基于预报器的综合LQG自校正控制器*

本文推导了一类多项式LQG自校正控制算法,采用了增量和非增量两种模型形式。全面考虑了权P(z~(-1)),Q(z~(-1))和滤波多项式T(z~(-1))的作用,能控制存在有色噪声和前馈干扰的复杂过程。与广义预测控制仿真比较,结果表明这两种控制器均有良好的适应能力和强的鲁棒性。     

Design of steady-state minimum variance controllers

A new technique to design optimal controllers is presented for plants described by rational transfer functions and additive disturbances with rational spectral densities. The objective is to minimize a weighted sum of the plant input and output steady-state variances subject to asymptotic stability of the closed-loop system.The technique is based on polynomial algebra. In fact, the design procedure is reduced to solving two linear polynomial equations whose unique solution directly yields the optimal controller transfer function as well as the minimized cost. This approach is simple, computationally attractive, and can handle unstable and/or nonminimum-phase plants with improper transfer functions.An integral part of the paper are effective computational algorithms, which include the spectral factorization, the solution of polynomial equations, and the evaluation of minimum cost.     

Optimal control of LQG problem with an explicit trade-off between mean and variance

For discrete-time linear-quadratic Gaussian (LQG) control problems, a utility function on the expectation and the variance of the conventional performance index is considered. The utility function is viewed as an overall objective of the system and can perform the optimal trade-off between the mean and the variance of performance index. The nonlinear utility function is first converted into an auxiliary parameters optimisation problem about the expectation and the variance. Then an optimal closed-loop feedback controller for the nonseparable mean–variance minimisation problem is designed by nonlinear mathematical programming. Finally, simulation results are given to verify the algorithm's effectiveness obtained in this article.     

Combining model reference adaptive controllers and stochastic self-tuning regulators

The similarities between model reference adaptive controllers (MRAC) for minimum phase plants where the control objectives are specified by reference models and stochastic self-tuning regulators (S-STURE) for minimum phase plants where the control objectives are specified by autoregressive moving average (ARMA) stochastic models are investigated.These similarities permit the extension, for these two classes of adaptive systems, of the duality existing in the linear case with known parameters between modal control and minimum variance control. The convergence analysis of these schemes in a combined deterministic and stochastic environment allows one finally to define schemes which behave as a desired MRAC in a deterministic environment and as a desired S-STURE in a stochastic environment. The problem of removing the positive real conditions for convergence in deterministic and stochastic environment is also discussed.     

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.     

Performance improvements of self-tuning controllers by multistep horizons: The MUSMAR approach

The problem of adaptively controlling a linear multivariable plant according to a quadratic cost functional defined over a control horizon of arbitrary length is discussed. In this context, the proposed algorithm, referred to by the acronym MUSMAR, is shown to be a natural generalization of standard self-tuning controllers. By increasing the control horizon length, the MUSMAR closely approximates a steady-state LQG controller inheriting the intrinsic robustness of LQG design. Analysis and simulations give evidence of several attractive features of the MUSMAR self-tuner when applied to plants for which standard adaptive controllers fail to converge or yield an unacceptable performance.     

Reduced order LQG controllers for linear time varying plants

The problem of reduced order LQG optimization is addressed in a finite horizon, linear time-varying (LTV) system setting. First-order necessary conditions for local optimality in the parameter space is provided in terms of four coupled matrix differential equations. This result provides a transparent generalization of the optimal projection equations of Hyland and Bernstein for the optimal, steady-state compensation of linear time-invariant (LTI) plants.     

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.     

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.     

Will the self-tuning approach work for general cost criteria?

