Identification and Control of an Unstable SOPTD system with positive zero

Abstract

The work deals with the identification and control of unstable Second Order plus Time Delay (SOPTD) system with positive zero. Presence of positive zero complicates the performance of the control system dynamics. There are many unstable systems which exhibit the second order plus time delay with positive zero such as drum boiler, distillation column. No work has been reported in the literature on identification of unstable SOPTD process with positive zero. In this work, a subspace based method and an optimization method are proposed to identify an unstable SOPTD model with positive zero followed by the PID controller design which can handle set-point changes and disturbance rejection. The subspace-based method uses input-output measurements to estimate the state space model. This method uses projections of block Hankel matrices followed by a singular value decomposition to determine the order of the system. It offers the key advantages on providing low parameter sensitivity with respect to perturbations for higher order systems. The model parameters are also identified using optimization technique by matching the closed loop responses of the process and the model. In any optimization technique, the initial guess plays an important role for proper convergence. A method is suggested to obtain the initial guess values for process gain, poles, zeros and delay. The parameters identified by subspace based method are compared with that obtained using optimization technique. For the models identified by the above two methods, controllers are designed and implemented. Simulation studies on linear and nonlinear systems are demonstrated to evaluate the performance of the proposed methodologies. The closed loop performances comparison can be made in terms of time integral errors and total variation in input variable. © 2018 Elsevier B.V.