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Volume 128
Issue 5
IEE Proceedings D (Control Theory and Applications)
Volume 128, Issue 5, September 1981
Volumes & issues:
Volume 128, Issue 5
September 1981
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- Author(s): S.A. Billings and D.H. Owens
- Source: IEE Proceedings D (Control Theory and Applications), Volume 128, Issue 5, page: 165 –165
- DOI: 10.1049/ip-d.1981.0036
- Type: Article
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165
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- Author(s): M.H.A. Davis
- Source: IEE Proceedings D (Control Theory and Applications), Volume 128, Issue 5, p. 166 –172
- DOI: 10.1049/ip-d.1981.0037
- Type: Article
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166
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The paper describes a recently developed reformulation of the optimal-filtering equations for a noisily observed diffusion process and discusses the computational implications. The computation involved is the solution of a parabolic partial differential equation whose coefficients are determined by the observed process. A Monte Carlo method of solution is proposed and given in detail as an example. It is argued that nonlinear filtering is now a practical proposition. - Author(s): D.P. Atherton
- Source: IEE Proceedings D (Control Theory and Applications), Volume 128, Issue 5, p. 173 –180
- DOI: 10.1049/ip-d.1981.0038
- Type: Article
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173
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The paper discusses methods, primarily those using frequency-domain techniques, for the analysis and design of nonlinear feedback control systems. The behavioural properties peculiar to nonlinear feedback systems are first discussed. This is followed by a review and discussion of the applicability of absolute stability criteria and describing-function methods for single-variable and multivariable systems. The calculation of limit cycles in relay systems, time-domain methods of analysis and simulation techniques are then considered. Finally, a few applications are considered which highlight both the applicability and limitations of the available analytical techniques for nonlinear systems. - Author(s): M.J. Denham
- Source: IEE Proceedings D (Control Theory and Applications), Volume 128, Issue 5, p. 181 –184
- DOI: 10.1049/ip-d.1981.0039
- Type: Article
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181
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In the paper, a review of recent results in the realisation theory of systems having multilinear input/output response functions is given. Such systems form a subclass of the more general class of polynomial systems, which in turn are a very special class of nonlinear system. It is shown that, in the bilinear case, the problem has essentially been resolved by two important results: an extension of the uniqueness result for canonical realisations of linear systems to the polynomial case, and a computable criterion for the quasireachability of realisations of bilinear response functions. These results, together with those of Kalman's early investigations into multilinear response functions, lead to an explicit canonical realisation procedure. In the general multilinear case, however, only a few results are available, and the many questions which remain to be resolved are described. - Author(s): A.J. Pritchard
- Source: IEE Proceedings D (Control Theory and Applications), Volume 128, Issue 5, p. 185 –187
- DOI: 10.1049/ip-d.1981.0040
- Type: Article
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185
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Using generalised inverses and their relationship to least-squares problems, controls and state estimators are derived for linear systems. These results are then extended to nonlinear systems using a fixed-point theorem. - Author(s): J.F. Barrett
- Source: IEE Proceedings D (Control Theory and Applications), Volume 128, Issue 5, p. 188 –194
- DOI: 10.1049/ip-d.1981.0041
- Type: Article
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188
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The paper deals with nonlinear systems whose input/output relation may be represented by a functional power series in Banach space. It is shown how certain types of forced analytic differential equation (including the analytic state-space equation) can be solved explicity by such functional series. Special attention is given to the convergence of the solution which is related to the bounded-input/bounded output stability of the system. - Author(s): P.C. Parks
- Source: IEE Proceedings D (Control Theory and Applications), Volume 128, Issue 5, p. 195 –200
- DOI: 10.1049/ip-d.1981.0042
- Type: Article
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195
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The first self-adaptive control systems were proposed some 25 years ago. The paper traces the historical development of model-reference adaptive control systems and especially their theoretical basis. The use of Lyapunov functions and hyperstability theory in analysis and synthesis is considered, the röle played by positive real transfer functions being particularly emphasised. Some practical applications and current and possible future theoretical developments are briefly described. - Author(s): A.I. Mees and C.T. Sparrow
- Source: IEE Proceedings D (Control Theory and Applications), Volume 128, Issue 5, p. 201 –205
- DOI: 10.1049/ip-d.1981.0043
- Type: Article
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201
