Robust Control of the Two-mass Drive System Using Model Predictive Control

Abstract

A demand for the miniaturization and reducing the total moment of inertia which allows to shorten the response time of the whole system is evident in modern drives system. However, reducing the size of the mechanical elements may result in disclosure of the finite stiffness of the drive shaft, which can lead to the occurrence of torsional vibrations. This problem is common in rolling-mill drives, belt-conveyors, paper machines, robotic-arm drives including space manipulators, servo-drives and throttle systems (Itoh et al., 2004, Hace et al., 2005 , Ferretti et al. 2005, Sugiura & Hori, Y., 1996, Szabat & Orlowska-Kowalska, 2007, O’Sullivan at al. 2007, Ryvkin et al., 2003 , Wang & Frayman, 2004, Vasak & Peric, 2009, Vukosovic & Stojic, 1998). To improve performances of the classical control structure with the PI controller, the additional feedback loop from one selected mechanical state variable can be used. The additional feedback allows setting the desired value of the damping coefficient, but the free value of the resonant frequency cannot be achieved simultaneously (Szabat & OrlowskaKowalska, 2007). According to the literature, the application of the additional feedback from the shaft torque is very common (Szabat & Orlowska-Kowalska, 2007). The design methodology of that system can be divided into two groups. In the first framework the shaft torque is treated as the disturbance. The simplest approach relies on feeding back the estimated shaft torque to the control structure, with the gain less than one. The more advanced methodology, called Resonance Ratio Control (RRC) is presented in (Hori et al., 1999). The system is said to have good damping ability when the ratio of the resonant to antiresonant frequency has a relatively big value (about 2). The second framework consists in the application of the modal theory. Parameters of the control structure are calculated by comparison of the characteristic equation of the whole system to the desired polynomial. To obtain a free design of the control structure parameters, i.e. the resonant frequency and the damping coefficient, the application of two feedbacks from different groups of mechanical state variables is necessary. The design methodology of this type of the systems is presented in (Szabat & Orlowska-Kowalska, 2007). The control structures presented so far are based on the classical cascade compensation schemes. Since the early 1960s a completely different approach to the analysis of the system dynamics has been developed – the state space methodology (Michels et al., 2006). The application of the state-space controller allows to place the system poles in an arbitrary position so theoretically it is possible to obtain any dynamic response of the system. The