Evaluation of Arm Processor-based Bionic Intelligent Controller for a Buck-boost Converter

This study focuses on performance-comparison of different tuning methods for a PI controller applied to a buck-boost converter. Comparison between the controllers is made by analysis of design methodology implementation issues and empirically measured performance. Design of PI controller is based on frequency response of the converter. The optimization of PI controller is based on ant colony algorithm. Experimental results show that, tuning the PI controller using ACO algorithm gave better performance than the conventional algorithm. This is mainly due to the fact ACO is capable of reducing the overshoot without oscillation.


INTRODUCTION
DC-DC converters are been widely used in computer hardware and many industrial applications.They are also the dc-dc converters are of two types a buck converter, which decreases the voltage level from an input dc source and a boost converter which increases the voltage level from an input dc source.Erickson (1991) has given that a buck-boost converter is a combination of buck and boost converter which can decrease or increase the voltage level from an input dc source.The buck-boost converter has a Right Half-Plane (RHP) zero and hence is also called Non Minimum Phase (NMP) system.Deriving a control system for a non-minimum phase system is more difficult than that for a minimum phase system as discussed in Siotine and Li (1991) and Arulselvi et al. (2004).It is necessary, that designing a controller for a non-minimum phase system requires avoiding the cancellation of unstable pole/zero to guarantee the internal stability of the closed-loop system.Conventionally, PI (or PID) control logic is proposed for the buck-boost converter using root-locus or poleplacement methods as discussed by Alvarez-Ramirez et al. (2001), Guo et al. (2002) and Tsang et al. (2008).These controllers are popular due to their simple structure, and they can usually provide a good closed loop response characteristic.However, these methods fail to determine suitable PI (or PID) control gains when the system parameters are uncertain.
Proportional-Integral-Derivative (PID) controllers are frequently used in the control process to regulate the time domain behavior of different types of dynamic plants.Despite its simple structure, it seems so hard to find a proper PID controller as discussed by Oonsivilai and Pao-La-Or (2008).Various methods have been proposed to enable us to tune these parameters that will handle this issue.
Ziegler-Nichols tuning method is the most standard one used.However it is often difficult to find optimal PID parameters with these methods.Therefore, many optimization techniques like fuzzy logic (Tzafestas and Papanikolopoulos, 1990;Visioli, 2001), neural network as discussed by Cao et al. (2007), neural-fuzzy logic as discussed by Seng et al. (1999), immune algorithm as discussed by Kim (2001), simulated annealing as discussed by Zhou and Birdwell (1994), and pattern recognition are developed to tune the PID controllers.Several optimum tuning PID techniques based on many random search techniques such as Genetic Algorithm (GA) as discussed by Wang and Kwok (1994) and Mitsukura et al. (1999), Particle Swarm Optimization (PSO) as discussed by Selvan et al. (2003) and Ant Colony Optimization (ACO) are also used as given in Hsiao et al. (2004).
Researchers have acknowledged the capacity of ACO to search for and locate an optimum solution.This method is mainly inspired by the fact that ants can find the shortest route between their nest and a food source.Ant Colony Optimization as discussed by Dorigo et al. (1999) and Dorigo and Caro (1999) is yet another metaheuristic approach for solving combinatorial optimization problems.A few illustrations of such problems can be found with the Travelling Salesman Problem (TSP) as discussed by Reinelt (1994), quadratic assignment problem as discussed by Stützle and Dorigo (1999), graph coloring problems as discussed by Costa and Hertz (1997), hydroelectric generation scheduling problems as discussed by Huang (2001), vehicle routing in Gambardella et al. (1999).
PI and PID controller have been widely used in DC-DC converters, mainly due to their simplicity.This paper focuses on optimizing a PI controller for Buck-Boost Converter using Ant Colony Algorithm (ACA).