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Nonlinear systems can have very complicated nontransient behaviour in addition to the static and periodic solutions familiar to everyone. Mathematicians have known for years about the existence of chaotic solutions (persisting modes of dynamic behaviour that have no simple recurrence properties, even though they are not stochastic), but it is only recently that much progress has been made in analysing them. The paper introduces some of the main features of the study of chaotic solutions and tries to relate them to more familiar topics such as feedback and spectra. The authors believe that chaos is more prevalent than is realised and they hope that readers will be alerted to the possibility that some effects which have been blamed on noise are actually instances of chaotic behaviour of a completely deterministic nature. - Author(s): P.J. Lawrence
- Source: IEE Proceedings D (Control Theory and Applications), Volume 128, Issue 5, p. 206 –210
- DOI: 10.1049/ip-d.1981.0044
- Type: Article
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An algorithm is presented for the estimation of the parameters of the Volterra kernels of non-linear systems using a composite-frequency input signal. Transformations are presented between the Volterra and Wiener descriptions of nonlinear systems, which, together with an aperiodic model of Gaussian white noise, reveal the uniqueness of harmonics in the response spectrum. A periodic approximation to Gaussian white noise is proposed and is used in conjunction with a parameterised version of the kernel functions, derived from the examination of general nonlinear structures, in a parameter-estimation algorithm. The results of a simulation study are summarised. - Author(s): V.Z. Marmarelis
- Source: IEE Proceedings D (Control Theory and Applications), Volume 128, Issue 5, p. 211 –214
- DOI: 10.1049/ip-d.1981.0045
- Type: Article
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p.
211
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A method is presented that makes practicable the identification of nonstationary Wiener systems. The method employs a single-record estimator for the evaluation of the time-variant system kernels, thus relaxing the strict requirement of the ergodic hypothesis that has so far limited applications of the Wiener theory to stationary systems. The estimator is unbiased and consistent under fairly weak conditions for the system function, thus opening a host of new possibilities in the analysis of nonstationary phenomena. - Author(s): C.J. Harris and R.K. Husband
- Source: IEE Proceedings D (Control Theory and Applications), Volume 128, Issue 5, p. 215 –218
- DOI: 10.1049/ip-d.1981.0046
- Type: Article
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p.
215
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In 1968, the scalar circle stability criterion was extended by Cho and Narendra to the off-axis case by the use of multipliers Q, Q−1 which have an RL or RC realise structure, so that the product of the linear portion of the feedback system and the multiplier was positive-real. Fabl, Freedman and Zames produced a multivariable on-axis circle criterion for systems whose linear part is normal for all frequencies. As yet the off-axis circle criterion has not yet been established for the multivariable case, although Cook (1976) has shown that a criterion of this type does provide the conditions for the absence of limit cycles. Utilising the loop transformation theorem and the passivity theorem, an off-axis multivariable circle stability criterion is established via the method of multipliers for nonlinear feedback systems with a normal linear operator. The criterion is shown to have a simple graphical interpretation based on the Nyquist plots of the eigenvalues of the system. - Author(s): R. Cameron and B. Kouvaritakis
- Source: IEE Proceedings D (Control Theory and Applications), Volume 128, Issue 5, p. 219 –222
- DOI: 10.1049/ip-d.1981.0047
- Type: Article
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p.
219
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For sampled data systems, it is possible to express discrete time convolution in terms of appropriate matrix multiplication. A limiting process then yields the steady-state response to a periodic input. The matrix involved in this operation is a circulant matrix based on the impulse response of the system. Circulant matrices are known to have useful structural properties and permit the association of the frequency domain with the time domain. The use of circulants in the analysis of nonlinear systems provides the means for converting the unwieldy nonlinear equations of continuous systems to simple matrix multiplications. It is then possible to apply numerical range techniques and rederive the circle criterion. The direct application of this approach yields a criterion which is less conservative than that obtained by the simple application of the small-gains theorem. Use of the approach in conjunction with a loop transformation, on the other hand, provides an alternative derivation of the circle criterion for discrete systems. The method can be extended to multivariable systems, and, because of its association with the time domain, it permits the assessment of system stability in the face of imperfect system descriptions, namely truncated impulse responses. - Author(s): G.T. Russell and J. Bugge
- Source: IEE Proceedings D (Control Theory and Applications), Volume 128, Issue 5, p. 223 –226
- DOI: 10.1049/ip-d.1981.0048
- Type: Article
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p.
