Robust H2 Controller Design and Tuning for the Acc Benchmark Problem and a Real-Time Application

IEEE Trans. Contr. Syst. Technol.

2008

This brief presents a method for an automated generation of improved representations of linear parameter varying (LPV) systems, which is based on principal component analysis applied to typical scheduling trajectories. The procedure can help to reduce the conservatism in controller design by finding tighter regions in the space of scheduling parameters that contain the set of given trajectories. In addition, this method allows to determine approximations of LPV models with a reduced number of parameters and facilitates a systematic tradeoff between the number of parameters and the desired accuracy of the model. The proposed technique is illustrated by the application to a model of a two-link robot. Performance achieved with the controller designed using the reduced model is compared with those obtained by a robust control approach.

“…Using the scheduling signal data (9) to determine the parameter bounds (19) (20) and combining those in new vertex vectors , the sets…”

Section: Accuracy Of Approximation and Parameter Setsmentioning

confidence: 99%

Section: Illustrative Examplementioning

confidence: 99%

See 1 more Smart Citation

PCA-Based Parameter Set Mappings for LPV Models With Fewer Parameters and Less Overbounding

Kwiatkowski

IEEE Trans. Contr. Syst. Technol.

2008

“…Note that the rows of Σ s V T s represent the principal components of the data matrix Θ n , and that the approximate mappingsÂ(.),B(.),Ĉ(.),D(.) in (4) are related to (1) by (11) and N −1 denotes row-wise re-scaling. At any given time, (9) can be used to compute the reduced parameter vector φ(t), while (10) together with (11) can be used to generate the approximate LPV model.…”

Section: B Parameter Reduction Algorithmmentioning

confidence: 99%

“…It was possible to reduce the spectral radius to ρ(A k ) < 5 · 10 4 in only four iterations. To compare the performance of the LPV controller with that achievable with a fixed-gain controller, a robust controller was designed using a robust H 2 approach and K-S iteration [11] with quadratic S-scaling. The nominal und uncertainty models have been derived from a set of linearized models along the reference trajectory.…”

Section: Controller Designmentioning

confidence: 99%

LPV Control of a 2-DOF Robot Using Parameter Reduction

Kwiatkowski

Proceedings of the 44th IEEE Conference on Decision and Control

Abstract-This paper demonstrates the benefit of a new method for reducing the number of scheduling parameters of LPV controllers, by applying it to a robot manipulator. A full LPV representation of a planar two-link robot with ten scheduling parameters is considered. The number of parameters can be reduced by applying principal components analysis to typical scheduling trajectories. The proposed method enables a systematic trade-off between the number of reduced parameters and the desired accuracy of the model. The practicality of the approach is illustrated with a design example: an LPV controller, designed using a parameter reduced model, is shown in simulation studies to outperform a robust, fixed-gain controller designed to minimize the worst-case H 2 norm .

Mixed H₂/H_∞ robust output feedback sliding mode control

Juma

Optim Control Appl Methods

2011

Self Cite

SUMMARYThis paper presents an output feedback sliding mode control scheme for uncertain dynamical systems. The design problem is solved in two steps, involving first a state feedback and then an output feedback problem. First, using the null space dynamics, the sliding surface for the unmatched uncertainty is designed. Then, by tuning the sliding surface, a robust controller is constructed for the whole uncertainty; this problem takes the form of static-output feedback. Based on this, a dynamic output feedback controller for the system augmented with the sliding surface is designed. The synthesis involves the solution of an Linear Matrix Inequality (LMI) and Bilinear Matrix Inequality (BMI) problem; the BMI problem is solved iteratively. The proposed approach is illustrated by applying it to a well-known robust benchmark problem and also experimentally on a spring mass system with variable stiffness. Simulation and experimental results show that the proposed method outperforms previous approaches in terms of robust performance.