Design and analysis of computer experiments using polynomial regression and Latin hypercube sampling in optimal design of PID controller

Abstract

Computational complexity and time-consuming iteration of simulation for tuning of Proportional-Integral-Derivative (PID) controller is a common drawback in many types of existing methods. This paper aims to propose a new method for achieving an optimal design for PID gains parameters with the least number of simulation runs. To achieve this purpose, we combine polynomial regression and Latin Hypercube Sampling (LHS) in order to Design and Analyze of Computer Experiments (DACE). In this method, the LHS is performed three times to design the associated sample points for different usage that includes training sample points to fit polynomial regression as a common surrogate model; validating sample points to scale standardized residuals; grid search sample points for investigating optimal point over whole design space. To show the flexibility and applicability of the proposed method, we serve a numerical case in the tuning of PID controller for linear speed control of Direct Current (DC) motor. Four different polynomial regression fit input/output (I/O) data over separately four model’s performances that includes Integral-Square-Error (ISE), Integral-Absolute-error (IAE), Integral-Time-Square-Error (ITSE), and Integral-Time-Absolute-Error (ITAE). Comparison of the result with two existing approaches such as traditional Zeigler-Nichols method and Taguchi-Gray Relational Analysis (Taguchi-GRA) confirms the reliability and superiority of the proposed method.