Optimal Walsh function input signals for parameter identification in identification systems. (English) Zbl 0568.93017
Orthogonality of Walsh functions is used to obtain independent parameter estimation equations for continuous-time dynamic systems. The conditioning of these equations is optimized by use of optimum inputs and is based on maximizing analytic nonlinear functions of Walsh coefficients. It is shown that an optimum data shift procedure can be used to optimize the estimation of time-delay and control gain.
MSC:
| 93B30 | System identification |
| 42C10 | Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) |
| 93C05 | Linear systems in control theory |
| 34K99 | Functional-differential equations (including equations with delayed, advanced or state-dependent argument) |
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
| 93B40 | Computational methods in systems theory (MSC2010) |
| 93C99 | Model systems in control theory |
References:
| [1] | Rao, G. P., Piecewise Constant Orthogonal Functions and Their Application to Systems and Control, (Lecture Notes in Control and Infomation Sciences (1983), Springer-Verlag: Springer-Verlag New York) · Zbl 0518.93003 |
| [2] | Bohn, E. V., Measurement of Continuous — Time Linear System Parameters Via Walsh Functions, I.E.E.E. Trans. Ind. Electron. Control Intrum., 38-46 (1982) |
| [3] | Mehra, R.; Lainiotes, D., System identification: Advances and Case Studies, (Mathematics in Science and Engineering, Vol. 126 (1976), Academic Press Inc: Academic Press Inc New York), 149-211 |
| [4] | Goodwin, G.; Payne, R., Dynamic System Identification: Experimental Design and Data Analysis, (Mathematics in Science and Engineering, Vol. B6 (1977), Academic Press Inc: Academic Press Inc New York), 124-157 · Zbl 0578.93060 |
| [5] | Bohn, E. V., Recursive Expressions for Evaluating Walsh Coefficients for Linear Dynamic Systems, Int. J. Systems Sci., Vol. 14, 673-682 (1983) · Zbl 0511.93034 |
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