M.J. Grimble

Design of integrated systems for the control and detection of actuator/sensor faults

Considers control systems operating under potentially faulty conditions. Discusses the problem of designing a single unit which not only handles the required control action but also identifies faults occurring in actuators and sensors. In common practice, units for control and for diagnosis are designed separately. Attempts to identify situations in which this is a reasonable approach and cases in which the design of each unit should take the other into consideration. Presents a complete characterization for each case and gives systematic design procedures for both the integrated and non‐integrated design of control and diagnosis units. Shows how a combined module for control and diagnosis can be designed which is able to follow references and reject disturbances robustly, control the system so that undetected faults do not have disastrous effects, reduce the number of false alarms and identify which faults have occurred.

Paper: Implicit and explicit LQG self-tuning controllers

The design of optimal controllers for use in self-tuning systems is considered. Linear Quadratic Gaussian (LQG) controllers are widely used elsewhere but have not until recently been applied in self-tuning systems, except in minimum output variance forms. The LQG controllers offer a guarantee of stability (when the plant parameters are known) which is particularly useful for nonminimum phase systems. The explicit LQG self-tuning controllers introduced in the following are relatively simple to implement. The first version of an implicit LQG self-tuning controller is also introduced. The magnitude of the transport delay terms need not be known a priori and integral action may be introduced easily. If required the desired closed-loop poles of the system can be prespecified.

Brief Controller performance benchmarking and tuning using generalised minimum variance control

The use of the generalised minimum variance control law for control loop performance assessment and benchmarking is considered. A novel derivation of the control law enables the link to minimum variance benchmarking to be explored and exploited. The main advantage lies in the generality of the weighted cost index and the simplicity of the results. The only price for this simplicity is the assumption on the choice of weightings. Simple expressions are provided for each of the cost terms that enable performance to be assessed, including the total performance index, variance of error and control signals and variance of weighted signals. These can be used to compare existing (classical) designs with optimal solutions using either models or real time normal operating records.

Optimal H∞ robustness and the relationship to LQG design problems

A solution to the Hx optimal-control problem is obtained by employing a standard LQG polynomial-based solution procedure. The derivation is straightforward and avoids many of the more abstract mathematical results usually employed. The relationship between the LQG and Hm design methods becomes transparent and the similarities and differences can be identified.

Non-linear generalized minimum variance feedback, feedforward and tracking control

A generalized minimum variance control law is derived for the control of nonlinear, possibly time-varying, multi-variable systems. The solution for the tracking and feedback/feedforward control law was obtained in the time-domain using a nonlinear operator representation of the process. The cost index involves both error and control signal costing terms and is normally quadratic but may also involve nonlinear functions. The feedback controller obtained is simple to implement and includes an internal model of the process. The tracking controller can include future reference change information, providing a predictive control capability. In one form the compensator might be considered a nonlinear version of the Smith Predictor that has feedforward action.

Polynomial systems approach to optimal linear filtering and prediction

The solution of the optimal linear estimation problem is considered, using a polynomial matrix description for the discrete system. The filter or predictor is given by the solution of two diophantine equations and is equivalent to the state equation form of the steady-state Kalman filter, or the transfer-function matrix form of the Wiener filter. The pole-zero properties of the optimal filter are more obvious in the polynomial representation, and new insights into the disturbance rejection properties of the filter are obtained. The plant or signal model can be stable or unstable, and allowance is made for both control and disturbance input subsystems, and white and coloured measurement noise (or an output disturbance subsystem). The model structure was determined by the needs of several industrial filtering problems. The polynomial form of filter may easily be included in a self-tuning algorithm, and a simple adaptive estimator is described.

Two degrees of freedom feedback and feedforward optimal control of multivariable stochastic systems

Abstract A polynomial matrix solution is obtained to the optimal LQG output regulator problem for a system with both input and output disturbances, dynamic feedback element and a cost-function with dynamic weighting terms. The cost-function can include both the usual LQG output and control terms and sensitivity/complementary sensitivity terms. The solution of this regulating problem is also shown to provide a two-degrees of freedom controller when a reference input is used for a tracking problem. Similarly a feedforward controller can also be derived from the results when a disturbance is measurable. Since in practice disturbances cannot usually be measured accurately provision is made for corrupting the measured spectrum and allowance is made for a measurement noise on this signal. The results are obtained for a general multivariable plant.

Optimal self-tuning filtering, prediction, and smoothing for discrete multivariable processes

An algorithm is proposed for self-tuning optimal fixed-lag smoothing or filtering for linear discrete-time multivariable processes. A z -transfer function solution to the discrete multivariable estimation problem is first presented. This solution involves spectral factorization of polynomial matrices and assumes knowledge of the process parameters and the noise statistics. The assumption is then made that the signal-generating process and noise statistics are unknown. The problem is reformulated so that the model is in an innovations signal form, and implicit self-tuning estimation algorithms are proposed. The parameters of the innovation model of the process can be estimated using an extended Kalman filter or, alternatively, extended recursive least squares. These estimated parameters are used directly in the calculation of the predicted, smoothed, or filtered estimates. The approach is an attempt to generalize the work of Hagander and Wittenmark.

Polynomial Matrix Solution of the H/Infinity/ Filtering Problem and the Relationship to Riccati Equation State-Space Results

A solution to the standard suboptimal H, filtering problem is presented using a new polynomial systems ap- proach. The polynomial matrix solution is closely related to the recent H, state-space-based Riccati equation results, and the links between the polynomial and state-equation methodologies are demonstrated. The H, filter is derived by solving a special type of minimum-variance filtering problem, using a technique based on game theory. The solution of this game problem in a stochastic setting, by polynomial methods, is novel. The cal- culation of the H, filter involves a J-spectral factorization and the solution of two coupled diophantine equations. There are several computational advantages over previous polynomial methods for calculating H, filters.

H/sub infinity / fixed-lag smoothing filter for scalar systems

The solution of the H/sub infinity / optimal linear fixed-lag smoothing problem is considered using a polynomial matrix description for the discrete system. The smoother is obtained from the solution of a linear equation and a spectral factorization calculation. The pole-zero properties of the optimal smoother are obvious in the polynomial representation, and insights into the measurement noise rejection properties of the smoother are obtained. Allowance is made for both dynamic cost weighting and colored measurement noise. The polynomial form of the smoothing filter may be incorporated into a self-tuning algorithm and a simple adaptive smoother is discussed. >