T. R. Crossley

Dead-beat control of sampled-data systems with bounded input

In this paper, a design procedure for the synthesis of dead-beat control policies for a class of sampled-data systems with bounded input is presented. The design algorithm is illustrated by a numerical example for a second-order system.

Properties of the mode-controllability matrix†

In this paper a number of important properties of the mode-controllability matrix of a linear continuous-time system are presented. It is shown that examination of the form of this matrix leads simply and directly to complete knowledge of the controllability characteristics of such a system.

Envelope curves to inverse Nyquist array diagrams

A numerical method for determining the envelope curves to a set of Gershgorin circles in a classical Inverse Nyquist Array diagram is presented. The use of these envelope curves reduces the amount of information displayed when computergraphic terminals are used in the design process. This reduction loads to significant savings in core-memory requirements if the computer terminal is of the refresh type and is not fitted with hardware for circular interpolation. In addition, the use of these curves ensures that only relevant design criteria are displayed, thus reducing the total information which is usually presented.

Generalized single-input modal control theory

A single-input modal control theory is developed whereby the loop gains of a single-input time-invariant multi-variable system may be calculated using simple formulae for the cases when both the open-loop plant matrix and the closed-loop plant matrix have a number of sets of distinct and confluent eigenvalues. The results may be applied in a sequential manner for multi-input systems with repeated sets of confluent eigenvalues provided that the appropriate mode-controllability conditions are satisfied. A number of illustrative examples are included.

Eigenvalue assignment in linear time-invariant closed-loop systems incorporating multi-variable three-term controllers†

In this paper a procedure for the design of feedback loops for a class of linear time-invariant systems is presented. These feedback loops contain multivariable three-term controllers whose parameters can be selected such that the matrix of the resulting closed-loop system can be assigned any prescribed set of eigenvalues.

A canonical form for a multivariable, multi-output linear control system†

A transformation procedure is developed for a completely observable, multi variable, multi-output, linear control system. The transformed system is made up of several simple sub-systems which have the output vectors and control input vectors of the original system as their inputs. The form of each sub-system is especially suitable for the design of a Luenberger observer

Modal design of continuous-time tracking systems

The mode-controllability structure of continuous-time tracking systems which are required to track polynomial vector command inputs of arbitrary degree is developed. It is shown that this structure provides a basis for the systematic design of the associated control policies.

Sequential synthesis of modal control policies for multi-input continuous-time systems

In this paper the computational complexities hitherto associated with the sequential synthesis of modal control policies for multi-input continuous-time systems are removed by the presentation of a set of new results concerning the eigenstructure of sequentially synthesized multi-input systems. The resulting design procedure is illustrated by considering a numerical example involving a sixth-order system with three control inputs.

An explicit form for the closed-loop system matrix of a partially uncontrollable linear system†

Abstract An explicit expression for the closed-loop system matrix of a partially uncontrollable linear system is presented. This matrix shows very clearly the eigenproperties of the closed-loop system and, in particular, the relationship between controllability and eigenvalue assignment.

Modal stochastic-response characteristics of multivariable linear systems†

A method is described which greatly facilitates the determination of the stochastic-response characteristics of a class of multivariable linear systems : the method is illustrated by the presentation of a, numerical example.