Improved PID controller design for an unstable second order plus time delay non-minimum phase systems

Abstract

Principally the fundamental limitations for achieving better control performance is caused due to the existence of positive zeros. This study proposes a method to stabilize the unstable non-minimum phase Second Order Plus Time Delay (SOPTD) process. It adopts the Taylor series expansion to produce the equal order of numerator and denominator for the closed loop transfer function. The coefficient of corresponding powers of s, s2and s3in numerators are equated to α, β, γ times of the denominator and solved for PID controller setting using multi-objective optimization problems. The stability of the controller is then analysed by minimizing the Integral Time weighted Absolute Error (ITAE) and maximum sensitivity function using MATLAB solvers. The observations from various simulation studies clearly suggests that the proposed method provides significant superior responses when compared with the methods reported.

Keywords

• Unstable systems
• Non-minimum phase system
• Robustness
• PID controller