A new method for H-infinity gain-scheduled controller design by convex optimization is proposed that uses only frequencydomain data. The method is based on loop shaping in the Nyquist diagram with constraints on the weighted infinity-norm of closed-loop transfer functions. This method is applied to a benchmark for adaptive rejection of multiple narrow-band disturbances. First, it is shown that a robust controller can be designed for the rejection of a sinusoidal disturbance with known frequency. The disturbance model is fixed in the controller, based on the internal model principle, and the other controller parameters are computed by convex optimization to meet the constraints on the infinity-norm of sensitivity functions. It is shown next that a gain scheduled-controller can be computed for a finite set of disturbance frequencies by convex optimization. An adaptation algorithm is used to estimate the disturbance frequency which adjusts the parameters of the internal model in the controller. The simulation and experimental results show the good performance of the proposed control system.

Abstract-Frequency response function (FRF) measurements take a central place in the instrumentation and measurement field because many measurement problems boil down to the characterisation of a linear dynamic behaviour. The major problems to be faced are leakage-and noise errors. The local polynomial method (LPM) was recently presented as a superior method to reduce the leakage errors with several orders of magnitude while the noise sensitivity remained the same as that of the classical windowing methods. The kernel idea of the LPM is a local polynomial approximation of the FRF and the leakage errors in a small frequency band around the frequency where the FRF is estimated. Polynomial approximation of FRF's is also present in other measurement and design problems. For that reason it is important to have a good understanding of the factors that influence the polynomial approximation errors. This article presents a full analysis of this problem, and delivers a rule of thumb that can be easily applied in practice to deliver an upper bound on the approximation error of FRF's. It is shown that the approximation error for lowly damped systems is bounded by (BLP M /B 3dB ) R+2 with BLP M the local bandwidth of the LPM, R the degree of the local polynomial that is selected to be even (user choices), and B 3dB the 3 dB bandwidth of the resonance, which is a system property.

Abstract-

A new method for the design of fixed-structure dynamic output-feedback Linear Parameter Varying (LPV) controllers for discrete-time LPV systems with bounded scheduling parameter variations is presented. Sufficient conditions for the stability, H2 and induced l2-norm performance of a given LPV system are given through a set of Linear Matrix Inequalities (LMIs) and exploited for design. Extension to the case of uncertain scheduling parameter value is considered as well. Controller parameters appear directly as decision variables in the convex optimisation program, which enables preserving a desired controller structure in addition to the low order. Efficiency of the proposed method is illustrated on a simulation example, with an iterative convex optimisation scheme used for the improvement of the control system performance.

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