that the employed bee in the same food source finds at the search step
, 
is the value of the parameter which is selected randomly, ‘D’ is the number of parameters to be optimized and 
is the number of food sources. Thus, the employed bees in every food source exploit the neighbourhood of their own food sources. If the newly generated parameter 
in every food source is expressed as
(22)
, which is a random number varying between 0 and 1. 
times with the condition that the randomly chosen procedure is less the probability
. At the end of this phase, the best parameter value which produces the minimum objective value is memorized. Once again, this objective value is compared with the global minimum obtained step 1, to check if this memorized objective value is less than that of the global minimum, i.e., if
, then
. 
are considered as the Global Parameters (
).
(23)
= upper bound of the parameters, 
= lower bound of the parameters, 
= number of parameters in the search space, 
= new value of the parameter.
. These values are obtained by optimizing the controller using ABC algorithm. The Buck converter parameters of the prototype are chosen as L =35 μH, C =150 μF. 