An approach for incomplete state feedback control systems design†

An alternative method for designing linear regulators with incomplete state feedback is presented. This approach is based on approximation of the impulse response of the closed-loop system with incomplete state feedback to the optimal closod-loop system with complete state feedback.     

Receding horizon H∞ control problems for sampled-data systems§

In this article, the receding horizon H_∞ control problems for sampled-data systems are considered. Since sampled-data systems can be rewritten as equivalent jump systems, the receding horizon H_∞ control problems for time-varying jump systems are considered first and the design methods of a state feedback receding horizon H_∞ controller and an output feedback receding horizon H_∞ controller are given. Then the obtained results are applied to sampled-data systems and the design methods of a state feedback receding horizon H_∞ controller and an output feedback receding horizon H_∞ controller are given. Two numerical examples are given to illustrate the theory.     

Computer generation of sensitivity functions for sampled-data control systems†

Methods have been presented previously (Suryanarayanan and Soudack 1970) for the generation of sensitivity functions for general non-linear sampled-data systems. In this paper, it is shown that economy of simulator components (for hybrid computer generation) or of computational time (for digital computer generation) is achieved for simultaneously generating a number of sensitivity functions in a class of linear sampled-data control systems. Extensive use of signal flow graph algebra is made for this purpose and comprehensive examples are presented.     

An LMI approach to robust H-infinity control for uncertain singular time-delay systems

The problem of robust H-infinity control for a class of uncertain singular time-delay systems is studied in this paper. A new approach is proposed to describe the relationship between slow and fast subsystems of singular time- delay systems, based on which, a sufficient condition is presented for a singular time-delay system to be regular, impulse free and stable with an H-infinity performance. The robust H-infinity control problem is solved and an explicit expression of the desired state-feedback control law is also given. The obtained results are formulated in terms of strict linear matrix inequalities （LMIs） involving no decomposition of system matrices. A numerical example is given to show the effectiveness of the proposed method.     

An approach for improved modal control of multi-input multi-output discrete time systems†

It is shown that the state feedback gains for a given multi-input multi-output discrete time system can be computed by matching a finite model output sequence members to prespecified ones. Relationship of the pole positioning control schemes to such matching is first examined and it is shown that better control is possible by adopting the method proposed in this paper. The results are illustrated through a numerical example.     

Lyapunov design of time-shared sampled-data control systems†

This paper is concerned with the problem of sampled-data control of a multi-variable system when only one control variable may be used at a time. A quasi-optimal system for time-sharing control is designed via the direct method of Lyapunov. The design specifies control lows and the decision criterion for utilization of the controller. It is shown that even with simplified decision criteria, stability properties are preserved. The method is developed for continuous plants containing at most a single integration. The results also apply to the classical adaptive-sampling problem where the objective is simply to conserve the number of controlling sampling intervals for a single process. A numerical example is presented of the time-shared control of four second-order systems, each containing an integration.     

Some computer-aided estimators in stochastic control systems identification†

A unified exposition of certain computer-aided statistical estimators for control systems identification is presented, together with some numerical results which show and compare the effectiveness of them     

An H∞ suboptimal robust control approach for systems with uncertainties and data dropouts

This paper studies the design of control systems subject to plant uncertainties and data losses in the channel connecting the plant sensor with the controller. The controller design has two main objectives. The first one is to robustify the control law against plant uncertainties. The other one is to achieve good performance by minimising the variance of the error signal. Data losses are modelled as an independent and identically distributed sequence of Bernoulli random variables. For analysis and design, this random variable is replaced by an additive noise plus gain channel model. To cope with structural uncertainties in the model of the plant, an H_∞ control technique is employed. The controller is synthesised in order to make the closed-loop system robust against structural uncertainties of the nominal model, while achieving optimal performance of the system in the presence of dropouts.     

An algebraic method for control systems design†

A computer-oriented algebraic method for the design of duplicator class control systems is established. To involves four steps: (1) Equation fitting, (2) parameter assuming, (3) system simplifying and (4) quotient matching. The power and simplicity of the method are demonstrated by several examples.     

An LMI approach for H ∞ analysis and control of discrete-time piecewise affine systems

In this paper we investigate some analysis and control problems for discrete-time hybrid systems in the piece-wise affine form. By using arguments from the dissipativity theory for non-linear systems, we show that H X analysis and synthesis problems can be formulated and solved via linear matrix inequalities by taking into account the switching structure of the considered system. In this paper we address the generalized problem of controlling hybrid systems whose switching structure does not depend only on the state but also on the control input.     

Optimum design of linear multivariate sampled-data control systems†

This paper deals with the optimum design of linear multivariate sampled-data control systems,

Section 2 is concerned with the design of such control systems which are optimum on the basis of deadbeat performance. This design procedure is general and can be applied similarly to any deterministic inputs such as step, ramp, etc.

