Self-tuning regulator applied to a binary distillation column

Utilization of a self-tuning regulator (STR) for control of top product composition of a binary distillation column has been investigated. Results from simulation studies and experimental evaluation of the STR on a pilot scale column are compared with the performance achieved using conventional proportional plus integral control. The STR resulted in significantly improved control for both servo and regulatory control.     

A self-tuning regulator for multivariable systems

The controller described in this paper is designed for multivariable plants with constant, unknown parameters. The algorithm operates on-line with the a priori information about the time delay. The order of the system may be given a priori. In the case where the order of the system is unknown it can be determined by a generalized likelihood-ratio statistical test which is described in this paper. The multivariable self tuning regulator consists of the two tasks of estimation and regulation. Estimation of the input-output system model parameters is based on the least-squares principle. The control is computed to minimize the combined cost of output deviation and control energy. Asymptotic properties of the estimation are discussed. Usefulness and simplicity of this approach are illustrated by examples.     

Variance constrained self-tuning control

A self-tuning regulator for a variance constrained optimal control problem is given. The criterion for control is to minimize the stationary variance of the output. In the cases when the regulator which gives minimum variance requires too large control signals an inequality constraint on the input variance is introduced. In practice it is easier to select a constraint on the variance of the input than to choose the relative weights in a quadratic loss function. The self-tuning regulator applies the Robbins-Monro scheme to adjust the Lagrange multiplier of the variance constrained control problem. The behaviour of the algorithm is illustrated by a simulated example. The asymptotic behaviour of the regulator is studied using a set of associated ordinary differential equations.     

Theory and applications of self-tuning regulators

This paper reviews work on self-tuning regulators. The regulator algorithms, their theory and industrial applications are reviewed. The paper is expository—the major ideas are covered but detailed analysis is given elsewhere.     

Comments on: ‘Implementation of self-tuning regulators with variable forgetting factors’

The similarities are pointed out between the variable forgetting factor given in the paper by Fortescue, Kershenbaum and Ydstie and that given in Wellstead and Sanoff. Moreover, it is shown that the method of Fortescue, Kershenbaum and Ydstie can be made significantly more efficient, computationally, than is indicated.     

A multivariable self-tuning controller

A multivariable self-tuning controller is derived extending the scalar version of Clarke and Gawthrop (1975). Because the control terms are penalized in the cost function, fluctuations and peaking in control signals are reduced compared with the multivariable minimum variance self-tuning controller (Borisson, 1979). Time-varying reference signals as well as certain nonminimum-phase systems can be handled without difficulty with the proposed controller. Several examples illustrate the power of the derived self-tuning controller.     

Multivariable adaptive predictive control of a binary distillation column

This paper presents a tutorial review of an adaptive predictive control system (APCS). Special emphasis is given to the key issues involved in the practical application of APCS to real processes. These practical issues are illustrated by actual application of SISO and MIMO control of a pilot scale binary distillation column. The experimental evaluation of this method reveals the simplicity of the adaptive algorithm and its excellent performance in an industrial type environment. The experimental results easily outperformed well-tuned classical PID controllers. A brief review of other applications of adaptive control to chemical processes is also included in this paper.     

A self-tuning regulator based on optimal output feedback theory

Self-tuning control of stochastic systems is considered. The underlying control problem is a parametric linear quadratic problem for fixed structure controllers. An explicit self-tuning regulator is described based on optimal output feedback theory. The proposed self-tuner is a generalization of state-space LQG self-tuners to parametric LQ problems. Two interesting application areas of parametric LQ self-tuners are autotuning of parameters of low-order regulators, such as PID-regulators, and adaptive decentralized control.     

Implementation of self-tuning regulators with variable forgetting factors

A modified version of the self-tuning regulator having limited adaptability has been successfully implemented on a large-scale chemical pilot plant. The new algorithm uses a least-squares estimator with variable weighting of past data; at each step a weighting factor is chosen to maintain constant a scalar measure of the information content of the estimator. It is shown that, for nearly deterministic systems, such an approach enables the parameter estimates to follow both slow and sudden changes in the plant dynamics. Furthermore, the use of a variable forgetting factor with correct choice of information bound can avoid one of the major difficulties associated with constant exponential weighting of past data—namely, ‘blowing-up’ of the covariance matrix of the estimates and subsequent unstable control. Accordingly, the control algorithm described here may be well suited to the regulation of plants which would otherwise require periodic re-tuning of control constants.     

A self-tuning regulator for distributed parameter systems

The control of distributed parameter systems with constant, but unknown parameters is considered. A weighted average of the distributed output on the spatial domain is defined as a new variable and is used to generate the control. The parameters of the model are estimated using recursive least squares estimation. The control is obtained using a minimum variance strategy based on the estimated parameters. Distributed disturbances and measurement noise are allowed to be present. Measurements at a finite number of points in the spatial domain are used in obtaining a discrete-time model. From the simulation of a one-sided heating diffusion process the self-tuning regulator is shown to have attractive characteristics and hence can be recommended for practical on-line control of distributed parameter systems.     