Buck boost converter:
A Buck-Boost converter is a step-down and step-up DC-DC converter.The output of Buck-Boost converter's output is regulated based on the duty cycle of the Pulse Width Modulation (PWM) input at fixed frequency.Whenever the duty cycle (dc) is less than 0.5, the output voltage of the converter will be lower than the input voltage.However, when the duty cycle is above 0.5 the output voltage of the converter is higher than the input voltage.A Buck-Boost converter's basic power stage is shown in Fig. 1. Figure 1 VI is input voltage source, V O is the output voltage, Sw is switching component, C is the capacitance, L is inductance, D is diode and R is the load resistance.
The converter contains two independence ac inputs, the control ˤ ӂ (s) and line ˰ I (s) and one output, ˰ o (s).
The converter contains two independence ac inputs, the control ˤ ӂ (s) and line ˰ I (s) and one output, ˰ o (s).The control-to-output transfer function (G vd ) is derived from small signal model of the converter as: Plug in numerical values illustrated in Table 1 (2)

CONTROLLER DESIGN FOR BUCK-BOOST CONVERTER PI controller:
In a controller it is necessary to compare the output voltage to a reference value Vref (sometimes called a demand voltage) and then take appropriate  remedial action to ensure that Vout = Vref.Usually, this is achieved by generating an error signal e = Vref-Vout which is minimized by the controller (sometimes referred to as a compensator) which then manipulates in such a manner so as to adjust Vout by varying the duty cycle (dc).
Referring to Fig. 2, the output voltage is compared to a reference producing an error signal, (e).The error signal is individually applied to each term of the compensator after which they are combined forming the duty cycle input command to the buck-boost converter.The proportional gain Kp acts as a feed-forward term allowing any changes in the error to be passed to the compensator output without delay.Kp must be carefully chosen because large values tend to induce instabilities in the system response.The integral term Ki is used to reduce the steady-state error at the expense of reducing the dynamic response.
The performance of each prototype controller is evaluated using the ISE (Integral Square Error), IAE (Integral Absolute Error) and ITAE (Integral Time Absolute Error) performance indexes.The ISE index evaluates a controller's performance by assigning it a score based on the error response of the system.Essentially, good performing controllers will have lower ISE scores than poor performing counterparts.To ensure that the phenomenon does not affect the controller's score, the absolute error is squared (which should be a small value in the vicinity of the transient event) which will also reduce its impact.Design of PI controller: The PI controller designed for a buck-boost converter is given in equation.The controllers can be introduced in either feed-back or feed-forward path which will control the steady state error and transient performance.In most of the practical control systems, the input to the controlling device is error.
In case of PI controller, the input to the controlling device is proportional as well as integral of the error function.The order of the system is increased when the system is combined with the controller.The effect of compensation on the system dynamics cannot be visualized easily.The higher the order of the system the more it becomes unstable.
Integral action remains active as long as the error is present.Thus, it makes a steady state error zero so the PI controller is designed based on the frequency domain specification.The controller transfer function is given in Eq. (3): The phase margin ϕ m at is determined from the settling time.Phase and Magnitude response equation is given in ( 4) and ( 5): Solving these two Eq.( 4) and (5) we get the K I and K P value: Ant Colony Optimization (ACO): Ant colony optimization algorithms are especially suited for finding solutions to difficult optimization problems.A colony of artificial ants helps to find good solutions, by using the emergent property of the ants' cooperative interaction.Ant colony algorithms are adaptive and robust in nature due to their similarities with ant.This property can be applied to different optimization problems as well as different versions of the same problem.
The main traits of artificial ants are derived from their natural model.Such borrowed traits include: • Cooperative existence in colonies with other ants • Indirect information transmission by depositing pheromone (stigmergic communication) • Repetitive local moves in a sequence to find the shortest path to a destination point • Applying a stochastic decision policy using local information alone to find the best solution.In order to a particular optimization problem, artificial ants are enriched with additional capabilities which are not present in real ants For a given optimization problem, the best solution is searched by finite sized ant colony.Each ant can find a solution or at least part of the solution to the optimization problem on its own, but the optimal solution can be