Designing of an updated MRAC with PD Feedback for Marginally Stable Second-order process with Dead Time

Abstract

The performance of standard PID controller is unsatisfactory for processes that vary over time. In those instances adaptive controllers can adjust the control behavior by adjusting the process dynamics and unwanted load changes. The required process performance criteria for the process are given as a reference model in the model reference adaptive control (MRAC). The adaptation algorithm modifies the control outcome depending on the difference between the outcome of the reference model and actual process with a fixed adaptation gain ($\lambda$). This paper focuses on the various MRAC technique for marginally stable second-order process with dead time. The first one is based on the MIT rule, the second one is based on the Lyapunov stability and the third is the modified MRAC method. In third method, proportional derivative (PD) feedback is connected to the standard MRAC model and the updated controller is called as MRAC-PD. The modified controller assure better response compared to other method. This controller provides better set point tracking with less oscillation and lower oscillations during unfavorable loading changes. This fact is also confirmed by using various performance indexes like integral absolute error (IAE), integral time absolute error (ITAE) and integral square error (ISE) under closed loop operation. Using Simulink, the methods are showcased.