最小能量有限拍鲁棒控制系统的设计

本文采用2自由度控制器,以传递函数分式分解理论为基础,提出了一种在保证系统内部稳定和最佳鲁棒性前提下,实现最小能量控制的有限拍系统设计法。设计过程本质上是控制能量与响应时间的折衷。本文导出了折衷的最终界限,并给出了确定最佳响应时间的方法。     

Ripple-free deadbeat control for sampled-data systems

In this paper the ripple-free deadbeat control problem for sampled-data systems is considered. This control objective is to settle the error to zero for all time after some finite settling time, in other words to eliminate the ripples between the sampling instants in deadbeat control of sampled-data systems. The necessary and sufficient conditions to solve this problem are derived and related to the system type, and a method of constructing the ripple-free deadbeat control system is presented.     

Adaptive deadbeat control

An adaptive algorithm is presented to incorporate deadbeat control as a principle design criterion. Since this algorithm does not require the solution of the diophantine equation at each sampling step, it possesses a computational advantage over the existing deadbeat control approaches, and so is suitable for application to adaptive systems. The meeting of the internal stability requirement enables this algorithm to handle easily any stable or unstable, minimum or non-minimum phase system. By selecting the zero assignment of the sensitivity function the system can be made to track a class of changeable reference signals and exhibit a deadbeat response with minimum settling time. Some constraints on the transfer function make sure that the derived controller is realizable. The non-linear saturated system and the lathe system are simulated to illustrate the validity of the proposed design algorithm.     

Two-degrees-of-freedom dead-beat control system with robustness

This paper deals with the design of a two-degrees-of-freedom (TDF) dead-beat controller with both optimal robustness and minimum settling time. Based on the parametrization of all stabilizing TDF controllers, optimal robustness and minimum-time control are achieved simultaneously. The minimum-time dead-beat control is constructed for arbitrary real-rational reference input. At the same time, optimal robustness is achieved under the constraint that the error between reference input and output asymptotically vanishes for any plant perturbation that does not violate the internal stability. It is proved that under the same robustness criterion, irrespective of its length of settling time, the optimal robustness of the TDF system is always superior to that of the one-degree-of-freedom (ODF) system as long as its settling time is finite, and they become identical only when the settling time of the ODF system goes to infinity. A numerical example is given to illustrate the theoretical results.     

Deadbeat sampled system direct synthesis

A direct synthesis method is presented for obtaining a discrete compensator to produce a finite-settling-time transient in response to a prescribed input with no intersample transient terms after the finite settling time. The method is applicable to a single constant-frequency sampler in a feedback system with any type of hold for any polynomial input. The method uses a fictitious sampler at the output with sample timeT/mto scan the intersample times and to obtain criteria for deadbeat transients. The criteria are derived from root locus considerations but are applied to Laplace transforms containing both functions ofsand functions ofzso that the only operations are analytic ones.     

Deadbeat control with disturbance rejection

A deadbeat control problem with disturbance rejection is considered for a SISO discrete time plant. Disturbances are supposed to enter into the input to the plant and the output from the plant. The two-degree-of-freedom controllers are employed to internally stabilize the feedback control system, to make the output of the plant track a reference signal and to reject the disturbances in the sense of the deadbeat response. Necessary and sufficient conditions for the problem to have a solution are shown. And the set of all controllers meeting the design requirements are represented using two free polynomials.     

Parametrization of all ripple-free deadbeat controllers

This paper is concerned with deadbeat control in sampled-data systems. Deadbeat control achieves finite-time settling (deadbeat settling) at sampling instants, but there may exist error called ripple “between” sampling instants even after the response is settled “at” sampling instants. The objective of this paper is to give a parametrization of all ripple-free deadbeat controllers (controllers which achieve deadbeat settling without ripple) in sampled-data systems. It is also shown that the following holds in general: minimum-time deadbeat control causes ripple when the pulse transfer function to be controlled has stable zeros.     

Finite settling time stabilisation: the robust SISO case

This article deals with the problem of robustness to multiplicative plant perturbations for the case of finite settling time stabilisation (FSTS) of single input single output (SISO), linear, discrete-time systems. FSTS is a generalisation of the deadbeat control and as in the case of deadbeat control the main feature of FSTS is the placement of all closed-loop poles at the origin of the z-plane. This makes FSTS sensitive to plant perturbations hence, the need of robust design. An efficient robustness index is introduced and the problem is reduced to a finite linear programme where all the benefits of the simplex method, such as effectiveness, efficiency and ability to provide complete solution to the optimisation problem, can be exploited.     

Two-degree-of-freedom dead-beat control system with robustness: multivariable case

A design procedure for two-degree-of-freedom (TDF) dead-beat controllers for multivariable systems is presented. Based on the parametrization of all stabilizing TDF controllers, a minimal-time dead-beat control system with optimal robustness is constructed for an arbitrary reference input. The optimal robustness is achieved under the constraint of robust tracking. A comparison of a TDF system with a one-degree-of-freedom (ODF) system reveals that, under the same robustness criterion, the optimal robustness of the TDF system is always superior to that of the ODF system irrespective of its settling time. It is also shown that the optimal robustness of the ODF system becomes identical to that of the TDF only when the settling time of the ODF system goes to infinity. Some numerical examples are given to illustrate the theoretical results.     