Section 3 is concerned with such control systems with respect to an integral form performance criterion. It is desired that the performance index takes the form of an integral, especially when the state variables of a control system are continuous with respect to time. For this reason, the minimum integral control is considered here.

The performance limits for such systems optimized for a deterministic input are considered in §4, and some interesting theorems are proved by using the w-transform.     

Exponential sampled-data control for T–S fuzzy systems: application to Chua's circuit

ABSTRACT

This study deals with the chaotic phenomenon of nonlinear Chua's circuit for power generator systems. Takagi–Sugeno (T–S) fuzzy model of a nonlinear system is established. By constructing a suitable Lyapunov functional, exponential stability conditions are obtained for fuzzy systems. Based on the sampled-data control theory, extreme sensitivity is visualised in the state trajectory depending on the initial conditions and sampled-data fuzzy controllers are designed in the form of linear matrix inequality (LMI). Finally, some numerical simulation results are shown that the sampled-data fuzzy control system adopts a well-designed methodology.     

Stability of aperiodic sampled-data systems — An augmented looped Lyapunov functional with wirtinger inequality approach

International Journal of Control, Automation and Systems - This paper is concerned with stability analysis of sampled-data systems with non-uniform sampling patterns. The stability problem is...     

Asymmetrical oscillations in non-linear sampled-data systems†

It is well known that in continuous systems, asymmetrical oscillations occur when the input-output characteristic of the non-linearity in the system is not symmetrical about the origin or when the system is subjected to forcing signals. In the case of sampled-data systems with integrating elements asymmetrical oscillations quite often occur even when the non-linearity is symmetric. To the best of the knowledge of the authors no analytical method to determine the bias component of the limit cycles is available in the technical literature. This paper presents a simple method for the quantitative estimation of the d.c. component of the limit cycles for a system of any order.     

Optimal design of sampled-data control systems by linear programming†

This paper is devoted to the design of digital compensators for a special class of fnite-settling-time, linear, sampled-data control systems which are required to track both step and ramp inputs with no steady-state error. A general procedure is given to design the digital compensator so that the system is optimum on the basis of the ITAE (integral of time-weighted absolute value of error) criterion, subject to the constraint that the peak overshoot of the system for a step input is less than a certain percentage. Linear programming is used to find the optimum solution. Suitable upper bounds are imposed on the variables involved so that the peak overshoot of the system for a unit step input may not exceed a given value. A method of incorporating a specification on the acceleration constant (K _a ) in the design is given, as also is a design example. For the case where finite settling time to a ramp input is not required, the design procedure is modified: a velocity constant (K _a specification is incorporated in the design in place of the K _a specification.     

A modified signal-flow graph for sampled-data systems†

A method of constructing a modified signal-flow graph, the H-graph, for sampled-data systems is formulated. This graph is obtained from the system graph by incorporating a maximum number of 3n edges for an n-sampler system, depending on the existence of paths between the input of the system and the samplers, and/or between the samplers. A set of rules to calculate the transmittances of these edges is framed. The transmittances of some of the edges in the system graph are modified. The output is obtained from the H-graph by Mason's formula. The concept of the signal-flow matrix has been extended to cover the sampled-data systems.     

Adaptive approach with the “Fast” model for dynamics identification and forecasting problems for relay control of an elastic satellite

We develop a physically implementable method of computer forecasting of the relay control dynamics for an elastic satellite given uncertain information about its elastic modes parameters. The method is based on preliminary identification of these parameters and further application of a simplified “fast” movement model, in which modes are replaced by their envelopes. Based on the forecasting results, one can decide upon adaptive tuning of the base control algorithm parameters.     

Convergence rate of least-squares identification and adaptive control for stochastic systems†

The strong consistency and the convergence rate of least-squares identification for the multidimensional ARMAX model are established under some decaying excitation conditions which are satisfied if both input and output do not grow too fast and the attenuating excitation technique is applied. The parameter-identification results are applied to adaptive-control systems with a quadratic loss function. The rate of convergence of the loss function to its minimum is also obtained.     

Mixed H∞ and passive control for linear switched systems via hybrid control approach

This paper investigates the mixed H_∞ and passive control problem for linear switched systems based on a hybrid control strategy. To solve this problem, first, a new performance index is proposed. This performance index can be viewed as the mixed weighted H_∞ and passivity performance. Then, the hybrid controllers are used to stabilise the switched systems. The hybrid controllers consist of dynamic output-feedback controllers for every subsystem and state updating controllers at the switching instant. The design of state updating controllers not only depends on the pre-switching subsystem and the post-switching subsystem, but also depends on the measurable output signal. The hybrid controllers proposed in this paper can include some existing ones as special cases. Combine the multiple Lyapunov functions approach with the average dwell time technique, new sufficient conditions are obtained. Under the new conditions, the closed-loop linear switched systems are globally uniformly asymptotically stable with a mixed H_∞ and passivity performance index. Moreover, the desired hybrid controllers can be constructed by solving a set of linear matrix inequalities. Finally, a numerical example and a practical example are given.