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.     

Parametrization of all stabilizing controllers of nonlinear systems

We consider a nonlinear multiobjective optimal control problem, where a controller is to be designed such that a number of constraints are to be satisfied for all possible disturbances. We show that, under mild continuity assumptions, such a controller exists if and only if, for every weighted combination of the constraints, there exists a controller satisfying the weighted constraint.     

Self-tuning deadbeat controllers

A deterministic self-tuning deadbeat control scheme is presented which is extremely simple to implement in the single-variable and multivariable cases. Its convergence properties are analysed by straightforward application of de Larminat's convergence results.     

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.     

最小拍无波纹直流电机控制系统仿真研究

在单位阶跃、单位速度和单位加速度3种典型输入下对直流电机的最小拍无波纹控制进行了研究.Matlab仿真结果表明,最小拍无波纹控制,输出能较快的跟随输入,且跟随后能基本消除静差.最小拍无波纹控制应用在直流电机控制系统中,能够使电机的转速在最少个采样周期内跟随期望转速,使系统达到无静差的稳态,表明了最小拍无波纹控制能实现较高的控制品质.     

On deadbeat controllers

The possibility of achieving a deadbeat regulation and tracking in linear multivariable systems independently of their initial conditions is investigated. Necessary and sufficient conditions for the existence of various deadbeat controllers are established in a constructive way. A detailed analysis of the control sequence generated by any deadbeat controller is then presented.     

Minimum-gain minimum-time deadbeat controllers

This paper considers the design of minimum-gain minimum-time deadbeat controllers (MGMTDC) for linear discrete-time systems. A new direct method for constructing the MGMTDC of minimum Frobenius norm is developed. Compared with many existing techniques, the proposed method gives analytic expressions for the constructed MGMTDC, requires less computational effort, and does not require that the transition matrix be nonsingular.     

Explicit parameterization of state deadbeat controllers

A general state deadbeat control problem, not restricted to the controllability indexes, is posed and solved. A result for the explicit parameterization of deadbeat controllers is obtained. With the parameterization, only the genuine independent free parameters appear in the deadbeat controllers     

Multipurpose deadbeat controllers for multivariable systems

A simple and direct deadbeat control design algorithm for discrete-time multivariable systems is introduced. Our brief was to synthesize a realizable controller to achieve the following objectives: (1) input-output decoupling, (2) deadbeat tracking of any prespecified class of changeable deterministic reference signals and (3) changeable deterministic disturbances rejection where the changeable reference signals and disturbances can be different at each channel. Since the internal stability requirement is satisfied, our design algorithm can easily handle both unstable and non-minimum phase systems. Some constraints on the transfer function are also derived to make sure that the derived controller is realizable. Since all solutions can be described in parametric form, some of the performance criteria can be combined.     

Stabilizing and deadbeat properties of receding-horizon controllers

It is shown that receding-horizon controllers with horizon length N ≥ v (v being the controllability index of the system) stabilize a given discrete-time linear multi-variable system. Necessary and sufficient conditions for a receding-horizon controller to be a deadbeat controller are also given. It is further shown that by modifying a receding-horizon controller m of the poles of the closed-loop system (where m is the dimension of the input space) can be assigned to zero with simultaneous stabilization. The deadbeat properties of such modified receding-horizon controllers are also investigated,     

Parametrization of stabilizing controllers with integral action

In the standard linear time-invariant multi-input/multi-output unity-feedback system, a parametrization of stabilizing controllers with integral action is obtained. These controllers guarantee asymptotic tracking of step reference inputs at each output channel with zero steady-state error     

The design of deadbeat controllers by state transition graph

Two kinds of deadbeat control problems are considered. One is the state deadbeat control problem and the other is the pointwise minimum-time deadbeat control problem. A simple graph called the state transition graph of a matrix is introduced, and simple algorithms based on it giving deadbeat controllers are presented. The set of pointwise minimum-time deadbeat controllers is characterized. The set of output feedback deadbeat controller is also considered     

A note on parameterization of the class of deadbeat controllers

The problem of parameterizing the class of deadbeat controllers for a given discrete-time system through the minimum number of parameters was solved by Schlegel [1]. This note shows how to utilize the above solution to study some problems in designing deadbeat controllers. First, an algorithm is developed to compute a controller which minimizes-in an average sense-a given objective function. Second, a necessary and sufficient condition is given for the existence of an output deadbeat controller. Finally, the problem of parameterizing the set of deadbeat controllers for those systems transformable to the phase-variable block-canonical form is reconsidered.     

Parametrization of nonlinear stabilizing controllers: theobserver-controller configuration

The paper uses the author's (1996) previous results to develop the parametrization of nonlinear stabilizing observer-controller compensators of a given nonlinear system. The configuration described permits a simple parametrization of stabilizing controllers using coprime factorisation techniques     

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.     

Parameterization of the class of deadbeat controllers via thetheory of decoupling

A novel approach is presented for parameterizing the class of minimum-time deadbeat controllers (MTDC) through the minimum number of parameters. The approach is based on the theory of decoupling and the properties of square decouplable systems. The main result is a compact parametric form for the class of MTDC of a discrete-time system. Contrary to many existing techniques, no special assumption on the invertibility of the transition matrix is required     

Output deadbeat controllers with stability for discrete-time multivariable linear systems

This short paper Treats the problem of designing output deadbeat controllers having the property that the control input to the system converges to zero as time goes to infinity, for discrete-time multivariable linear systems. Two configurations of controllers are considered: one is of state feedback; the other is a dynamic controller using an observer. The existence of such controllers is examined, and the methods are presented for designing such controllers when they exist. The controller using a state feedback obtained in this paper is optimal in the sense that the controller settles the output in zero for any initial state in the minimum number of steps. On the other hand, the dynamic controller is not optimal in that sense, but it minimizest, wheretis defined as an integer such that the controller drives the output to zero in no more thantsteps for any set of initial conditions of the system and the observer.     

Parametrization of all minimal square spectral factors

Two different parametrizations of minimal square spectral factors are given. These parametrizations extend recent results by Picci and Pinzoni since they characterize spectral factors without specification on the zero or pole structure.     

Parametrization of stabilizing controllers for multivariable servo systems with two degrees of freedom

A necessary and sufficient condition for the existence of a servo controller is derived using the fractional representation approach for the plant, whose measured variables are not necessarily coincident with its controlled outputs. An independent parametrization of the servo controllers and the attainable transfer characteristics is proposed. The possible classes of all controllers with integrity in the error channel or measured output channel is also clarified using the derived parametrization.     

On the parametrization of all decentralized stabilizing controllers

A novel parametrization of all decentralized stabilizing controllers is provided in terms of a single parameter Q that is constrained to satisfy a finite number of quadratic equations. The results are presented in a general algebraic framework and apply to linear time-invariant systems. Implications of this parametrization for decentralized control system performance are also discussed.