IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 56, NO. 6, JUNE 2009 1963 Constrained Model Predictive Control of the Drive System With Mechanical Elasticity Marcin Cychowski, Member, IEEE, Krzysztof Szabat, and Teresa Orlowska-Kowalska, Senior Member, IEEE Abstract—In this paper, the application of model predictive control (MPC) for high-performance speed control and torsional vibration suppression in the drive system with flexible coupling is demonstrated. The control methodology presented in this pa- per relies on incorporating the drive’s safety and physical lim- itations directly into the control problem formulation so that future constraint violations are anticipated and prevented. In order to reduce the computational complexity, the standard MPC controller is replaced by its explicit form. The resulting explicit controller achieves the same level of performance as the con- ventional MPC, but requires only a fraction of the real-time computational machinery, thus leading to fast and reliable im- plementation. The simulation results are confirmed by laboratory experiments. Index Terms—Constrained control, elastic couplings, industrial drives, model predictive control (MPC). I. I NTRODUCTION D RIVE SYSTEMS are a cornerstone of modern industrial processes including rolling-mills, conveyor belts, robot manipulators, and textile or paper machines [1]–[6]. These systems are typically composed of a motor coupled to a load machine through a metal shaft. Large inertias of the motor-load system together with a long shaft create an elastic system. The torsional characteristics of the mechanical coupling, which are often neglected in the drive control synthesis, greatly influence the torque transmission properties of the drive system and results in increased angular vibrations of the shaft. Excessive shaft twists and poorly damped torsional vibrations are detri- mental to the drive’s performance greatly compromising prod- uct quality and system reliability, and in some cases leading to instability and failure of the entire drive system [3]–[9]. The problem of suppressing torsional vibrations in two-mass drive systems has been a subject of extensive research efforts resulting in several different control proposals. In this group, proportional plus integral (plus derivative) [PI(D)] controllers are the most widely employed types of control solutions for modern electrical drive systems [1], [9]. These algorithms are simple, well established, and accepted by industry but lack Manuscript received August 30, 2008; revised February 9, 2009. First published February 27, 2009; current version published June 3, 2009. This work was supported in part by Enterprise Ireland under the Applied Research Enhancement Program (Grant RE/05/003). M. Cychowski is with the Department of Electronic Engineering, Cork Institute of Technology, Cork, Ireland (e-mail: marcin.cychowski@cit.ie). K. Szabat and T. Orlowska-Kowalska are with Wroclaw University of Technology, Institute of Electrical Machines, Drives and Measurements, 50-372 Wroclaw, Poland (e-mail: krzysztof.szabat@pwr.wroc.pl; teresa. orlowska-kowalska@pwr.wroc.pl). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIE.2009.2015753 the ability to shape the system speed response and suppress the torsional oscillations simultaneously. If high-performance closed-loop control is required, the application of additional feedbacks from selected state variables is necessary [6], [7], [9]–[13]. As shown in [9], the inclusion of one additional feedback control loop guarantees effective damping of torsional oscillations although shaping of the system speed response within a wide range of set points cannot be realized. These two objectives can be achieved by incorporating feedback loops from all system state variables (torsional torque, load speed, and disturbance torque) [6], [9], [12], [13]. A more detailed literature review on this topic can be found in [9] and [13]. In drive systems with significant parameter variations, more sophisticated control paradigms such as nonlinear or adaptive control can be adopted in order to achieve the required dynamic performance of the system [13]–[16]. In [7] and [15], sliding- mode control is demonstrated which achieves good dynamic properties and a satisfactory level of robustness to plant parame- ter variations. A strategy based on a self-tuning regulator and nonlinear Kalman filter is proposed in [13]. In this paper, the desired transient properties of the drive system are obtained by allowing for the simultaneous adaptation of the control law and the observer gain matrix. The application of neuro-fuzzy adap- tive control has been suggested in [14] demonstrating feasibility and good robustness properties. More detailed reviews can be found in [13]–[15]. In practice, all industrial processes are subject to constraints. Specific process variables must not violate specified bounds due to safety limitations, environmental regulations, consumer specifications, and physical restrictions [17], [18]. In two- mass drive systems for instance, the produced motor torque can only operate within its physical limits (imposed by the drive inverter) while the mechanical coupling must never be exposed to stresses exceeding the shaft’s ultimate tensile stress limit for safety reasons. While violating the electromagnetic torque constraint might in some applications be acceptable, exceeding the shaft torque constraint may result in damage to the shaft and ultimately in the failure of the entire drive system. Considering everything previously mentioned, it is surprising that this important practical problem has received very little attention from the drive control community. The main focus has primarily been on ensuring that the physical limitation of the motor torque variable (control input) is respected [13], [19]. An approach for direct torsion control based on the sliding-mode principle has been presented in [7]. In this paper, the torsion of the shaft (expressed as a difference between motor and load angular positions) is explicitly incorporated as a control variable. The drawbacks of the technique are the 0278-0046/$25.00 © 2009 IEEE