D.W. Clarke

Generalized predictive control—Part I. The basic algorithm

Current self-tuning algorithms lack robustness to prior choices of either dead-time or model order. A novel method—generalized predictive control or GPC—is developed which is shown by simulation studies to be superior to accepted techniques such as generalized minimum-variance and pole-placement. This receding-horizon method depends on predicting the plants output over several steps based on assumptions about future control actions. One assumption—that there is a “control horizon” beyond which all control increments become zero—is shown to be beneficial both in terms of robustness and for providing simplified calculations. Choosing particular values of the output and control horizons produces as subsets of the method various useful algorithms such as GMV, EPSAC, Peterkas predictive controller (1984, Automatica, 20, 39–50) and Ydsties extended-horizon design (1984, IFAC 9th World Congress, Budapest, Hungary). Hence GPC can be used either to control a “simple” plant (e.g. open-loop stable) with little prior knowledge or a more complex plant such as nonminimum-phase, open-loop unstable and having variable dead-time. In particular GPC seems to be unaffected (unlike pole-placement strategies) if the plant model is overparameterized. Furthermore, as offsets are eliminated by the consequence of assuming a CARIMA plant model, GPC is a contender for general self-tuning applications. This is verified by a comparative simulation study.

Generalized predictive control—Part II. Extensions and interpretations

Abstract The original GMV self-tuner was later extended to provide a general framework which included feedforward compensation and user-chosen polynomials with detuned model-reference, optimal Smith predictor and load-disturbance tailoring objectives. This paper adds similar refinements to the GPC algorithm which are illustrated by a set of simulations. The relationship between GPC and LQ designs is investigated to show the computational advantage of the new approach. The roles of the output and control horizons are explored for processes with nonminimum-phase, unstable and variable dead-time models. The robustness of the GPC approach to model over- and under-parameterization and to fast sampling rates is demonstrated by further simulations. An appendix derives stability results showing that certain choices of control and output horizons in GPC lead to cheap LQ, “mean-level”, state-dead-beat and pole-placement controllers.

Application of generalized predictive control to industrial processes

A novel algorithm called generalized predictive control (GPC) is shown to be particularly effective for the self-tuning control of industrial processes. The method uses long-range predictive control ideas with a carefully chosen controlled autoregressive and integrated moving average (CARMA) plant model and various horizons that allow for a rich variety of control objectives. The procedure can adapt to process dead time and model order, and a multivariable version gives tight control of complex plants without prior knowledge of the interactor matrix. Applications of GPC to a cement mill, a spray-drying tower, and a compliant robot arm give performance better than that of fully tuned proportional-integral-derivative regulators.<<ETX>>

Paper: Self-tuning control of nonminimum-phase systems

The instability that arises from the pole-zero cancellation of elementary self-tuners and most MRAC algorithms has given rise to a misapprehension that nonminimum-phase systems can pose insoluble problems with the application of adaptive control. Since most practical processes exhibit some form of nonminimum-phase behaviour (particularly when controlled digitally) this appeared to restrict the usefulness of self-tuning methods. However, during the last few years new algorithms have been suggested which partly overcome these difficulties and have been shown to be effective in industrial trials. The paper describes the practical features that a self-tuning controller must possess and discusses how plant dead-time and excess continuous-time poles can lead to discrete-time nonminimum-phase zeros. The source of instability of elementary self-tuners is analysed and various suggested approaches for overcoming this problem are reviewed. These include the use of a generalized minimum variance cost-function incorporating control weighting, factorization methods which avoid cancellation of the offending zeros, adaptive control based on state-space linear quadratic Gaussian (LQG) theory, and explicit pole-placement via solution of a Diophantine or Bezoutian equation. Gawthrops hybrid controller, which avoids those nonminimum-phase zeros due to continuous-time pole excess, is briefly discussed. A series of simulations in which a nonminimum-phase plant is subjected to a pattern of set-point changes is presented to show some of the features of the algorithms. In applications the order of the process is unlikely to be known (or indeed be finite); the pole-placement algorithm which is particularly effective in the known-order case is shown to lack robustness to underspecified order. The use of a large control weighting however restores stability to the generalized minimum-variance controller. The conclusions are that with appropriate design and engineering judgement adaptive control is viable even for nonminimum-phase processes.

