Linear Time-invariant Control Systems Research Articles

Suboptimal control of linear time-invariant systems subject to control structure constraints

A method is presented for designing controllers for linear time-invariant systems whose states are not all available or accessible for measurement and where the structure of the controller is constrained to be a linear time-invariant combination of the measurable states of the system. Two types of structure constraints are considered: 1) each control channel is constrained to be a linear, time-invariant combination of one set of measurable states; 2) each control channel is constrained to he a linear, time-invariant combination of different sets of measurable states. The control system, subject to these constraints is selected such that the resulting closed-loop system performs as near to some known optimal system as is possible, i.e., suboptimal. The nearness of the optimal system to the suboptimal system is defined in two ways and thus, two types of suboptimal controllers are found.

On the controllability of linear systems with delay in control

The controllability of linear time-invariant systems with a time delay in the control function is studied.

Suboptimal control of linear time-invariant systems with incomplete feedback

An algorithm is developed for determining a sub-optimal control of a linear time-invariant system with incomplete feedback. The set of admissible controls is constrained to be a constant linear feedback control of the system output. The merits of the control thus developed relative to that of known techniques are discussed, and two examples are solved to illustrate the method.

On the determination of the optimal constant output feedback gains for linear multivariable systems

The optimal control of linear time-invariant systems with respect to a quadratic performance criterion is discussed. The problem is posed with the additional constraint that the control vector u(t) is a linear time-invariant function of the output vector y(t) (u(t) = -Fy(t)) rather than of the state vector x(t) . The performance criterion is then averaged, and algebraic necessary conditions for a minimizing F\ast are found. In addition, an algorithm for computing F\ast is presented.

Suboptimal control of linear time-invariant systems subject to control structure constraints

Suboptimal control of linear time-invariant systems subject to control structure constraints

Testing the controllability of linear time-invariant systems

A method for studying the controllability of a linear time-invariant system by considering the controllability of a smaller subsystem is proposed. The method is most effective when the system under study has a large number of inputs and states.

Generation of sensitivity functions for linear systems using low-order models

New proofs are given for the recently demonstrated total symmetry and complete simultaneity properties for the companion canonic form for single-input linear time-invariant controllable systems. These proofs result in a convenient closed-form expression for the complete simultaneity property. The use of these properties to generate by one n th-order sensitivity model all the sensitivity functions \frac{\partialx_{i}}{\partialv_{j}}|_v^{0}, i=1,...,n, j=1,...,r, for a single-input linear time-invariant controllable n th-order system which depends on r different parameters is reviewed. This method represents an improvement over known methods for generating the sensitivity functions, which generally require a composite dynamic system of order n(r+1) . This result is then extended to the case of multi-input normal linear systems, where, at most, 2m-1 dynamic n th-order systems are needed in addition to the system to generate all the sensitivity functions of the system state with respect to any number of parameters ( m is the dimension of u ). It is shown that the algebraic calculations that must be made in the m -input case are much less than m times the calculations needed for the single-input case. The implications of these results for the computer aided sensitivity analysis of systems are discussed.

Sensitivity of an eigenvalue of a multivariable control system

A formula for the evaluation of the sensitivity function of an eigenvalue is proposed. The result is arrived at by consideration of the problem of sensitivity of an eigenvalue of a linear multivariable time-invariant control system subjected to parameter variations.