A Simplified Numerical Approach to Feedback Controller Design

Abstract

T here exist several well-established techniques for feedback control design for dynamic systems. The technique employed depends on the structure of the controller, i.e., conventional proportionalintegral-derivative (PID), linear or nonlinear state feedback, and so on.For the control of industrial chemical processes, PID control is widely used, accounting for some 95% of all control loops (Wang and Shao, 1999). Therefore, it is not surprising that much attention has been paid to tuning this type of controller. Luyben (2001) presents a comparison of PID tuning methods for processes possessing varying degrees of dead-time. One of these methods is the classic Ziegler-Nichols tuning method, which determines the controller gain, integral time, and derivative time by using either the system ultimate gain or process reaction curve (Ziegler and Nichols, 1942;Dutton et al., 1997).Other PID design methods include frequency response and root locus, classical approaches to tuning parameter determination (Franklin et al., 1991;Smith and Corripio, 1985). Autotuning algorithms (Wang and Shao, 1999;Friman and Waller, 1997;Luo and Chen, 1998) and trial-and-error tuning by plant personnel are also commonly employed methods for tuning PID controllers.The Ziegler-Nichols process reaction curve, autotuning, and trialand-error approaches, while useful in many circumstances, have the potential disadvantage of introducing transients to the process, risking process upsets and unstable response. Closed-loop autotuning algorithms help to circumvent these potential problems. However, an autotuning feature is not available on many industrial PID controllers, so it is not always a viable alternative.Approaches to feedback control design that are based on state-space methods have gained popularity for chemical process control (Ray, 1989). One class of linear optimal control problem is the linear regulator, in which optimal, time-varying gains are computed which minimize a quadratic performance index. Ray (1989), Sage et al. (1977), and Kirk (1970) discuss solutions to the linear regulator problem, including solution via backward integration of the Riccati equation and by direct numerical techniques that require fi rst-and sometimes second-derivative information. For infi nite time problems, such as the continuous control of a chemical process, the time-varying gains become constant, resulting in constant gain proportional controllers. Integral control may be implemented as well, in order to eliminate steady-state offset (Franklin et al., 1991). Ray (1989) discusses application of optimal control theory to nonlinear systems and associated numerical solution techniques. Non-optimal state-space methods (Franklin et al., 1991) utilize pole placement or comparison with prototype response models such as Bessel functions, Integral of Time Multiplied by Absolute Value of Error (ITAE), or Integral of the Square of the Error (ISE) criteria in order to select appropriate controller gains. * Author to whom correspondence may be addressed. E-mail address: ...