Optimization of PID Controller for Brushless DC Motor by using Bio-inspired Algorithms

: This study presents the use and comparison of various bio-inspired algorithms for optimizing the response of a PID controller for a Brushless DC Motor in contrast to the conventional methods of tuning. For the optimization of the PID controllers Genetic Algorithm, Multi-objective Genetic Algorithm and Simulated Annealing have been used. PID controller tuning with soft-computing algorithms comprises of obtaining the best possible outcome for the three PID parameters for improving the steady state characteristics and performance indices like overshoot percentage, rise time and settling time. For the calculation and simulation of the results the Brushless DC Motor model, Maxon EC 45 flat ф 45 mm with Hall Sensors Motor has been used. The results obtained the optimization using Genetic Algorithms, Multi-objective Genetic Algorithm and Simulated Annealing is compared with the ones derived from the Ziegler-Nichols method and the MATLAB SISO Tool. And it is observed that comparatively better results are obtained by optimization using Simulated Annealing offering better steady state response.


INTRODUCTION
The generic dc motors have high efficiency and have a high starting torque versus falling speed characteristics, which helps to counter the sudden rise in load and thus find their application in industries since ages (Katal et al., 2012).Since dc motors suffer from the deficiencies like:  The lack of periodic maintenance  Mechanical wear-outs  Acoustic noise  Sparkling  Brushes effect, etc., so, the current focus has adapted the development of brushless direct current models The Brushless Direct Current (BLDC) motors are typically dc voltage driven permanent synchronous motors and are gaining grounds in aeronautics, medicine, consumer and industrial automation applications.The BLDC motors have better:  Speed versus torque characteristics  High efficiency  High dynamic response  Noiseless operation  Low maintenance and many more (Padmaraja, 2003;Krause et al., 2002) and the best advantage in terms of higher ratio of torque obtained to the size of motor Proportional, Integral and Derivative-PID controllers are playing an imperative role in the industrial control applications.Because of their simplicity and wide acceptability, they are still the best solutions for the industrial control processes (Åström et al., 2001).Modern industrial controls are often required to regulate the closed-loop response of a system and PID controllers account for the 90% of the total controllers used in the industrial automation.The simple block level representation of the PID controller based system can be obtained as in Fig. 1.
The general equation for a PID controller for the above figure can be given as Norman (2003): = The difference between the desired output and output obtained In this study, the optimization of the PID controller gains has been carried out using Genetic Algorithms (GA), Multi-Objective Genetic Algorithm (MOGA) and Simulated Annealing (SA) in contrast to the Ziegler-Nichols (ZN) method and the automated tuning provided in MATLAB viz.SISO Tool.Then, these gain parameters can be optimally tuned with respect to the objective function, stated as "Sum of the integral of the squared error and the squared controller output deviated from its steady-state" (Goodwin et al., 2001).
According to the results obtained in this paper, considerably better results have been obtained in the case of the Simulated Annealing (SA) when compared to those obtained by Genetic Algorithm, Multiobjective Genetic Algorithm, Ziegler-Nichols method and the MATLAB SISO Tool in respective the step response of the system.

Mathematical model of brushless DC motor:
In this study the model of a BLDC motor has been considered, unlike the dc motor, the commutation of the BLDC can only be done by electronic control (Padmaraja, 2003).The operation of BLDC motor can be realized in many modes (phases), generally 3 phases.The main advantage of 3-Phase is better efficiency and quiet low torque and has best precision in control (Texas Instruments).
In this study, the use of Maxon EC flat ф 45 mm, brushless, 30 Watt motor with Hall Sensors has been used.The schematic illustration of the considered system is shown in Fig. 2. Using Kirchhoff's Voltage Law (KVL), the following equation is obtained: where, V s = The DC Source voltage i = Armature current Similarly while considering the mechanical properties, Newton's second law of motion gives the relative dependence of torque of the system as the product of the inertial load, J and the rate of angular velocity, ω m , as: where, T e = Electric torque k f = Friction constant J = Rotor inertia ω n = The angular velocity T L = The supposed mechanical load      3).MATLAB along with the optimization using the various bio-inspired algorithms like Genetic Algorithm, Multi-objective Genetic Algorithm and Simulated Annealing.The value of parameters obtained using Ziegler-Nichols rules (Ziegler and Nichols, 1942) were used in the formation of the boundary limits for the intervals for the design parameters in soft-computing algorithms, to control the controller by minimizing the error and hence the determination of the optimum parameters for the plant.
The computation of the PID parameters is done by the Ziegler-Nichols rules, SISO Design Tool, Genetic Algorithms, Multi-objective Genetic Algorithm and Simulated Annealing and their closed loop step responses are shown in Fig. 4 to 9. Figure 11 shows the comparative response of all the controllers over a single plot and Fig. 12 shows the comparative values of the various steady-state parameters.Table 7 shows the numeric comparison of the results of various steadystate parameters.From Table 7 and Fig. 11 and 12, it's clearly evident that Simulated Annealing solutions present zero oscillatory response and reduced rise and settling times in contrast to the Ziegler-Nichols, SISO, Genetic Algorithm and Multi-objective Genetic Algorithm.Concluding, Simulated Annealing offers superior results in terms of system performance and controller output for the tuning of PID controllers.

CONCLUSION
The use of Simulated Annealing for optimizing the PID controller parameters as presented in this study offers advantages of decreased overshoot percentage, rise and settling times for the Maxon EC flat ф45 mm, brushless, 30 Watt motor.Results when compared with the other tuning mythologies as presented in this study, the Simulated Annealing has proved superior in achieving the steady-state response and performance indices.

Fig. 1 :
Fig. 1: Block diagram of a PID control based system with unity feedback

Fig
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Fig. 8: (a) A of th