Experimental verification of SMC with moving switching lines applied to hoisting crane vertical motion control A. Nowacka-Leverton a,n , M. Micha"ek b , D. Pazderski b , A. Bartoszewicz a a Technical University of Lo ´dz ´, Institute of Automatic Control, Lo ´dz ´, Poland b Poznan ´ University of Technology, Chair of Control and Systems Engineering, Poznan ´, Poland article info Article history: Received 10 November 2011 Received in revised form 9 April 2012 Accepted 13 May 2012 Available online 12 June 2012 Keywords: Switching line design Sliding mode control State constraints Hoisting crane abstract In this paper we propose sliding mode control strategies for the point-to-point motion control of a hoisting crane. The strategies employ time-varying switching lines (characterized by a constant angle of inclination) which move either with a constant deceleration or a constant velocity to the origin of the error state space. An appropriate design of these switching lines results in non-oscillatory convergence of the regulation error in the closed-loop system. Parameters of the lines are selected optimally in the sense of two criteria, i.e. integral absolute error (IAE) and integral of the time multiplied by the absolute error (ITAE). Furthermore, the velocity and acceleration constraints are explicitly taken into account in the optimization process. Theoretical considerations are verified by experimental tests conducted on a laboratory scale hoisting crane. & 2012 ISA. Published by Elsevier Ltd. All rights reserved. 1. Introduction Position control of hoisting cranes and other cable-driven mechanisms have recently become an important research issue [5–7,13–15,17–19]. Hoisting cranes are widely present in the industry as well as in everyday life (for example lifts in high buildings). In many practical applications a reference set-point value of the crane payload should be achieved monotonically (without overshoots or oscillations) and as fast as possible, however subject to acceleration and velocity constraints. Position control of rope-suspended systems is also complicated by the fact that the suspension rope can exert only unidirectional force on the payload. Consequently, the rate of motion velocity change should not exceed the gravitational acceleration during the payload lowering in order to maintain positive tensions in cables and preserve forcing capability. Moreover, it is expected in practice that the properties mentioned above will be achieved in the presence of (bounded) model uncertainties or external disturbances. In this paper we present an application of the sliding mode technique [1,8–12,16,21] for a point-to-point motion control of a hoisting crane payload under parametric uncertainties of the system model. We consider two alternative control strategies, both of them employing time-varying sliding lines [2–4,20,22]. The lines are designed in such a way that the system representa- tive point on the phase plane belongs to them already at the initial time. As a consequence, the reaching phase is eliminated leading to robustness of the closed-loop system with respect to model uncertainties and external disturbances from the very beginning of the control process. We propose and compare alternative line synthesis procedures using two quality criteria. Design procedures proposed in the paper ensure that the accel- eration and velocity constraints imposed by a user are satisfied and the non-oscillatory, fast error convergence in the resultant control systems is obtained. At this stage it is worth to point out that dynamic properties of every control system operating in the sliding mode can be analysed with respect to two different time scales. The first one – called ‘‘fast motion’’ time scale – may be applied to analyse the system behaviour in any, even an infinitely small time period. With reference to this time scale the system velocity is a non-differentiable function of time and the system acceleration is undefined on any finite interval. This is because in any finite time period the control signal switches an infinite number of times between its two different values: the one generated when the switching variable is positive, and the other one obtained when this variable is negative. With reference to this time scale the system acceleration cannot be determined at any non-zero measure set, i.e. at any set of practical engineering importance. On the other hand, the second time scale – some- times called ‘‘slow motion’’ or macroscopic time scale – makes it possible to analyse the ‘‘average’’ system dynamics. With refer- ence to this time scale the system velocity is a differentiable function of time and the system acceleration indeed exists. These Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/isatrans ISA Transactions 0019-0578/$ - see front matter & 2012 ISA. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.isatra.2012.05.003 n Corresponding author. E-mail address: aleksandra.nowacka-leverton@p.lodz.pl (A. Nowacka-Leverton). ISA Transactions 51 (2012) 682–693