Transactions of the Institute of Measurement and Control

Control engineering studies during the design of an industrial process frequently use simulation methods which require its operation to be represented in mathematical terms. This contribution reviews the salient features of various types of pumps and compressors encountered in such processes and presents models which embody these properties in a form suitable for use on a computer.

In general, these represent a compromise between the extremes of simplicity and rigour which has proved satisfactory in this context. Each application should, however, be the subject of engineering judgment on the degree of approximation which will be consistent with the quality of the data available and the objectives for which the simulation is being performed.

A solution is obtained to the infinite time optimal tracking problem for a multivariable system. The derivation is more direct than the usual approach through Parseval's theorem and it relates Hilbert space gradient techniques to the complex frequency domain.

where W * : Lⁿ ₂ (0, ∞) → L ^m ₂ (- ∞, ∞). By considering the properties of the impulse response matrix it may be confirmed that the system represented by the operator W * has a response (W*y) (t) existing for negative time, even though y is zero for negative time. It is clear that W * represents a non-causal system.

The paper analyses water distribution system pumping elements in order to derive models suitable for incorporation in network simulation and optimisation schemes. This includes derivation of an independent control variable to give simulated pump operation on a continuous or discrete basis allowing for head dependent flows. Derivation of the necessary conditions for operation at maximum efficiency are also presented. Typical pumping operations are investigated in order to develop and justify cost models for various optimisation techniques in terms of electricity charges.

The steps to be followed in the identification of process dynamics are developed logically. These steps cover experiment design, the use of physical laws and a priori knowledge, model structure determination, parameter estimation and model validation. The presentation is directed toward guiding the control engineer in industry to the intelligent use of the copious, well-documented supply of theory and case studies. Emphasis is laid upon techniques which have proven practical value.

The subject is dealt with in three parts, covered in three consecutive papers. Part I, published in the last issue, presented a method of calculating the coefficients required in digital algorithms for prediction (including interpolation and extrapolation), differentiation and integration, both on and off line. It provides the means of computing rapidly, by hand or with the aid of a small calculator, the coefficients required for algorithms of any order up to eight.

Parts II and III consider the errors inherent in using the algorithms derived in Part I and draw significant conclusions about the interaction of quantisation level, sampling frequency, order of the algorithm and the effects of these quantities on the accuracy of the results. Part II, which follows, deals with prediction and integration algorithms; Part III will deal with differentiation.

A method is shown for the design of series compensators for type 1 and type 0 control systems. It is based on the use of the contour of constant closed loop phase angle, α = - 90°, and assumes second order response specifications such as closed loop relative damping. The compensator parameters are determined from the intersection point of the open loop frequency response locus and a design curve which originates at a design point. The method yields directly an equivalent second order model which may be used to approximate the transient response of the compensated closed loop system.

A system is described which excites continuous oscillations in a resonator at two frequencies simultaneously. The resonator, typically in the form of a disc, can have modes which are close together in frequency and a double mode oscillator facilitates measurement of the difference in frequency. Such a measurement can be used to accurately determine Poisson ratio for the material of the disc. The resonator is excited by means of a nonlinear feedback loop which is designed to give stable double mode oscillations with frequencies close to the natural modes of the resonator. Several results from describing function theory are used to predict the behaviour of the system and the analysis is compared with the results of an analogue computer simulation.

The performance of multivariable non-linear stirred tank chemical reactor has been used to compare the practicability of an optimal controller and two types of suboptimal controller. The optimal controller, which by its nature required lengthy calculations, was suitable for open-loop control only and therefore sensitive to modelling errors. By contrast a suboptimal controller, which used the method of quasilinearisation to solve the two point boundary value problem, needed only a small amount of computation time and was capable of on-line implementation. This controller was much less sensitive to modelling errors, and also had the advantage of decoupling the control variables. An extension of this controller incorporated a feedback feature which compensated further for modelling errors and, in addition, unmeasured disturbances. This controller, which is expected to be of interest to the process industries facing inaccurate-model problems, produced responses close to the true optimal response even when the actual model used was in gross error.