The concept of signal dependent sampling is introduced into discrete-continuous control systems and a comparison has been made between periodic find signal dependent sampling systems. A sampling interval criterion is proposed and it is further shown how this imposes an auxiliary contraint on a discrete-continuous system. Performance surfaces in an object function-parameter space sire compared on the basis of the asymptotic equivalence of the non-linear signal dependent system and its linear periodic counterpart for a general second-order plant. A further comparison has been mode of the sampling requiremonts, necessary to minimize a particular object function, for the two different types of system.

An Analysis and Evaluation of Signal Dependent Sampling in Discrete-continuous Feedback Control Systems†

A study of feed back control systems with time-shared analogue elements is described. Continuous, ideal impulse commutated and finite pulse commutated systems have been compared for specific examples. Particular emphasis has been placed on the practical problem of reducing interaction between loops and in particular the effect of varying the commutation duration has been determined. A design procedure for time-sharing systems is suggested.

Multi-variable Time-shared Control Systems and the Reduction of Interaction†

The effects on the stability of continuous first and second-order systems due to pure time delays in the control loop are examined and stability boundaries are presented. Similar stability boundaries for sampled first and second-order systems are presented and compared against the boundaries for the continuous case. The effects of the time delay in a sampling system are further investigated in the z plane by means of root loci with time delay as parameter. Derivation of the root loci produce formulae which could be useful for synthesis on the z plane. Computational verification is presented throughout and from the analysis the advantages and disadvantages of having a sampler in a second-order system are considered.

The inter-relation of sampling and transport lag in determining control system stability

This paper addresses itself to an examination of the stability of a socond-order system having a periodically operated switch in its feedback loop. There is a discussion of the desirable form for stability plots and some thought is given to use of sub-Nyquist rate sampling. Rotations are derived for stability boundaries in terms of switch closure time, switch frequency and the parameters of the fixed portion of the system.

Stability of finite-width sampled-data systems†

In this, the second of two papers related to the non-linear properties of discrete-continuous control systems with signal dependent sampling constraints, results are presented which evidence their non-linear behaviour for simple transients. Furthermore, the concept of ‘deficiency’ has been extended to discrete properties associated with ‘discrete linearity’ in a series of ‘weaker’ definitions. Consideration has been given to the relationships with other systems and such concepts as the ‘deficiencies’ of continuous and discrete equivalence of systems have been defined. In addition, further consideration has been given to concepts relevant to modelling, for example, the pairing of discrete-continuous systems with other systems.

Non-linear Properties of Discrete-continuous Feedback Control Systems with Signal Dependent Sampling. Part II. Non-linear Properties†

This paper describes the practical problem of determining errors in the State vector resulting from the representation of a finite pulse width sampler by an impulse sampler in a sampled-data control system. It is shown that the response of the impulse sampling system is the limit of the response of the corresponding finite pulse width system with on associated gain factor, as the pulse width tends to zero. Conditions for the convergence of the errors in the state vector and the asymptotic equivalence of the two systems are; considered. Results show that this representation is only valid as long as the pulse width is small enough, otherwise the representation may result in appreciable errors.

C. P. Goh

Papers

A Determination of the Errors in the State Vector arising from the Impulse Representation of a Finite Pulse Width Sampled-data System†