LMI-based design of an I-PD+PD type LPV state feedback controller for a gantry crane

• Published in: Transactions of the Institute of Measurement and Control Vol. 41; no. 6; pp. 1640 - 1655
• Main Authors: Aktas, Ayhan, Yazici, Hakan, Sever, Mert
• Format: Journal Article
• Language: English
• Published: London, England SAGE Publications 01-04-2019; Sage Publications Ltd
• Subjects: Computer simulation; Control systems design; Control theory; Controllers; Convexity; Feedback control; Gantry cranes; L2 gain; Linear matrix inequalities; Mathematical models; Matrix methods; Optimization; Parameters; Performance indices; Pole placement; State feedback; Tracking control; gantry crane systems; linear parameter-varying systems; PID control; Anti-sway control; linear matrix inequalities; L2 gain
• ISSN: 0142-3312; 1477-0369
• DOI: 10.1177/0142331218785683

In this paper, an alternative gain-scheduled PID tuning procedure is proposed for gantry crane control systems. In order to avoid excessive overshoot and aggressive control action due to the proportional kick and/or derivative kick effects, an I-PD+PD type control law is considered. The scheduling parameter is considered the cable length due to the payload lifting and lowering movements. A linear parameter-varying (LPV) gantry crane model is constructed to enable gain-scheduled controller design with a linear matrix inequalities (LMIs) framework. Based on the LPV model, a convex optimization problem is formulized to minimize L2 gain under regional pole location constraints. Then, a fixed gain L2 gain state feedback I-PD+PD type controller and a conventional pole placement state feedback I-PD+PD controller are designed to investigate the efficiency of the proposed controller. A pole placement controller is tuned to minimize the very common ITAE (integral of time multiplied by absolute error) performance index. Simulation results show that the proposed controller has superior tracking performance under time-varying cable length, when compared with nominal fixed gain controllers.