H.J.A.F. Tulleken

Generalized binary noise test-signal concept for improved identification-experiment design

Abstract When accurate identification of a parametrized linear process model is required, an external disturbance (test signal) will often be introduced to improve the statistical information content of the measured data. In industrial practice a specific (pseudo) random binary sequence or binary noise is frequently used. This is a stochastic signal which randomly switches between two fixed signal levels at discrete points in time. The paper shows that this test signal has serious shortcomings when used in conjunction with one-step-ahead prediction error estimators. Such estimators appear to given an unfair advantage to higher-frequency components. As a higher intensity of lower frequencies seems desirable, a generalized binary noise concept (GBN) is introduced, which involves a generalized stochastic distribution of the switching moments. This allows manipulation of the frequency spectrum of the input signal, such that most energy is concentrated in the lower frequencies. It is argued that the GBN concept indeed gives much better identification results than the conventional concept, considering the stochastic features of GBN and an analytical result on optimal GBN design for stable, first-order processes. In addition, using stochastic simulation techniques, near-to-optimal GBN designs are specified for four types of stable, second-order processes for several signal-to-noise ratios and observation lengths of the experiment. It turns out that not only bias but also variance of the model step response is reduced dramatically. Finally, using theoretical and simulation results, a practical guideline for GBN design is presented, together with a Pascal procedure for GBN generation, which demonstrates the conceptual simplicity and industrial appeal of the GBN concept.

Grey-box modelling and identification using physical knowledge and Bayesian techniques

Abstract Advanced control design requires a model that describes process behaviour adequately. Such a model can be constructed using physical modelling or statistical identification techniques. Both have their disadvantages: physical models are rigorous and thus often expensive to construct, while “black-box” model structures are not necessarily compatible with physical reality. Since both approaches have undeniable merits as well, their combination seems to be attractive and rewarding. This paper discusses an approach to statistical estimation where a “best” linearly parametrized dynamic regression model is identified, which is also consistent with specified knowledge about process responses. Such characteristics are forced upon the black-box models, yielding a “Grey-Box” model set. It will be shown that crucial physical knowledge such as process stability and sign of stationary gains can be translated into linear inequality constraints on the black-box model parameters. In order to select “best” estimators in the Grey-Box class, a Bayesian approach is adopted. Given a prior distribution, associated with the physical knowledge and given the data likelihood, a posterior distribution is constructed. Maximum and average A Posteriori estimators are analysed. Explicit solutions are given for special cases of Gaussian likelihood and a prior, which is uniformly or piece-wise linearly distributed on a linearly constrained Grey-Box model class. Finally, simulation results and an application to a distillation process show the advantage of the contrained estimates under realistic experiment conditions. Considerable variance reductions at the cost of a somewhat larger bias can be achieved, indicating the potential for, e.g. adaptive control applications.

Grey-Box Modelling and Identification, Using Physical Knowledge and Bayesian Techniques

Abstract Advanced control design requires a model that gives an adequate description of process behaviour. This model can be constructed via physical principles or statistical identification techniques. Both have their disadvantages: physical models are often involved and expensive to construct while ‘black-box’ models are not necessarily compatible with physical reality. Therefore, a combination of the two approaches seems attractive and rewarding. This paper discusses an approach to statistical estimation in which a linearly parametrised regression model is identified, that is consistent with specified physical knowledge and explains the data ‘best*. In the first step this physical knowledge is forced upon the black-box model set yielding a ‘Grey-Box’ model set. It will be shown that crucial physical knowledge such as stability and signs of stationary gains can be translated into linear inequality constraints on black-box model parameters. Secondly, in order to select ‘best’ estimators in the Grey-Box class, a Bayesian approach is adopted. Given a prior distribution, associated with the physical knowledge and given the data likelihood, a posterior distribution is constructed. Using this, Maximum and Average A Posteriori Estimators are defined and analysed. Explicit solutions are given for the special case of Gaussian likelihood and a prior which is uniformly distributed on a linearly constrained Grey-Box model class. Finally, a simulation result shows the advantage of the constrained estimators in the case of non-ideal, realistic experimental conditions. Considerable variance reductions at the cost of a somewhat larger bias can be achieved, indicating the potential of the approach for e.g. adaptive control.

A supervisor for control of mode-switch processes

Many processes operate only around a limited number of operation points. In order to have adequate control around each operation point, and adaptive controller could be used. When the operation point changes often, a large number of parameters would have to be adapted over and over again. This makes application of conventional adaptive control unattractive, which is more suited for processes with slowly changing parameters. Furthermore, continuous adaptation is not always needed or desired. An extension of adaptive control is presented, in which for each operation point the process behaviour can be stored in a memory, retrieved from it and evaluated. These functions are co-ordinated by a ?supervisor?. This concept is referred to as a supervisor for control of mode-switch processes. It leads to an adaptive control structure which quickly adjusts the controller parameters based on retrieval of old information, without the need to fully relearn each time. This approach has been tested on experimental set-ups of a flexible beam and of a flexible two-link robot arm, but it is directly applicable to other processes, for instance, in the (petro) chemical industry.

