Controller considerations for attenuating noise in process variables in presence of uncertainties in plant parameters

Abstract

This paper analyzes the effect of uncertainties on noise amplification in the internal model control (IMC) and classical control design technique. It is observed that IMC based on integral absolute error (IAE) design criteria (IMC-IAE) boosts noise in the process variables, system output as well as in control input for certain class of systems. Moreover, the resulting control system becomes highly sensitive at high frequency with uncertainty in plant parameters which further boosts noise in process variables. Integral square error (ISE) based IMC (IMC-ISE) is, however, free from the issues of sensitivity and noise amplification at high frequencies and not analyzed in this paper. This issue also exists in well known classical controllers such as PID controller, lead, lag, lead-lag compensators, etc. The solution to this problem is to choose the controller such that the open loop transfer function (OLTF) and hence the closed loop transfer function (CLTF) are strictly proper, and a formal proof to this effect is laid down in this paper. Further, simulation study is carried out to show the impact of noise and the effect of plant uncertainty in output and control input for IMC-IAE control system. The proposed theory is validated experimentally on a DC servo system by comparing noise power of the control input for IMC-IAE and PID controllers.