Showing papers by "Derek P. Atherton published in 2006"

A refinement procedure for PID controllers

Abstract: Proportional-Integral-Derivative (PID) controllers are still extensively used in industrial systems. In the literature, many publications can be found considering PID controller design for processes with resonances, integrators and unstable transfer functions. However, due to structural limitations of PID controllers, generally, a good closed-loop performance cannot be achieved with a PID, for controlling the aforementioned processes, and usually a step response with a high overshoot and oscillation is obtained. PI-PD controllers provide very satisfactory closed-loop performances in the case of controlling processes with resonances, integrators and unstable transfer functions. This paper introduces a simple approach to get parameters of a PI-PD controller from parameters of a PID controller so that a good closed-loop system performance can be realized. Extensive simulation examples are given to illustrate the value of the approach proposed.

Design of stabilizing PI and PID controllers

Abstract: In this paper, a new method for the calculation of all stabilizing PI controllers is given. The proposed method is based on plotting the stability boundary locus in the (kp , ki )-plane and then computing the stabilizing values of the parameters of a PI controller for a given control system. The technique presented does not require sweeping over the parameters and also does not need linear programming to solve a set of inequalities. Thus, it offers several important advantages over existing results obtained in this direction. The proposed method is also applied for computation of all stabilizing PI controllers for multi-input multi-output (MIMO) control systems with consideration given to two-input two-output (TITO) systems using decoupling technique. Beyond stabilization, the method is used to compute all stabilizing PI controllers which achieve user-specified gain and phase margins. Furthermore, the method is extended to tackle 3-parameters PID controllers. The limiting values of PID controller paramete...

Relay autotuning : An overview and alternative approach

Abstract: This paper discusses the use of relay-produced limit cycles for selecting the parameters of fixed controllers, with particular reference to the proportional−integral−derivative (PID) controller. This work shows how the current ideas relate to the early work of Ziegler and Nichols, particularly their loop cycling test. The evaluation of limit cycles in relay feedback systems is discussed, and details of their possibilities for determining parameters of an assumed plant transfer function or the value of the plant critical point are given. To conclude, it is shown how the approximate value of points on the plant frequency response locus can be determined from using the relay in parallel with the controller, which can be done without opening the control loop.

Describing Function Method

Abstract: This section is primarily concerned with developing the background of the describing function for a single sinusoidal signal and showing how it can be used in the analysis and possibly the design of a nonlinear feedback system. After the definition of the describing function, its value is obtained for several specific nonlinear characteristics and then it is shown how the information can be used to explore the possibility of limit cycles in a nonlinear feedback loop. It is shown how the stability of any limit cycles may be ascertained and two examples of use of the DF in control systems problems are given. Uses of the DF for evaluating the closed loop frequency response and for designing compensators to eliminate limit cycles are discussed. The latter part of the presentation discusses describing functions for other signals, including those consisting of more than one component, and their possible uses in studying some aspects of feedback loop analysis and design.

State feedback design to obtain standard form responses

Abstract: The paper presents a procedure for designing state feedback controllers to achieve a standard form closed loop system step response. Apart from addressing directly the step response in the design it also allows consideration of time scaling and control signal magnitude, important aspects not often considered in other approaches. The method can be used for a forward loop transfer function with one or no zero. Thus if a PI controller is used the plant transfer function must have no zero.

Relay autotuning of PID controllers

Abstract: This section is concerned with the relay autotuning method for setting the parameters of a fixed form controller, usually a PID controller. It is first explained how the method is an extension of a concept first discussed by Ziegler and Nichols for setting PID controller parameters based on an estimate of the gain margin, or process critical point. The theoretical approaches to analyzing the limit cycle obtained in an autotuning experiment are explained. The merits and some problems of using the describing function method of analysis for estimating the critical point are discussed. Setting of the PID controller parameters based on the critical point information is then covered and an example given. Finally a few further points are mentioned regarding practical aspects of PID control

Basic Nonlinear Control Systems

Abstract: This section is written to introduce the reader to nonlinearity and its effect in control systems, and also to 'set the stage' for the subsequent articles. Nonlinearity is first defined and then some of the physical effects which cause nonlinear behaviour are discussed. This is followed by some comments on the stability of nonlinear systems, the existence of limit cycles, and the unique behavioral aspects which nonlinear feedback systems may possess. Finally a few brief comments are made on designing controllers for nonlinear systems.

Simple analytical rules for PI-PD controllers to tune integrating and unstable plants

Abstract: Proportional-Integral-Derivative (PID) controllers are still extensively used in industrial systems. In the literature, many publications can be found considering PID controller design for processes with integrators and unstable transfer functions. However, due to structural limitations of PID controllers, generally, good closed loop performance cannot be achieved with a PID for controlling aforementioned processes and usually a step response with a high overshoot and oscillation is obtained. On the other hand, PI-PD controllers are proved to give very satisfactory closed loop performances for these processes. Hence, the paper introduces a simple approach to obtain parameters of a PI-PD controller for the control of integrating and unstable processes. Simulation examples are given to illustrate the value of the approach proposed.