Showing papers by "Edward J. Davison published in 1972"

The output control of linear time-invariant multivariable systems with unmeasurable arbitrary disturbances

Abstract: Necessary and sufficient conditions are derived for a minimal order linear time-invariant differential feedback control system to exist for a linear time-invariant multivariable system with unmeasurable arbitrary disturbances of a given class occurring in it, such that the outputs of the system asymptotically become equal to preassigned functions of a given class of outputs, independent of the disturbances occurring in the system, and such that the closed-loop system is controllable. The feedback gains of the control system are obtained so that the dynamic behavior of the closed-loop system is specified by using either an integral quadratic optimal control approach or a pole assignment approach. The result may be interpreted as being a generalization of the single-input, single-output servomechanism problem to multivariable systems or as being a solution to the asymptotic decoupling problem.

Design of industrial regulators. Integral feedback and feedforward control

Abstract: A theory of control and observation for linear constant multivariable systems with constant disturbances is presented that leads to design methods for linear regulators of both integral feedback and feedforward types. The properties of systems having more control inputs than the minimum required to regulate the outputs (systems with redundant controls) are examined. It is shown that the independent use of such redundant controls confers no significant benefit. The design of dynamic observers appropriate for such systems is developed. Extensions to a wide class of analogous stochastic systems are indicated. Examples are presented to illustrate the methods used.

Solution of the exact model matching problem

Abstract: A more general exact model matching problem of linear multivariable systems using state or output feedback is considered. Two methods are given for solving this problem.

On the global controllability of perturbed controllable systems

Abstract: By using a recent theorem of Davison and Kunze [1], it is shown that, if certain conditions hold such that the system \dot{x} = A(x,t)x + B(x,t)u is globally controllable, then the perturbed system \dot{x} = [A(x,t) + \epsilon\tilde{A}(x,t)]x + [B(x,t) + \epsilon\tilde{B}(x,t)u , where \tilde{A} and \tilde{B} are bounded, is also globally controllable, provided e is small enough. In particular, if \dot{x} = A(t)x + B(t)u is controllable, then so is the perturbed system \dot{x} = [A(t) + \epsilon\tilde{A}(x,t)]x + [B(t) + \epsilon\tilde{B}(x,t)]u .

Two numerical techniques to solve differential game problems

Abstract: In this paper two computational techniques are presented, to solve non-linear differential games which have a value. It is assumed that there may be interaction in the dynamics of the players and that the conflicting index of performance of the game is a scalar function of the final state of the players of the miss-distance type. The first of these techniques is based on the Newton-Raphson method in function space in association with one of the two following non-iterative procedures to solve linear differential games with quadratic pay-off function : the generalized Riccati transformation or the transition matrix method. The second computational technique presented is based on the gradient of the Hamiltonian function with respect to the strategies. Some numerical examples are given to illustrate the methods.

Optimal control of linear time-invariant systems with polynomial-type measurable disturbances

Abstract: The optimal control of a linear time-invariant multivariable system with an integral quadratic index of performance and with measurable polynomial-type disturbances occurring in both the output and state derivative is considered in the paper. It is shown that the optimal control consists of a feedback controller and a feedforward controller. The feedback controller is the same feedback controller obtained when no disturbances are present, and an explicit expression is given for the feedforward controller. Some numerical examples are included to illustrate this optimal-control result.

A note on the simple modes of multivariable systems

Abstract: In this correspondence it is shown that, for any completely controllable and completely observable linear time-invariant multivariable system, there exists an output feedback law such that the closed-loop system has only simple modes. A constructive method for finding such an output feedback law is given.