Robust gain-scheduling H∞ control of uncertain continuous-time systems having magnitude- and rate-bounded actuators: An application of full block S-procedure

• Published in: Journal of the Franklin Institute 2021-10, Vol.358 (16), p.8226-8249
• Main Authors: Kucukdemiral, Ibrahim B., Yazici, Hakan
• Format: Article
• Language: English
• Subjects: Actuators; Algorithms; Attenuation; Conservatism; Continuous time systems; Control methods; Feedback control systems; Gain scheduling; H-infinity control; L2 gain; Norms; Robust control; Sea vessels; Signal processing; Slew rate; Studies; Time varying control systems
• ISSN: 0016-0032; 1879-2693; 0016-0032
• DOI: 10.1016/j.jfranklin.2021.08.017

This paper addresses a novel robust gain-scheduling(GS) state-feedback (SF) H∞ (induced L2) control method for uncertain continuous-time(CT) systems having actuators with hard rate and magnitude bounds. The proposed method relies on acceleration form representation of the uncertain CT system. The technique enables the user to represent the control signal and its slew rate as auxiliary outputs along with the main controlled output. Two different norms, namely the induced L∞ and L2 are used to control the system effectively. While the L∞ gain from the exogenous disturbance inputs to the control signal related outputs is used to deal with actuator saturation problem, L2 gain from the disturbance inputs to the performance outputs is utilised in attenuation of the effects of the disturbances. To achieve these goals with minimal conservatism, we develop new forms of dilated Matrix Inequality (MI) conditions for peak-to-peak gain and L2 gain with no additional conservatism. Then, we propose a novel robust GS control methodology to deal with the problem via dilated MIs and a modified full block S-procedure method (MFBSPM). The utilisation of MFBSPM ensures that the robust control design method of this note applies to any uncertain system having rational parameter dependence. Finally, the efficiency of the presented method is portrayed through extensive simulations of the responses of a marine vessel to wave excitations in which the vessel model is assumed to have magnitude and rate limited active fin stabiliser.