Microcomputer based self-tuning and self-selecting controllers

Classical control system design techniques are extended to include cases with large parameter and state variations. New results on stability of adaptive gain control systems are obtained and a new method to design self-selecting controllers is presented.It is then shown that microcomputers are well suited for hybrid implementation of the resulting control systems.Several examples and a short survey on industrial applications are also given.     

Predictor-based self-tuning control

Linear finite-memory output predictors updated in real-time appear to be a suitable internal representation of the system in a digital self-tuning controller. A new time-domain method of quadratic-optimum control synthesis for systems described by such predictors is presented. The synthesis covers both the servo problem and the regulation problem, including the program control (with preprogrammed command signal) and the feedforward from measurable external disturbances. Unlike the standard Riccati equation, the method leads to algorithms (or explicit formulae in low-order cases) which are numerically robust and therefore suitable for real-time computation using microprocessors with reduced wordlength.     

A self-tuning multistep predictor application

A self-tuning multistep predictor is presented. It predicts the output of a stochastic process with unknown, possibly slowly time-varying parameters over a range of several sampling periods in the future. At each sampling instant it is tuned by using a recursive least-squares parameter estimator in real time. By doing this, the combination predictor-estimator converges fast to the optimal predictor for processes with known parameters (self-tuning property). The method seems to have powerful capabilities as an aid in controlling complex industrial processes which are until now only operated under manual control. The predictor can be used by the operator in selecting an appropriate control action (decision making). A typical application, the control of a blast furnace, is extensively dealt with in the paper.The paper opens new perspectives in the domain of self-tuning controllers, and it has practical importance as is indicated by the blast-furnace experiment.     

A multivariable self-tuning controller with integral action

In this paper a novel stochastic self-tuning control algorithm for multivariable linear systems described by Controlled Autoregressive Integrating Moving Average (CARIMA) models is proposed. In particular, the presence of an integral action on each component of the error vector ensures the robust offset rejection for any constant load disturbance acting on the plant. The leading assumption is made that the system interactor matrix is known a priori. The algorithm is derived by resorting to the generalized minimum variance approach. Two simulation examples illustrate the main features of the method.     

Cautious stochastic computer control applied to concrete mixing

An application of direct digital control of a concrete mixing process is presented. The process which is irreversible is modelled as a linear stochastic system. The control problem is formulated as a final value control problem. A general final value prediction problem is formilated and solved. The regulator becomes an adaptive stochastic regulator. Its control actions are based on the uncertainty in the control-error which is calculated as the difference between the setpoint and the predicted final value. The resulting algorithm is implemented on a small minicomputer based control system and is used in every day production since more than a year ago.     

Self-tuning control of a pH-neutralization process

A self-tuning regulator has been used in control of a pH-neutralization process. The process is difficult to control due to great variations in process sensitivity with pH and due to process nonlinearities. Experiments on a pilot plant demonstrate that a self-tuning pH-regulator including exponential forgetting and quadratic optimal control has satisfactory static and dynamic properties even though the process is nonlinear. It is also demonstrated that the self-tuning algorithm can adapt to changes in process conditions, and it may be a useful alternative to traditional PI-controllers.     

Identification of a simulated Shell distillation column using time series analysis methods

This paper presents details of a multivariate time series identification of the simulated Shell distillation column described in the introductory paper by Cott. The approach applied here involves the use of time series identification techniques and may be considered as representative of the system identification procedures adopted by Shell Canada for quadratic dynamic matrix control (QDMC) applications. Results indicate that techniques of time series analysis are very flexible and capable of producing satisfactory step response models under both low and high signal to noise conditions.     

Self-tuning regulators for a class of multivariable systems

Control of a class of multivariable systems described by linear vector difference equations with constant but unknown parameters is discussed. A multivariable minimum variance strategy is first presented. This gives a generalization of the minimum variance strategy for single-input single-output systems. A multivariable self-tuning regulator based on the minimum variance strategy is then proposed. It uses a recursive least squares estimator and a linear controller obtained directly from the current estimates. The asymptotic properties of the algorithm are discussed. If the estimated parameters converge, the resulting controller will under certain conditions give the minimum variance strategy. The analysis also gives insight into the case when several single-input single-output self-tuning regulators are operating in cascade mode.     

Self-tuning control of a chip refiner motor load

On a chip refiner the gain of the transfer function between the refiner motor load and the plate gap is subject to a slow drift due to plate wear and to sudden changes in sign due to collapse of the pulp pad. A self-tuning regulator was designed to control motor load by manipulating the plate gap. It uses a recursive least-squares estimator with a variable forgetting factor in conjunction with a Dahlin regulator. Results of plant trials on an industrial thermomechanical pulp production unit show that this regulator is capable of tracking the slow gain drift and of taking proper action in case a pulp pad collapse occurs.