We expose a fundamental limitation of the self-tuning procedure for adaptive control of linear stochastic systems. Specifically, if the cost criterion measuring the performance of the unknown system is anything other than a minimum (output) variance criterion, then the procedure of estimating the unknown parameters of the linear system and then applying a control input which is optimal for the given cost criterion and the parameter estimates, will not self-tune to the optimal control law. Since our arguments are based on the analysis of an ordinary differential equation of Ljung, and since we do not, in our general context, have a proof that this O.D.E. represents the asymptotic behaviour of the system, further work is needed. An exception to the above situation is the class of systems with a large enough delay, for which self-tuning to the optimal, and indeed, convergence to the true parameters, cannot be ruled out.     

Continuity properties of LQG optimal controllers

It is shown that the LQG optimal controller is a continuous function of the plant. The result is proved for a class of plants which contains the class of strictly proper finite-dimensional plants. The topology employed is the one generated by convergence of the closed-loop transfer functions in an induced _∞ sense. This topology is slightly stronger than the usual ₂ gap metric convergence on transfer functions.     

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.     

Towards probabilistic synchronisation of local controllers

The traditional use of global and centralised control methods fails for large, complex, noisy and highly connected systems, which typify many real-world industrial and commercial systems. This paper provides an efficient bottom-up design of distributed control in which many simple components communicate and cooperate to achieve a joint system goal. Each component acts individually so as to maximise personal utility whilst obtaining probabilistic information on the global system merely through local message-passing. This leads to an implied scalable and collective control strategy for complex dynamical systems, without the problems of global centralised control. Robustness is addressed by employing a fully probabilistic design, which can cope with inherent uncertainties, can be implemented adaptively and opens a systematic rich way to information sharing. This paper opens the foreseen direction and inspects the proposed design on a linearised version of coupled map lattice with spatio-temporal chaos. A version close to linear quadratic design gives an initial insight into possible behaviours of such networks.     

Active fault tolerant control using state-space self-tuning control approach

This paper presents a new fault tolerant control scheme for unknown multivariable stochastic systems by modifying the conventional state-space self-tuning control approach. For the detection of faults, a quantitative criterion is developed by comparing the innovation process errors occurring in the Kalman filter estimation algorithm, which, for faulty system recovery, a weighting matrix resetting technique is developed by adjusting and resetting the covariance matrices of the parameter estimate obtained in the Kalman filter estimation algorithm to improve the parameter estimation of the faulty systems. The proposed method can effectively cope with partially abrupt and/or gradual system faults and/or input failures with fault detection. The modified state-space self-tuning control scheme can be applied to the multivariable stochastic faulty system without requiring prior knowledge of system parameters and noise properties.     

奇异线性系统最优估计的多项式方法

基于多项式ARMA新息模型方法提出了随机奇异线性离散时间系统的稳态最优估计.估值器的增益矩阵是通过新息分析和射影方法推得;其计算归结为求解一个多项式方程和谱分解.这一结果是最优估计多项式方法在奇异系统中的应用.     

隐式多变量广义自校正控制器

本文提出了具有在线选择加权阵的两种多变量自校正控制器.加权阵的在线选择和自校正控制算法都采用隐式方案来实现.本文还证明了该自校正控制器具有全局收敛性.     

Tableau methods for analysis and design of linear systems

Certain classes of elementary operations on the system matrix of a linear system are defined, and then their use is illustrated for the calculation of canonical forms, the largest (A,B)-invariant and controllability subspaces in ker(C), transmission zeros, and minimal inverses. Questions of numerical accuracy are discussed. The results are directly codable as efficient numerical algorithms, and may be extended to the use of orthogonal transformations.     

On low frequency and long-run effects in self-tuning control

Long-term performance of self-tuning controllers is analysed for low frequency disturbance corrupted single input-single output systems described by five variants of the linear difference equation model. Having the drifts classified, the appropriate models to allow for drift effects are specified and standard recursive least squares parameter estimation schemes are applied. Optimal single-stage control strategies are comparatively analysed both from the steady-state accuracy and stability points of view. As a result, an ‘extended self-tuning controller’ is developed and its superiority over classical ones is demonstrated. The related problem of ‘blow-up’ protection for self-tuning controllers is also investigated and some effective measures are proposed.     

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.