Given-Performance PID-SMC for 4-DOF Tower Crane Systems Under Input Constraints

Abstract

This paper focuses on the rapid jib and trolley positioning and payload sway suppression of the 4-degree of freedom (4-DOF) tower crane systems under uncertain system dynamics, external disturbances and control input constraints. A new adaptive proportional-integral-derivative sliding mode control (PID-SMC) method is proposed, which is model-free, does not need to linearize the system, and dispense with the uncertainty upper bound information required by traditional sliding mode control (SMC). In particular, a new time-varying scale function is used to constrain the system error to ensure the given-performance, that is, the actual transient-state and steady-state control performance of the system can be predetermined according to practical application requirements, and the quantified steady-state and transient-state properties of the 4-DOF tower crane system are obtained for the first time. In addition, although the actuator saturation upper bound is completely unknown the above mentioned given-performance can also be guaranteed by designing new parameter adaptive law. Finally, the effectiveness and superior performance of the control method are verified through rigorous theoretical analysis and experiments conducted on a 4-DOF tower crane platform. Note to Practitioners—The primary objective of this study is to tackle the challenges associated with rapid target positioning and effective suppression of swing in 4-DOF tower crane systems, amid presence of multiple practical problems. Traditional SMC strategies typically presume the prior knowledge of upper bounds for uncertainties—a condition that is seldom met in actual operations. Furthermore, their disregard for transient performance criteria further curtails their applicability in real-life scenarios. To overcome these limitations, we integrate an adaptive law for the estimation of previously indeterminable uncertainty boundaries. The incorporation of a performance function also allows us to impose stringent controls over both transient-state and steady-state performance, thereby enhancing operational efficiency and guaranteeing safety. Moreover, to address the issue of actuator saturation, this paper utilizes a parameter adaptive strategy that maximizes the utilization of the actuator’s potential without resorting to overly cautious presumptions regarding controller limits. In our future work, we plan to apply and validate this control methodology in actual tower crane applications.