A survey of simple transfer-function derivations from high-order state-variable models

The problem of the derivation of simple transfer function models from high order state variable models is reviewed. Methods of reduction are classified according to whether they involve 1.(a) the computation of the time or frequency responses 2.(b) the derivation, as an intermediate step, of a transfer function which is the ratio of two polynomials, the denominator being of the same order as the state variable model, or 3.(c) a set of characterising functions. Particular reduction methods considered are those based on fitting the step or frequency responses, on determining the intermediate, high order transfer function and reducing it by continued fraction expansion and on fitting the moments of the impulse response. An example illustrating these methods is given. The form of the simple model, the criteria of goodness of fit and the practical difficulties involved in the use of these methods are discussed.

[1]  N. Midoux,et al.  Note on a method of fitting a two-parameter distributed model to an experimental residence time distribution: Application to gas flow in gas-Liquid packed column , 1970 .

[2]  S. C. Chuang.  Application of continued-fraction method for modelling transfer functions to give more accurate initial transient response , 1970 .

[3]  H. H. Rosenbrock,et al.  Transfer matrix of a linear dynamic system , 1965 .

[4]  J. H. Anderson,et al.  Reply: Geometrical approach to reduction of dynamical systems , 1967 .

[5]  F. Lees.  The derivation of simple transfer function models of oscillating and inverting processes from the basic transformed equations using the method of moments , 1971 .

[6]  Naresh K. Sinha,et al.  A new method for reduction of dynamic systems , 1971 .

[7]  C. Sanathanan,et al.  Transfer function synthesis as a ratio of two complex polynomials , 1963 .

[8]  C. F. Chen,et al.  An algebraic method for control systems design , 1970 .

[9]  F. Lees,et al.  Coupling between the liquid flow and liquid concentration responses in unsteady-state plate distillation and gas absorption column models , 1971 .

[10]  H. Wall,et al.  Analytic Theory of Continued Fractions , 2000 .

[11]  L. G. Gibilaro.  Models for mixing in stirred vessels , 1967 .

[12]  M. Matsubara.  On the equivalent dead time , 1965 .

[13]  Denis Royston Towill,et al.  Transfer Function Techniques for Control Engineers , 1970 .

[14]  R. J. Altpeter,et al.  INVERSE RESPONSE IN PROCESS CONTROL , 1962 .

[15]  L. Gibilaro,et al.  A generalization of the tanks-in-series mixing model , 1968 .

[16]  E. C. Levy.  Complex-curve fitting , 1959, IRE Transactions on Automatic Control.

[17]  J. C. Orcutt,et al.  Axial dispersion and heat transfer in liquid‐liquid spray towers , 1967 .

[18]  C. F. Chen,et al.  A novel approach to linear model simplification , 1968 .

[19]  Charles Donald Holland.  Unsteady State Processes with Applications in Multicomponent Distillation , 1967 .

[20]  B. A. Buffham,et al.  A probabilistic time delay description of flow in packed beds , 1970 .

[21]  F. P. Lees,et al.  Correspondence item: The determination of transfer functions from state variable models , 1972 .

[22]  F. P. Lees,et al.  The determination of the moments of the impulse response of chemical processes from the basic transformed equations , 1969 .

[23]  Jr. B. Morgan.  Sensitivity analysis and synthesis of multivariable systems , 1966 .

[24]  Walter R. Evans,et al.  Control-system dynamics , 1964 .

[25]  D. Faddeev,et al.  Computational Methods of Linear Algebra , 1959 .

[26]  Chih-fan Chen,et al.  Elements of control systems analysis , 1968 .

[27]  E. Davison,et al.  On "A method for simplifying linear dynamic systems" , 1966 .

[28]  L. Meier,et al.  Approximation of linear constant systems , 1967, IEEE Transactions on Automatic Control.

[29]  Naresh K. Sinha,et al.  Optimum approximation of high-order systems by low-order models† , 1971 .

[30]  P. Payne.  An improved technique for transfer function synthesis from frequency response data , 1970 .

[31]  R. Nagarajan.  Optimum reduction of large dynamic system , 1971 .

[32]  Simple methods for identifying linear systems from frequency or time response data , 1971 .

[33]  Z. Mehdi,et al.  ‘Prediction of the Transient Response Sensitivity of High Order Linear Systems Using Low Order Models’ , 1970 .

[34]  D. Faddeev,et al.  Computational methods of linear algebra , 1959 .

[35]  Peter Harriott,et al.  Process Control , 1964 .

[36]  Leon Lapidus,et al.  Digital computation for chemical engineers , 1962 .

[37]  Chi-Tsong Chen.  A formula and an algorithm for continued fraction inversion , 1969 .

[38]  Determination of Relative Variance and Other Moments for Generalized Flow Networks or System Transfer Functions , 1970 .

[39]  Ernest F. Johnson.  Automatic Process Control , 1958 .

[40]  F. P. Lees,et al.  The reduction of complex transfer function models to simple models using the method of moments , 1969 .