Derek P. Atherton

Linear feedback control : analysis and design with MATLAB

Preface 1. Introduction to feedback control 2. Mathematical models of feedback control systems 3. Analysis of Linear control systems 4. Simulation analysis of nonlinear systems 5. Model based controller design 6. PID controller design 7. Robust control systems design 8. Fractional-order controller - an introduction Appendix. CtrlLAB: a feedback control system analysis and design tool Bibliography Index of MATLAB functions Index.

Brief Obtaining controller parameters for a new Smith predictor using autotuning

The paper extends recent work on a modified Smith predictor strategy, which leads to significant improvements in its regulatory capacities for reference inputs and disturbances. High-order or long dead time stable, integrating and unstable plants are modelled as lower-order plant models with a longer time delay. The controllers are designed so that the delay-free component of the output is tuned to be either a first- or second-order response if there are no modelling errors in the assumed plant transfer function. Plant model transfer functions and the controller parameters are estimated using exact analysis from the peak amplitude and frequency of the process output obtained from a single-relay feedback test. Illustrative examples show the simplicity and superiority of the proposed controller design method over previously published approaches both for the setpoint response and for the load disturbance rejection.

Parameter estimation from relay autotuning with asymmetric limit cycle data

Obtaining the parameters for PID controllers based on limit cycle information for the process in a relay controlled feedback loop has become an accepted practical procedure. Often the only information used is the frequency and amplitude of the limit cycle, which then using the describing function analysis provides estimates for the ultimate gain and frequency of the process. Alternatively, limit cycle measurements may be used to estimate the parameters of an assumed transfer function, usually again using describing function analysis. Both these methods can work well but may lead to problems in cases where the describing function analysis is inaccurate. In this paper, it is shown how the parameters of first and second order plant transfer functions, stable or unstable, with time delay can be found exactly, assuming no measurement errors, from measurements of the parameters of a single asymmetrical limit cycle in a relay controlled feedback loop. Examples are given to compare the approach with results using the describing function method and also to show how good controller design based on a first or second order time delay model can be achieved for plants of higher order.

Maneuvering target tracking using adaptive turn rate models in the interacting multiple model algorithm

This paper presents an interacting multiple model algorithm (IMM) utilizing adaptive turn rate models to track a maneuvering target. The turning rate is calculated at each time step from the velocity and acceleration estimates of the center filter as the magnitude of the acceleration divided by the speed of the target. The comparison of the tracking performance of the proposed algorithm is made with that of an IMM algorithm, utilizing a straight line motion model in conjunction with a single turn rate model which uses an estimate of the turn rate and also to that of an IMM algorithm utilizing three constant turn rate models.

Limitations of PID controllers

The objective of the paper is to outline the limitations of classical PID controllers acting on the error signal for control of a plant modelled as a linear transfer function. It is shown how a modified form of controller, a PI-PD controller, which corresponds to PI control of a plant transfer function changed by the PD feedback can produce improved control in several situations. This implementation avoids the derivative kick problem associated with derivative action in the forward path, which still exists when a filter is included. Further, the PD in the inner feedback loop enables placement of the open loop poles in appropriate positions thereby providing good control for open loop system transfer functions having resonances, unstable, or integrating poles. The simulation results show significantly improved performance of the proposed control method particularly for the latter processes.

A new Smith predictor and controller for unstable and integrating processes with time delay

A new Smith predictor for control of an unstable process with time delay and a process with an integrator and long dead-time is proposed. The controller decouples the setpoint response from the load response. The design approach is based on standard forms of the closed loop system response and on the Nyquist stability analysis. Simulation results show high performance for the setpoint response and load disturbance rejection.

A suboptimal reduction algorithm for linear systems with a time delay

In this paper, a suboptimal model reduction algorithm is presented for models with time delay. This method is an extension to the present authors’ method for models without a time delay. An objective function is defined to minimize the weighted integral squared value between the outputs of the reduced order model and the original model when they are subjected to the same input signal. Examples are given to show the advantages of using the reduced-order modelling technique provided.

Mixture Reduction Algorithms for Uncertain Tracking

Abstract Bayesian solutions of tracking problems that involve measurement association uncertainty, give rise to Gaussian mixture distributions, which are composed of an ever-increasing number of components. To implement such a tracking filter, the growth of components must be controlled by approximating the mixture distribution. A popular and economical scheme is the Probabilistic Data Association Filter (PDAF), which reduces the mixture to a single Gaussian component at each time step. However this approximation may destroy valuable information, especially if several significant, well-spaced components are present. In this paper we present two new algorithms for reducing Gaussian mixture distributions. These techniques preserve the mean and covariance of the original mixture, and the final approximation is itself a Gaussian mixture. Both algorithms operate by combining components or groups of components until their number is reduced to some specified limit. Further reduction will then proceed while the approximation to the main features of the original distribution is still good. The two algorithms have been used to control the growth of components which occurs with the solution to the problem of tracking a single object, in the presence of uniformly distributed false measurements. Simulation results are presented which compare the performance of the resulting tracking filters and the PDAF.

Maneuvering target tracking with an adaptive Kalman filter

This paper presents a simple yet efficient adaptive Kalman filter for tracking targets expected to perform varying turn maneuvers. The process noise covariance level of a second order Kalman filter is adjusted at each time step according to the calculated turn rate. The turning rate is estimated from the magnitude of the calculated acceleration divided by the estimated speed of the target. At each scan the previous and current velocity estimates are used to calculate the acceleration. The comparison of the performance of the proposed algorithm is made with that of an interacting multiple model (IMM) algorithm, employing three models with different levels of process noise covariance and also to that of a second order Kalman filter. Two different assumptions have been made for selecting the process noise values for the the IMM and Kalman filter algorithms, in the first case it was assumed that there was no prior information about the target motion whereas in the second case it was assumed that the largest turn rate that the target of interest could perform was known. The IMM algorithm utilizing three models gives slightly better estimates during the nonmaneuvering periods, but the proposed algorithm is superior to the IMM algorithm during maneuvering periods in terms of estimation errors. Also the proposed algorithm requires 78% less computation, almost the same number of calculations required by a single fixed process noise Kalman filter, than the IMM algorithm.

Design of stabilizing PI and PID controllers

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 parameters which stabilize a given system are obtained in the (kp , ki )-plane for fixed values of kd and (kp , kd )-plane for fixed values of ki . However, for the case of PID controller, a grid on the derivative gain or integral gain is needed for computation of all stabilizing PID controllers. Examples are given to show the benefits of the method presented.