The self-validating sensor: rationale, definitions and examples

Abstract Traditionally, the industrial sensor has been viewed as a simple signal generator. The application of microprocessor technology, digital communications and fault detection techniques, coupled with increasing demands for measurement quality assurance, have rendered inadequate such a simplistic view. In this paper a new sensor model is proposed which encompasses new demands and capabilities. This self-validating sensor performs self-diagnostics and generates a variety of data types, including the on-line uncertainty of each measurement. A demonstration system is described. based upon a coriolis mass flow meter.

A state-space description for GPC controllers

Abstract Generalized predictive control (GPC)-type control algorithms traditionally derived in the polynomial domain are derived in this paper in the state-space domain, but following the polynomial approach due to Clarke et al. (1987). Relations between the polynomial and state-space parameters are presented. Some possible state-space representations which were used earlier in different publications are discussed. The problem of deriving the GPC algorithm in the state-space domain is solved for the unrestricted case as well as for the case of restricted control and output horizons. Some properties of the state estimate for this problem are presented; in particular, two methods of Kalman filtering—optimal and asymptotic—are proposed. The solution is valid for any possible (minimal or non-minimal) state-space representation. Another approach to this problem is by the ‘dynamic programming method’ and solving the Riccati equation (Bitmead et al. 1990). This approach is also presented in this paper but the me...

Observer design in receding-horizon predictive control

This paper considers the robust implementation of a class of predictive control methods represented by GPC. Such controllers are in two-degrees-of-freedom form where there are dynamics in both the forward and the feedback paths. The ‘tuning knobs’ of predictive controllers determine the characteristic polynomial PC , and for a given PC the observer or prefiltering polynomial T in the feedback path determines the robustness of the closed loop. Previous intuitive guidelines on the selection of T are shown to be limited in their effectiveness. For an open-loop stable plant, a simple criterion is provided which allows the feedback dynamics to be specified so as to enhance robustness. The T polynomial is then chosen to satisfy this criterion. In addition, robust design through T is related to an H∞ -optimal control scheme using the so-called Q-parametrization. Despite its simplicity, the new proposed approach to the design of T is seen to result in robustness comparable with that obtained from the H∞ method.

Implementation and application of microprocessor-based self-tuners

The implementation of a class of self-tuning controllers using a portable microcomputer system is described. The self-tuning control theory is shown to provide a variety of control objectives such as model-reference, optimal Smith prediction and the minimization of a general k-step-ahead cost-function. Hardware and software details of the portable computer, SESAME, are presented with particular reference to the use of a new high-level language, Control Basic. Studies of the application of self-tuning to the control of room-temperature, acid neutralization, and batch chemical reactors in industry are outlined.

A self-validating thermocouple

Traditionally the sensor has been the system component neglected by control engineers, yet it has long been recognized that accurate and reliable sensor readings are vital for good controller performance. Self-validating sensors can improve reliability through self-diagnosis and by the provision of on-line metrics (measurement accuracy and its trustworthiness). One benefit of validation is the potential to sustain satisfactory loop performance even in the presence of sensor faults. This paper describes a self-validating thermocouple that can discover several types of internal fault, including the practically important aspect of loss-of-contact with the process environment, and shows how the associated uncertainties can be calculated. The operation of the device is demonstrated through a series of experiments.

A self-validating digital Coriolis mass-flow meter: an overview

Abstract A new implementation of a Coriolis mass-flow meter transmitter is described. It is based on digital components, and has improved performance compared with the commercial, mostly analogue, transmitter using the same flowtube (transducer). Improvements are found in flowtube control, measurement precision, and performance with two-phase and partially-empty conditions, including batching from empty. The new transmitter is viewed as a second-generation sensor validation (SEVA) demonstrator, in which experience from validating the commercial analogue transmitter has led to a redesign using digital technology. The resulting SEVA transmitter provides improved measurement performance and reduced vulnerability to fault conditions, as well as on-line estimates of measurement quality and fault compensation (Henry and Clarke, Control Engineering practice, 1 (4) (1993) 585–610).