A new approach for robust fixed-order Ifx;; controller design by convex optimization is proposed. Linear timeinvariant single-input single-output systems represented by a finite set of complex values in the frequency domain are considered. It is shown that the H 00 robust performance condition can be approximated by a set of linear or convex constraint~with respect to the parameters of a linearly parameterized controller in the Nyquist diagram. Multimodel and frequency-domain uncertainty can be directly considered in the proposed approach by increasing the number of constraints. The proposed method is compared with the standard Hoc control problem. It is shown by an example that for an unstable uncertain model a PID controller can be designed with the proposed approach which gives better H00 performance than a 7th order unstable controller obtained by the standardHoc solution.978-1-4244-3124-3/08/$25.00 ©2008 IEEE

In this paper we derive a reduced model, that is, a model in terms of independent generalized coordinates, for the equations of motion of closed-chain mechanisms. We highlight the fact that the model has two special characteristics which make it different from models of open-chain mechanisms. First, it is defined locally in the generalized coordinates. We therefore characterize the domain of validity of the model in which the mechanism satisfies the constraints and is not in a singular configuration. Second, it is an implicit model, that is, parts of the equations of motion are not expressed explicitly. Despite the implicit nature of the equations of motion, we show that closed-chain mechanisms still satisfy a skew symmetry property, and that proportional derivative (PD)-based control with so-called simple gravity compensation guarantees (local) asymptotic stability. We discuss the computational issues involved in the implementation of the proposed controller. The proposed modeling and PD control approach is illustrated experimentally using the Rice planar delta robot which was built to experiment with closed-chain mechanisms.

A new method for robust fixed-order H ∞ controller design by convex optimization for multivariable systems is investigated. Linear Time-Invariant Multi-Input Multi-Output (LTI-MIMO) systems represented by a set of complex values in the frequency domain are considered. It is shown that the Generalized Nyquist Stability criterion can be approximated by a set of convex constraints with respect to the parameters of a multivariable linearly parameterized controller in the Nyquist diagram. The diagonal elements of the controller are tuned to satisfy the desired performances, while simultaneously, the off-diagonal elements are designed to decouple the system. Multimodel uncertainty can be directly considered in the proposed approach by increasing the number of constraints. The simulation examples illustrate the effectiveness of the proposed approach.

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The consistency of identification methods for input-output models of Linear Parameter Varying systems is considered. In order to perform a consistency analysis the applicability of ergodicity is required, which is not obvious with these types of nonstationary systems. It is therefore shown that, when the scheduling parameter satisfies certain conditions, an ergodicity-type result can be applied to the signals considered. An analysis is then carried out for two cases: that of noise-free measurements of the scheduling parameter, and then the more realistic case of noisy scheduling parameter measurements. The latter is shown to be an errorsin-variables type problem. Since the least squares technique does not give consistent estimates, the instrumental variables method is proposed to achieve this property. The analysis carried out is reinforced by simulation results.

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Convex parameterization of fixed-order robust stabilizing controllers for systems with polytopic uncertainty is represented as an LMI using KYP Lemma. This parameterization is a convex innerapproximation of the whole non-convex set of stabilizing controllers and depends on the choice of a central polynomial. It is shown that with an appropriate choice of the central polynomial, the set of all stabilizing fixed-order controllers that place the closed-loop poles of a polytopic system in a disk centered on the real axis, can be outbounded with some LMIs. These LMIs can be used for robust pole placement of polytopic systems.