Gain-scheduled output-feedback control of uncertain input-delay LPV systems with saturation via polytopic differential inclusion

Abstract

This paper examines the control design for parameter-dependent input-delay linear parameter-varying (LPV) systems with saturation constraints. A linear differential inclusion approach is implemented to formulate the saturation nonlinearity. Subsequently, a gain-scheduled dynamic output-feedback controller is structured to conform to the saturation representation. By means of a Lyapunov–Krasovskii functional, sufficient delay-dependent conditions are derived for the analysis and feedback control synthesis of the closed-loop system in the presence of uncertainties and exogenous disturbances. Disturbance rejection objectives following an induced ${\mathcal{L}}_2$-norm and an ${\mathcal{L}}_2-{\mathcal{L}}_{\mathrm{\infty }}$ norm formulation are examined. Estimation of the domain of attraction with the parametrisation of the admissible LPV controllers is presented. Three different optimisation objectives with respect to disturbance rejection, disturbance tolerance, and domain of attraction expansion are formulated. The proposed design methodology is examined in the context of the air-fuel ratio (AFR) regulation in a spark ignition (SI) engine with a speed-dependent delay and model parameters in the presence of canister purge disturbances and AFR dynamics uncertainty. The injector is restricted in the amount of fuel it can deliver to the cylinder. The three-way catalytic converter's performance in terms of oxygen storage and emission reduction is taken into consideration. Closed-loop simulation results are provided to validate the methodology.

Keywords:

• Linear parameter-varying (LPV)
• time-delay
• linear matrix inequalities (LMIs)
• actuator saturation
• domain of attraction
• differential inclusion
• spark ignition (SI) engines
• air-fuel ratio (AFR) control

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Saeed Salavati

Saeed Salavati earned his PhD in mechanical engineering from the University of Houston, Houston, TX, USA in 2021. He received his M.S. and B.Sc. degrees both in mechanical engineering from Amirkabir University of Technology in 2011 and 2008. His research interests include optimisation and health monitoring with applications to robust control of time-delay and linear parameter-varying systems, robotics, automotive and aerospace systems.

Karolos Grigoriadis

Karolos Grigoriadis is a professor at the University of Houston, Houston, TX, USA. He received his Ph.D. from Purdue University in 1994, his M.S. degree from Purdue University in 1989, and his B.Sc. degree in mechanical engineering from National Technology University of Athens in 1987. His research interests include dynamic systems and control, linear and nonlinear systems theory, robust and fault-tolerant control, and system optimisation.