Designing controller parameters of an LPV system via design space exploration. (May 2021)

• Record Type: Journal Article
• Authors: Abolpour, Roozbeh; Dehghani, Maryam; Sadabadi, Mahdieh S.
• Is Part Of: European journal of control. Volume 59(2021)
• Page Start: 47
• Page End: 57
• Publication Date: 2021-05
• Subjects: Characteristic polynomial -- Design space exploration algorithm -- LPV system -- Undesired infeasible points -- Stabilizability; Control theory -- Periodicals; Automatic control -- Periodicals; Automatic control -- Mathematics -- Periodicals; Electronic journals; 629.805
• DOI: 10.1016/j.ejcon.2021.02.001
• Languages: English
• ISSNs: 0947-3580

Abstract

Highlights: The paper deals with design problem of LPV systems through directly exploring the primary design space. The LPV system affinely depends on two groups of parameters namely time-varying system's parameters and constant design parameters. The algorithm directly searches the primary design space to find a feasible solution that is capable to stabilize the model. To find the appropriate controller, the design space is iteratively divided until reaching a feasible solution. The algorithm is able to satisfy some convex or linear constraints on the model due to searching the design space. Abstract: This paper deals with the stabilizability problem of liner parameter varying (LPV) systems. It is assumed that LPV models affinely depend on time-varying uncertain and time-invariant design parameters. The uncertain parameters, their time-derivations, and design parameters belong to polygonal convex spaces. The stabilizability problem of such systems is studied. Extending the stability conditions to stabilizability conditions generally causes nonlinearity issues due to the coupling between the Lyapunov and design variables. To cope with this issue, a design space exploration algorithm (DSEA) is proposed to accurately determine the design parameters with a feasibility performance similar to stability analysis approaches. DSEA removes the undesired parts of the design subspace that cannot stabilize the model. Then, it checks the corner points of the remaining subspaces to find a stabilizing point. This procedure continues until a stabilizing point is found or the whole design subspaces are detected to be undesirable. Three hundred random LPV systems are generated to compare the feasibility performance of DSEA with existing approaches. Also, the proposed approach is used to stabilize the LPV model of a microgrid consisting of several distributed generation units and energy storage systems. The simulation results show the superiority of DSEA over the existing approaches.