achieved only when many ants work together.Since the optimal solution can only be achieved through global cooperation of all the ants in a colony, it is a promising result of such cooperation.The ants do not communicate directly while searching for a solution, but they communicate indirectly by adding pheromone to the environment.The ant finds the shortest path for a particular problem from a given starting state by moving through a sequence of neighboring states.It moves based on a nondeterministic local search policy influenced by its own internal state (private information), the pheromone trails and local information encoded in the environment (together public information).Ants use this private and public information to decide when and where to deposit pheromones.The amount of pheromone deposited by an ant is proportional to the quality of the movement made by an ant.It concludes more the pheromone, the better the solution, obtained.Once an ant has found a solution; it dies, that is, it is deleted from the system.
The series controllers are very frequent because of higher order systems.For a continuous system, the transfer function of a PI controller defined in Eq. (3).The design implies the determination of the values of the constants K p and K I , meeting the required performance specifications.
The textbook version of the PI controller in continuous time is: where, e (t) = r (t) -y (t) is the difference between the reference signal r (t) and the output, y (t) of the controlled process.
The PI controller is implemented to improve the dynamic response in addition to reducing or eliminating the steady state error.To characterize the performance of the PI controller systems, performance of the transient response such as rise time (t r ), the Integral Square Error (ISE), Overshoot (O s ), settling time (t s ), Integral Absolute Error (IAE), Integral Time Absolute Error (ITAE), Integral Time Square Error (ITSE) are computed.Tuning the parameters of the PI controllers using the multi objective ant colony optimization is indicated in Fig. 3.
As shown in Fig. 4, the gains K p and K I of the PI controller are generated by the multi objective ACO algorithm for the buck boost converter.The present The population is represented by a 100*2 matrix, where the ant selects the optimum parameters K p and K I of the PI control system by minimizing an objective function L A .The graph (Fig. 4) illustrates the design of PI problem using ant colony algorithm.In this study, each parameter of K p and K I is coded by 100 numbers (nodes), respectively.Therefore, only one node represents the optimum solution values of the parameters K p and K I .
The basic step in applying optimization method is to choose the optimization criteria that are used to evaluate fitness.Since the PI controller has many performance indexes of the transient response, then they can be combined into one objective function composed of the weighted sum of objectives.The objective function must be set: where, F = [f 1 f 2 f 3 f 4 f 5 f 6 f 7 ] T : vector of objective functions, f 1 : setting Time (T s ), f 2 : Overshoot (O S ), f 3 : rise Time (T r ), f 4 : Integral Absolute Error (IAE), f 5 : Integral Square Error (ISE), f 6 : Integral Time Absolute Error (ITAE), Φ = [λ 1 λ 2 λ 3 λ 4 λ 5 λ 6 λ 7 ]: vector of nonnegative weights and f 7 : Integral Time Square Error (ITSE).
The purpose of multi-objective optimization problem is to strike a balance between numerous conflicting objectives.Considering all objectives in these problems, we may find more than one solution that optimizes all the objectives and there is no apparent superiority of any of these solutions over others.We can never have a single-best solution which would be better than the remainder.Therefore, a set of solutions which are better than remainder solutions called the Pareto front is faced.Among the feasible solutions, solutions belonging to the Pareto front are called as non-dominated solutions, while the remaining solutions are called as dominated.As none of the Pareto set solutions were found to be better than the any of the non-dominated solutions, all of them are equally acceptable as long as the objectives are met.
ACO uses a pheromone matrix τ = {τ ij } for the construction of potential good solutions.The initial values of τ are set τ ij = τ 0 for all (i, j), where τ 0 >0.
The probability ˜ (t) of choosing a node j at node i is defined in (9).At each evolution of the algorithm, the ant constructs a complete solution using ( 9), starting at source node: where, η ij representing heuristic functions, constant αdetermine the relative influence of pheromone values where constant-β determine the relative influence of the heuristic values and at a given time, T A : is the path effectuated by the ant A.
The pheromone evaporation is a way to elude unlimited increase of pheromone trails and it allows the forgetfulness of the poor decisions: Where the quantity of pheromone on each path, NA represents number of ants, ρ indicates the evaporation rate.Evaporation rate lies between zero and one (0<ρ≤1).
The following general algorithm can describe the proposed algorithm.

