This chapter explores the development of deadbeat control and one-step-ahead control Deadbeat control and one-step-ahead control, each have a long history, the two were developed in separate research streams, and it was many years before these streams merged It compares and contrast deadbeat and one-step-ahead control strategies, to contribute to the unification of the two areas, and to clear up some possible points of confusion The chapter discusses that system identification, deadbeat control, and one-step-ahead control are possible because discrete-time systems are described by difference equations, which define an algebraic relation between the system inputs and outputs Such procedures cannot be applied to continuous-time systems, whose inputs and outputs are related by differential equations As a result, for example, deadbeat response in a continuous-time system cannot be achieved via linear time invariant feedback No matter how rapid the step response of a continuous-time control system is made, the exponentially decaying error vanishes only as time goes to infinity

Techniques in Deadbeat and One-step-ahead Control

This paper shows that the sensitivity of state feedback control systems can be re­ duced by additional state derivative feedback, for a fixed closed loop eigenstructure. The price of this sensitivity reduction is in general noise response amplification. Two indices which quantify stability robustness and response sensitivity are given for time invariant continuous time and discrete time systems, together with an index of response to disturbances and noise. Closed form expressions for the gradients of these indices are given. A two step design procedure is proposed which consists of first selecting a closed loop eigenstructure, then minimizing one of the sensitivity in­ dices under a magnitude constraint on the noise response. Examples are given to il­ lustrate this original design procedure.

Sensitivity reduction by state derivative feedback.

A connection between state-space and doubly coprime matrix-fraction descriptions of multivariable systems

In Chapters Two to Five we devote our attentions primarily to issues regarding parameter-sensitivity analysis. In spite of different uncertainties which may exist in a dynamical system, we expect that our controller will ultimately maintain qualitatively and/or quantitatively the overall system operation as desired. Or it will maintain this operation within a prespecified class of such operations which this is really the key issue in any robustness methodology. Therefore we must incorporate in control synthesis algorithm any information regarding possible discrepancies in system “output”, in order to generate new controllers that can stand against the consequences of some possible uncertainties. This incorporation is by no means a simple task, and before we let our expectations exceed our means, we examine some of our earlier assumptions and review the class of problems which currently can be analyzed.

Sensitivity Reduction and Robustness

This paper presents a control design procedure for linear time invariant systems using output proportional plus derivative feedback. The traditional linear quadratic performance index is used with additional terms to penalize disturbance and noise response and eigenvalue and response sensitivities. The sensitivity terms represent measures of stability robustness. It is shown that the derivative feedback improves the measure of performance. This design procedure has been applied to obtain an improved autopilot for the lateral dynamics of an L1011 aircraft.

Control of Linear Systems by Output Proportional Plus Derivative Feedback

A method is proposed for the design of constant-gain feedback-control laws for linear multivariable discrete-time systems which reduce trajectory sensitivity to small system parameter variations and ensure the closed-loop eigenvalues at the origin The given quadratic index of performance including a sensitivity term is minimized in an average sense An efficient computational procedure based on direct cost optimization using gradient type algorithm is also reported An example is worked out to illustrate the proposed technique

P. Pratapchandran Nair

Papers

On the design of a sensitivity-reducing optimal dead-beat controller