State deadbeat control of nonlinear systems: Construction via sets

A geometric generalization of the discrete-time linear deadbeat control problem is studied. The proposed method to generate a deadbeat tracker for a given nonlinear system is constructive and makes use of sets that can be computed iteratively. For demonstration, derivations of the deadbeat feedback law and tracker dynamics are provided for an example system. Based on the method, a simple algorithm that computes the deadbeat gain for a linear system with scalar input is given.     

Optimal control for multi-stage and continuous-time linear singular systems

In this paper, optimal control problems for multi-stage and continuous-time linear singular systems are both considered. The singular systems are assumed to be regular and impulse-free. First, a recurrence equation is derived according to Bellman's principle of optimality in dynamic programming. Then, by applying the recurrence equation, bang-bang optimal controls for the control problems with linear objective functions subject to two types of multi-stage singular systems are obtained. Second, employing the principle of optimality, a equation of optimality for settling the optimal control problem subject to a class of continuous-time singular systems is proposed. The optimal control problem may become simpler through solving this equation of optimality. Two numerical examples and a dynamic input–output model are presented to show the effectiveness of the results obtained.     

Finite horizon optimal hybrid reference control for improving transient response of feedback control systems

Hybrid reference control (HRC) has been known to improve transient response of a stabilised closed-loop continuous tracking system. In this paper, an optimal HRC strategy, which minimises a finite horizon quadratic performance index in the control and state error, is investigated based on the assumption that the full plant states are available for measurement. A special case of constrained optimisation problems leads to the optimal deadbeat control strategy. Conditions for asymptotic stability to default reference signal are also derived.     

Double objective optimal multivariable ripple-free deadbeat control

This paper presents novel results on optimal multivariable deadbeat control. Given a discrete-time, stable, linear, time invariant plant model, we give a simple parameterization of all stabilizing ripple-free deadbeat controllers of a given order. The free parameter is then optimized in the sense that a quadratic index is kept minimal. The optimality criterion has the advantage of accounting for both tracking performance and magnitude of the control effort. The proposed design procedure is simple to use and allows the tuning of the controller with a scalar weighting factor. Simulation results are included to illustrate the effectiveness of the proposed design algorithm.     

Continuous-time deadbeat control for sampled-data systems

In this paper, the continuous-time deadbeat control problem for the sampled-data systems is considered. We derived the class of all controllers that achieve the continuous-time deadbeat control     

Minimal-time minimal-order deadbeat regulator with internal stability

This paper is concerned with the output deadbeat (finite settling time) regulation with internal stability for linear discrete-time multivariable systems. The two cases are treated separately; the one is the regulation by state feedback and the other is the regulation through function observers. For both cases, the basic solvability conditions, the minimal settling time and the characterizations of the minimal-time regulators are derived. Throughout the paper, the well-posedness condition plays a fundamental role. A deterministic version of the so-called separation theorem in LQG problem is derived, namely, the minimal-time state-feedback regulator combined with the minimal-time minimal-order function observer yields the overall minimal-time minimal-order regulator by output feedback.     

Robust ripple-free deadbeat control design

This paper deals with the design of ripple-free deadbeat controllers with performance or performance robustness optimized over controllers within a prescribed settling time. The performance objective of interest is the minimization of the maximum absolute tracking error. This leads to consider linfinity optimization problems. On the contrary, the optimization of the performance robustness leads to consider l1 optimization problems. An example is provided to illustrate the results.     

On the general solution of the state deadbeat control problem

In this note, the state deadbeat control problem is considered. It is shown that, after appropriate change of basis of input and state spaces, the general solution of the state deadbeat control problem can be expressed completely by the rows of the powers of system matrix. This result yields a very simple procedure for the calculation of a state feedback deadbeat control gain. It also provides the number of free parameters which could be used for further design purposes. The results are illustrated by an example at the end of the note     

Optimal ripple-free deadbeat control using an integral of time squared error (ITSE) index

This paper describes an optimal ripple-free deadbeat control strategy for single-input–single-output (SISO) linear sampled data plants. The cost function to be minimized is a linear combination of a time-weighted cumulative term that penalizes the tracking error, that is, an integral of time squared error (ITSE) cost term, and a cumulative term which penalizes the control signal deviations from its steady-state value. The optimization problem turns out to be convex, and closed-form solutions are obtained. An example is included to illustrate our results.     

The discrete linear time invariant time-optimal control problem—An overview

A review of two decades of investigation into one of the fundamental problems of control theory, the discrete linear time invariant time optimal control problem, is presented. Two classes of multi-input time optimal controller, one based on system controllability and the other on eigenvalue assignment, are considered in some detail. Also discussed are the dual state reconstruction problem, the deadbeat control of linear systems with inaccessible state, and other extensions. The exposition is a unifying one and involves only that matrix algebra commonly encountered in control theory.     

Jump linear quadratic Gaussian control in continuous time

The optimal quadratic control of continuous-time linear systems that possess randomly jumping parameters which can be described by finite-state Markov processes is addressed. The systems are also subject to Gaussian input and measurement noise. The optimal solution for the jump linear-quadratic-Gaussian (JLQC) problem is given. This solution is based on a separation theorem. The optimal state estimator is sample-path dependent. If the plant parameters are constant in each value of the underlying jumping process, then the controller portion of the compensator converges to a time-invariant control law. However, the filter portion of the optimal infinite time horizon JLQC compensator is not time invariant. Thus, a suboptimal filter which does converge to a steady-state solution (under certain conditions) is derived, and a time-invariant compensator is obtained