Begin:
Step 1: Initialize randomly potential solutions of the parameters (K i , K p ) by using uniform distribution.
Initialize the heuristic value and the pheromone trail.
Initialize the Pareto set to an empty set.
Step 2: Place the A th ant on the node.
Compute the heuristic value associated in the multi objective L A .Choose the successive node with probability: where, η ij = 1/K j , j = [P, I]: representing heuristic functions, at a given time T A : represents the path effectuated by the ant A. The quantity of pheromone on each path may be defined as: where, L A is the value of the objective function found by the ant A. Till the current iteration, L min is the best optimal solution brought out by the set of the ants.
Step 3: Use pheromone evaporation given by ( 10) to avoid an infinite progression of pheromone trails and allow the forgetfulness of bad choices: where, NA : Number of ants ρ : The evaporation rate 0<ρ≤1 Step 4: Evaluate the obtained solutions according to the different objectives.
Update the Pareto archive with the nondominated ones.
Reduce the size of the archive if necessary.
Step 5: Display the optimum values of the optimization parameters.
Step 6: Globally update the pheromone, according to the optimum solutions calculated at Step 5.

Iterate from
Step 2 until we reach the maximum number of iterations.End

RESULTS AND DISCUSSION
Simulation and experimental results: In this section, the numerical results obtained using the proposed algorithm is presented and discussed.The various of the parameters in ACO are, m = 100 (numbers of ants), α = 0.5, β = 0.5, ρ = 0.5 and maximum generation = 50.The objective function is given in Eq. ( 8): ) min( The objective function here is f 2 : the overshoot to measure the performance of the closed-loop system, f 4 : Integral Time Absolute Error and f 5 : the integral square error f 6 : Integral Absolute error that should be minimized.Therefore the vector of weights is Φ = (0 1 0 1 1 1 0).The closed loop PI controller cascaded with the converter was tuned for the values K P and K i first by using multi objective ant colony algorithm.Hence, the percent maximum overshoots, the settling time, the rise time and the integral of the squared error were computed.
The graphs of the obtained three-dimensional Pareto optimal fronts for the generated problem corresponding to the buck-boost converter shown in Fig. 5.
Figure 6 Report the evaluation of the objective function of the converter.It is observed that the objective function value decreases substantially., K i ) is distributed average value.After several iterations, the multi objective ant colony algorithm generated the best solutions of the PI parameters (K best p , K best i ).After that, each parameter (K distributed randomly and uniformly with an average value which is equal to the value founded in the last generation.Finally, the multi objective ant colony algorithm generated the optimal solutions ( The prototype of Buck-Boost converter tested in the laboratory is shown in Fig. 7.
Figure 8 shows the experimental result of duty cycle varying the line voltage of the converter.Varying line voltage and load it will adjust the duty cycle and make the voltage as stable.
Figure 9 shows the transient response of the buck boost converter during the staring up.During the starting up converter settling time is 2.8 have steady state error.several iterations, the multi objective ant colony algorithm generated the best solutions of the PI After that, each parameter (K best p , K best i ) is distributed randomly and uniformly with an average which is equal to the value founded in the last generation.Finally, the multi objective ant colony algorithm generated the optimal solutions (K opt p , K opt i ).Boost converter tested in shows the experimental result of duty cycle varying the line voltage of the converter.Varying line voltage and load it will adjust the duty cycle and

CONCLUSION
Conventional PI controller and optimized PI controllers were designed and implemented for a Buck Boost converter.The linear PI controller was designed for the converter using frequency response techniques.The conventional PI controller was applied during steady-state to achieve stable steady Optimized PI controller was designed based on ACO.The performance of the controllers was compared based on the experimental results.Experimental results show that fast transient response and stable steady response could be achieved for the buck converters using optimized PI converter.

Figure 9
Figure 9 shows the transient response of the buckstaring up.During the starting up converter settling time is 2.8 µsec and it

Table 1 :
Parameters of buck boost converter