223
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The automatic guidance of an unmanned submersible using an acoustic navigation system requires a state estimator that can predict the vehicle position during the navigation sample period, filter the random measurement disturbance and estimate the mean disturbance due to sea current. The hydrodynamic parameters of the vehicle are nonlinear and can vary with the magnitude and direction of the relative fluid velocity within the duration of the period of the navigation sample. A prediction-correction algorithm is described that incorporates real-time gain adaption to minimise the filter-error variance and a correction to offset the bias of the model and sea current disturbances. - Author(s): S.J. Dodds
- Source: IEE Proceedings D (Control Theory and Applications), Volume 128, Issue 5, p. 227 –232
- DOI: 10.1049/ip-d.1981.0049
- Type: Article
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p.
227
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A bang-bang control law for digital-processor implementation is presented which directly implements a nonlinear switching surface for sub-time-optimal control of a single-input time-invariant linear plant of arbitrarily high order with unbalanced control levels. The control law requires a complete state vector and must usually be used with a state estimator or observer. Results are presented for attitude control of a space satellite having a single flexible mode with zero damping. The control law is a development of a predictive controller for a plant comprising cascaded pure integrators in which an analogue model of the plant is repeatedly run ahead in time to predict the future plant behaviour under both signs of extreme drive. The sign of real plant drive is determined using sign-change counts in the model runs. Direct digital implementation of this predictive control law results in unequal, and possibly excessive, periods between plant drive updating. These problems are eliminated in the proposed control-law algorithm by computing the number of sign changes direcly, generating the required sign of plant drive by means of a set of equations involving only the state estimate and the assumed plant-drive levels. Rapid determination of the plant drive is facilitated by the presence of only elementary mathematical operations in the algorithm. Application to a linear plant other than cascaded integrators is facilitated by generating the real-time plant model of the state estimator by transforming the plant state equation to the companion form, ensuring stable control in the neighbourhood of the state origin. In fact, no instabilities have been noted in simulations carried out to date, even for starting points relatively far removed from the origin of the state space. - Author(s): J.O. Gray and N.B. Nakhla
- Source: IEE Proceedings D (Control Theory and Applications), Volume 128, Issue 5, p. 233 –241
- DOI: 10.1049/ip-d.1981.0050
- Type: Article
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The paper is concerned with recent developments in the application of harmonic approximants to predict limit-cycling conditions in multivariable feedback systems. Emphasis is placed on computational procedures giving graphical interpretations in the frequency domain which will be useful in the subsequent design of suitable linear compensator elements. Early work based on the single-harmonic approximant is reviewed, and it is shown how this can be subsequently extended and refined to generate more accurate solutions based on higher-order-harmonic approximants. Some of the numerical problems involved are described, and solutions are proposed which make efficient use of the computational effort available. An example is given which allows results obtained from the various methods described to be directly compared. - Author(s): P.E. Crouch
- Source: IEE Proceedings D (Control Theory and Applications), Volume 128, Issue 5, p. 242 –252
- DOI: 10.1049/ip-d.1981.0051
- Type: Article
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p.
242
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The predominance of linear models in systems theory has tended to obscure the natural structure possessed by given nonlinear physical systems, either through linearisation, model order reduction, or choice of co-ordinates. The purpose of the paper is to motivate the reintroduction of geometric structure into systems theory. First, a brief introduction to the more common geometric structures is given, also showing their linear counterparts. It is then shown how these structures arise in systems theory by introducing the nonlinear control problems involved with mechanical manipulators, electrical networks, rotating electrical machinery and attitude control of spacecraft. The paper is concluded by considering the application of some of the geometric structures to nonlinear Hamiltonian and potential input/output systems. - Author(s): D.Q. Mayne
- Source: IEE Proceedings D (Control Theory and Applications), Volume 128, Issue 5, page: 252 –252
- DOI: 10.1049/ip-d.1981.0052
- Type: Article
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p.
252
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Special issue on: nonlinear systems theory and design
New approach to filtering for nonlinear systems
Analysis and design of nonlinear feedback systems
Recent results in realisation theory of systems with discrete-time bilinear and multilinear response maps
Observers and minimum-energy controls for nonlinear systems
Banach-space theory of analytic systems
Stability and convergence of adaptive controllers-continuous systems
Chaos
Estimation of the Volterra functional series of a nonlinear system using frequency-response data
Practicable identification of nonstationary nonlinear systems
Off-axis multivariable circle stability criterion
Limit-cycle predictions in sampled data systems
Adaptive estimator for automatic guidance of an unmanned submersible
Bang-bang control law for single-input time-invariant plant
Prediction of limit cycles in multivariable nonlinear systems
Geometric structures in systems theory
Conference report: Control and its applications
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