Asymptotic properties of linear multivariable continuous-time tracking systems incorporating high-gain error-actuated controllers

In this paper, the asymptotic properties of tracking systems incorporating linear multivariable plants which are amenable to high-gain error-actuated control (Porter and Bradshaw 1979) are characterized in terms of the eigenstructure of the closed-loop plant matrices. It is shown that the closed-loop eigenstructure is such that the tracking behaviour of systems incorporating high-gain error-actuated controllers designed in accordance with the synthesis technique of Porter and Bradshaw (1979) is increasingly dominated by the modes associated with the first-order infinito characteristic roots as the gain is increased and that increasingly ‘ tight ’ control is therefore achieved. These theoretical results are illustrated in the case of a closed-loop system incorporating a third-order plant and a high-gain error-actuated controller by the presentation of the computed closed-loop eigenstructure and of the results of computer simulation studies.     

Minimum settling-time control policies for cascaded production-inventory systems

In this paper, the technique of entire eigenstructure assignment is used to derive minimum settling-time control policies for a class of production—inventory systems which can be described by linear multivariate discrete-time state equations. It is shown that this technique can be readily used to derive minimum settling-time control policies for production-inventory systems which consist of a set of production-inventory sub-systems connected in cascade. The advantage obtained by using control policies derived in this way, compared with control policies derived by consideration of each sub-system in isolation, is clearly demonstrated.     

Singular perturbation methods in the design of tracking systems incorprating inner-loop compensators and fast-sampling error-actuated controllers

Singular perturbation methods are used to exhibit the asymptotic structure of the transfer function matrices of discrete-time tracking systems incorporating linear multivariate plants which are amenable to fast-sampling error-actuated digital control only if extra plant output measurements are generated by the introduction of appropriate transducers and processed by inner-loop compensators. It is shown that these results greatly facilitate the determination of controller and transducer matrices which ensure that the closed-loop behaviour of such discrete-time tracking systems becomes increasingly non-interacting as the sampling frequency is increased. These general results are illustrated by designing a fast-sampling error-actuated digital controller for an aircraft.     

Control policies for production-inventory systems with bounded input

In this paper nearly time-optimal control policies are derived for a class of linear time-invariant models of production-inventory systems which comprise a cascade of basic production-inventory subsystems with bounded input. The sub-optimal control policies are obtained by constructing the sampled-data model of the production-inventory system where the sampling period is chosen to give the maximum control input for the given shipping rate. The theory is illustrated by the presentation of the results of simulation studies which show the transient behaviour of two production-inventory subsystems in cascade.     

Optimal control of production-inventory systems

Optimal policies for the pontrol of a class of production-inventory systems are derived. Typical response characteristics are presented which illustrate the effects of using different weighting parameter values in the performance cost functional.     

Design of production-inventory control systems incorporating fast-sampling control policies with implementation lead time

In this paper, singular perturbation methods are used to synthesize fast-sampling error-actuated control policies for two production-inventory system models in which there is a finite time delay of several sampling periods between the formulation and the implementation of the control policies. In the first model it is assumed that the demand for the product cannot be influenced by the management of the production-inventory system, and in the second model it is assumed that the demand for the product can be influenced by advertising and that the desired instantaneous demand rate is specified by management. In both cases, it is shown that the system will exhibit good transient and steady-state behaviour when controlled by such control policies. Furthermore, it is also shown that non-interacting control can be achieved when effective expenditure on advertising is introduced in order to influence the demand for the product, and that the provision of this extra flexibility thus leads to improved transient behaviour.     

Design of linear multivariable continuous-time tracking systems

In this paper, simple matricial methods are used to develop a basis for the design of multivariable continuous-time tracking systems which are generalized versions of classical single-input single-output servomechanisms.     

Design of linear multivariable continuous-time tracking systems incorporating error-actuated controllers

In this paper, the controllability results of Porter and Bradshaw (1974) are applied to the dosign of linear multivariable continuous-time tracking systems incorporating plants with inaccessible states for which appropriate error-actuated controllers exist. The design method is illustrated by the presentation of the results of computer simulation studies     

Singular perturbation methods in the synthesis of control policies for multi-stage production-inventory systems

In this paper, singular perturbation methods are used to synthesize control policies for a class of multi-stage production-inventory systems. It is shown that when the production-inventory sub-systems are connected in cascade, the control of each sub-system in isolation leads to undesirable transient behaviour. However, the control of the composite system is shown to yield improved transient behaviour. Furthermore, it is also shown that trade-off between rapid adjustments in production rate and large inventory-level deviation can be achieved by selecting an appropriate value for the feedback gain parameter.