Optimal PID Controller Autotuning Design for MIMO Nonlinear Systems Based on the Adaptive SLP Algorithm
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ISSN:1598-6446 eISSN:2005-4092 http://www.springer.com/12555
Optimal PID Controller Autotuning Design for MIMO Nonlinear Systems Based on the Adaptive SLP Algorithm Jirapun Pongfai, Chrissanthi Angeli, Peng Shi, Xiaojie Su, and Wudhichai Assawinchaichote* Abstract: In this paper, an adaptive swarm learning process (SLP) algorithm for designing the optimal proportional integral and derivative (PID) parameter for a multiple-input multiple-output (MIMO) control system is proposed. The SLP algorithm is proposed to improve the performance and convergence of PID parameter autotuning by applying the swarm algorithm and the learning process. The adaptive SLP algorithm improves the stability, performance and robustness of the traditional SLP algorithm to apply it to a MIMO control system. It can update the online weights of the SLP algorithm caused by the errors in the settling time, rise time and overshoot of the system based on a stable learning rate. The gradient descent is applied to update the weights. The stable learning rate is verified based on the Lyapunov stability theorem. Additionally, simulations are performed to verify the superiority of the algorithm in terms of performance and robustness. Results that compare the adaptive SLP algorithm with the traditional SLP, a neural network (NN), the genetic algorithm (GA),the particle swarm and optimization (PSO) algorithm and the kidney-inspired algorithm (KIA) based on a two-wheel inverted pendulum system are presented. With respect to performance and robustness, the adaptive SLP algorithm provides a better response than the traditional SLP, NN, GA, PSO and KIA. Keywords: Autotuning, inverted pendulum, learning algorithm, multiple-input/multiple-output (MIMO), optimal control, PID controller, swarm algorithm.
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INTRODUCTION
In many industrial applications, proportional integral and derivative (PID) controllers are used extensively to improve the transient of the system because of their simple structure, robustness, high performance and easy maintenance [1–10]. A PID controller is governed by its 3 tunable parameters, i.e., proportional gain (KP ), integral gain (KI ) and derivative gain (KD ), which determine the performance of the PID controller. However, these parameters cannot determine performance by themselves, especially in nonlinear systems. The common procedure used in industry to tune the parameters is matching the parameters with the operating conditions and tuning the parameters for all conditions [5]. However, normal industrial process control is dynamic and thus unpredictable, with unmodeled fallibility and sudden changes in conditions. The pro-
cedure is improperly used because requires a retuning of parameters to achieve the required control. Therefore, in recent decades, artificial intelligence (AI) has been extensively used to overcome the PID tuning problem in nonlinear control systems and improve the control performance via autotuning with, for example, a genetic algorithm (GA) [11, 12], a neural network (NN) [13], fuzzy logic (FL) [14], parti
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