Optimizing the PID controller for slow varying set point

Abstract

This paper presents the considerations for the design of a closed loop controller application for an electric heater, which is normally characterized by long rise and settling times. The control requirements for these types of systems often include tracking a desired temperature profile, with dynamically changes Set Point, which varies at a rate similar or slower to the process time constant. The temperature profile, varies at a significantly slower rate than the natural time constant of the controlled process. Two different PID tuning methods were considered and analyzed for the task described above. First, the PID controller was designed based on Internal Model Control (IMC) approach and derived from the process model estimated from the system step response. Secondly, optimization algorithms were applied to estimate the PID parameters and obtain the desired Set Point (SP) step response directly [6]. IMC based PID controller is an effective and simple method for designing a closed loop controller, that can be apply for variety types of industrial processes. However, IMC is strongly dependent on the controlled process model, since it is based on its inverse transfer function, an accurate system model is required in order to ensure the desired closed loop performance. The performance of the resulting IMC-PID parameters were calculated and tested in a series of simulations as described in following section. It was tested for tracking both step response and a slow ramp profile. Although simulation results showed good transient respond for SP step change, the initial delay settling time and tracking error were found unacceptably long when applied to track a slowly varying set point profile. Since the control requirements in our application are strict and call for a fast response as well as convergence rate and very close tracking, this controller was determined to be inadequate for the task. In order to overcome this problem, we propose to apply the optimization approach directly to slow ramp profile tracking. Simulation results show that this approach allows achieving significantly shorter delay and settling time and almost completely eliminating the tracking error. These results are validated in real furnace test trials. These results lead to the conclusion that regular IMC-PID tuning and optimization procedures designed for step respond, are not suitable for tracking slow ramp. Consequently, the controller design procedure must take the required process profile into careful consideration.