H∞ Controller Design for Spectral MIMO Models by Convex Optimization

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. A simulation example illustrates the eﬀectiveness of the proposed approach. by a simulation example on an unstable system.

H-infinity Controller Design for Spectral MIMO Models by Convex Optimization

Gorka Galdos Sanz de Galdeano, Alireza Karimi, Roland Longchamp

A recent method for robust fixed-order H-infinty controller design by convex optimization proposed in [1] is investigated in this paper for the tuning of multivariable controllers. Linear Time-Invariant Multi-Input Multi-Output (LTI-MIMO) systems represented by a finite 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. Simultaneously, diagonal elements of the controller are tuned to satisfy the desired performances, while the off-diagonal elements decouple the system. Multimodel uncertainty can be directly considered in the proposed approach by increasing the number of constraints. An application example illustrates the effectiveness of the proposed approach.

2009

Robust fixed-order H infinity Controller Design for Spectral Models by Convex Optimization

Gorka Galdos Sanz de Galdeano, Alireza Karimi, Roland Longchamp

A new approach for robust fixed-order

H_\infty

controller design by convex optimization is proposed. Linear time-invariant 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 infinity robust performance condition can be approximated by a set of linear or convex constraints 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 H infinity 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 H infinity performance than a 7th order unstable controller obtained by the standard H infinity solution.

IEEE2008

Gain-Scheduled Controller Design by Linear Programming

Alireza Karimi, Marc Kunze, Roland Longchamp

A linear programming approach is proposed to tune fixed-order linearly parameterized gain-scheduled controllers for stable SISO linear parameter varying (LPV) plants. The method is based on the shaping of the open-loop transfer functions in the Nyquist diagram with constraints on the robustness margins and on the lower bound of the crossover frequency. Two optimization problems are considered: optimization for robustness and optimization for performance. This method directly computes an LPV controller from a set of frequency domain models in different operating points or from an LPV model and no interpolation is needed. In terms of closed-loop performance, this approach leads to extremely good results. However, closed-loop stability is ensured only locally and for slow variations of the scheduling parameters. An application to a high-precision double- axis positioning system illustrates the effectiveness of the proposed approach.

2007

Robust fixed-order H infinity Controller Design for Spectral Models by Convex Optimization

Gorka Galdos Sanz de Galdeano, Alireza Karimi, Roland Longchamp

A new approach for robust fixed-order

H_\infty

IEEE2008