Application of the grey-box approach to parameter estimation in physicochemical models

It is demonstrated that the grey-box concept can be applied to certain rigorous models. The principle idea is to simplify the model structure (by means of time discretization and, if necessary, transformation) such that it takes on a form familiar in the black-box approach. In parallel, relevant process characteristics are highlighted and transformed to provide grey-box model constraints. As a result, the parameter estimation becomes more transparent and can be obtained at considerably lower computational costs than is possible with standard physical parameter estimation. In addition, more general stochastic model components (i.e. system noise) can be handled with relative ease. A drawback is the nontrivial formulation of a convex hull of the admissible parameter region associated with the (discrete-time) grey-box model. The merits and pitfalls of this approach are demonstrated with kinetic parameter estimation in a continuous and a batch reactor model.<<ETX>>

INTELLIGENT ADAPTIVE CONTROL OF MODE-SWITCH PROCESSES

Abstract The intelligence of controllers has increased over the decades. However, the number of applications of adaptive controllers is still restricted, due to practical limits of the implemented continuous adaptation. For processes which operate only in a limited number of modes (so called mode-switch processes), constant adaptation is not needed or desired. In this paper an intelligent extension of adaptive control will be presented, in which process behaviour can be stored in a memory, retrieved from it and evaluated for each mode of operation. This intelligent memory concept leads to an adaptive control structure which, after a learning phase, quickly adjusts the controller parameters based on retrieval of old information, without the need to relearn every time. This approach has been tested on a simulation model of an assembly robot, but it is directly applicable to many processes in the (petro)chemical industry.

A Generalised Binary Noise Test-signal Concept for Improved Identification-experiment Design

Abstract When accurate identification of a parametrised process model is required, an external test signal will often be introduced to improve the statistical information content of the measured data. In industrial practice a specific (pseudo)random binary sequence or binary noise is frequently used. This signal is a discrete-time ‘white-noise’ stochastic process with guaranteed bounded amplitudes, which is easy to generate. The paper shows that this test signal has serious shortcomings when used with one-step-ahead prediction error estimators for the processing of the data generated. Such estimators appear to give an unfair advantage to higher-frequency components. As a higher inten-sity of lower frequencies seems desirable, a Generalised Binary Noise concept (GBN) is introduced, which involves a generalised stochastic distribution of the switching moments. This allows of manipulation of the frequency spectrum of the input signal, such that most energy is concentrated in the lower frequencies. This is shown by covariance and spectrum analysis. It is argued that the GBN concept indeed gives much better identification results than the conventional concept by exploiting some other stochastic features of GBN and an analytical result on optimal GBN design for stable, first-order processes. In addition, using stochastic simulation techniques, near-to-optimal GBN designs are specified for four types of stable, second-order processes for several signal-to-noise ratios and observation lengths of the experiment. It turns out that not only bias but also variance of step response parameters of the model identi-fied is reduced dramatically. Finally, using the theoretical and the simulation results, a practical guideline for near-to-optimal GBN design is presented, together with a Pascal procedure for GBN generation, which demonstrates the conceptual simplicity and industrial appeal of the GBN concept

Time-Varying Parameter Estimation Combining Directional and Uniform Forgetting

Abstract The paper starts with a unified description of uniform and directional forgetting of old information only and of incoming information also, clarifying the mutual differences. Based on this unification, a new method is introduced. Compared to uniform forgetting, the novel method (like directional forgetting) forgets the same amount of information in the direction of incoming information, but (unlike directional forgetting) it forgets also a fraction of the information in other directions. This frac ti on is determined from UD-decomposition of the covariance matrix, such that directional forgetting prevails when the probability of covariance blow-up is high. The proposed method is able to follow fast parameter variations with low probability of covariance blow-up. This method as well as known methods have been applied to simulations of a two-parameter process with systematic combinations of constant, gradually changing and suddenly changing parameters, for several signal-to noise ratios. The mean squared parameter estimate error without covariance blow-up appeared to be the lowest for the new method.

NEURAL NETWORK BASED CONTROL OF MODE-SWITCH PROCESSES

In ‘mode-switch processes’, the dynamics are fairly the same in one mode of operation, but are truly different in another one. For such processes, this paper presents a ‘supervisory system’ which is based on the storage and retrieval of controllers designed at various modes. Modes are recognized by a neural network based decision-rule which rewards and penalizes the active controller on the basis of its closed-loop performance. This approach has been tested in a chemical reactor simulation where the objective is to reject disturbances. However, the concept can be applied to other processes as well.

An Intelligent Supervisor for Adaptive Mode-Switch Control

Abstract An adaptive controller is described, based on the idea that information gathered when new controller settings are computed is not forgotten hut stored in a memory. If the same situation is encountered again, this information can he retrieved from the memory and used for immediate adjustment of the controller. Various methods of data storage and retrieval are discussed. Best results are obtained with a method which from a number of models which run in parallel with the process, selects the model which describes the present process behaviour most adequately. Experimental results with a flexible beam and with a two-link flexible robot arm demonstrate that this approach is an attractive alternative for conventional adaptive or robust control systems.