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978-3-86853-954-7, Reihe Ingenieurwissenschaften
Identification of Linear Parameter-Varying Input-Output Models
141 Seiten, Dissertation Technische Universität Hamburg-Harburg (2011), Softcover, A5
This thesis focuses on the identification of Linear parameter-Varying (LPV) input-output models. Three problems are considered: the approximation of the nonlinear scheduling function of LPV systems, the unbiased identification of LPV systems, and the state-space realization of LPV input-output models.
The approximation of the nonlinear scheduling function of LPV systems is conducted by using cubic spline basis functions which are more easily tunable and less oscillatory than polynomial functions. A Separable Least-Squares (SLS) algorithm is proposed to reduce the number of parameters by separating them into linear and nonlinear parameters. Moreover for unstable systems, models are identified in closed-loop by using a two-step method with a neural network as a noise filter. Simulation and experimental results are given; they demonstrate the efficiency of the presented approach.
Concerning the unbiased identification of LPV systems, the bias error is reduced by using the "instrumental variable with auxiliary model" method. To improve the performance while still maintaining simplicity, an auxiliary model with output error structure, which is estimated by the output error method, is used. The proposed approach gives a significant improvement in terms of bias error and variance. A comparison with an existing method is illustrated with several simulation examples.
A state-space realization of LPV input-output models using a Linear Time-Invariant (LTI) framework introduces undesired dynamic dependence on the parameters. To solve this problem, the identification of LPV systems in a Left Polynomial Representation (LPR) is proposed. By using skew polynomials, a systematic realization procedure for LPV systems is presented. The resulting state-space models involve only static dependence on the scheduling parameters and are in observable form and minimal. Therefore standard LPV controller synthesis techniques can be used without loosing closed-loop performance. The efficiency of the proposed method is demonstrated by applying it to a laboratory scale magnetic levitation plant and an arm-driven inverted pendulum.