Hybrid Input Shaping and Feedback Control Schemes of a Flexible Robot Manipulator Z. Mohamed*. M. A. Ahmad** * * Faculty of Electrical Engineering, Universiti Teknologi Malaysia, 81310 UTM Skudai, Johor, Malaysia (Tel: 607-5535290; e-mail: zahar@fke.utm.my) ** Faculty of Electrical Engineering, Universiti Malaysia Pahang, 25000 Kuantan, Malaysia (e-mail: ash_usc@hotmail.com) Abstract: This paper presents investigations into the development of hybrid control schemes for input tracking and vibration control of a flexible robot manipulator. A constrained planar single-link flexible manipulator is considered and the dynamic model of the system is derived using the assume mode method. To study the effectiveness of the controllers, initially a collocated PD control is developed for control of rigid body motion. This is then extended to incorporate input shaper control schemes for vibration control of the system. The positive and modified specified negative amplitude input shapers are designed based on the properties of the system. Simulation results of the response of the manipulator with the controllers are presented in time and frequency domains. The performances of the hybrid control schemes are examined in terms of level of input tracking capability, vibration reduction, time response specifications and robustness to parameters uncertainty in comparison to the PD control. Finally, a comparative assessment of the amplitude polarities of the input shapers to the system performance is presented and discussed. 1. INTRODUCTION The control strategies for flexible manipulator systems can be classified as feedforward and feedback control. A number of techniques have been proposed as feed-forward control strategies for control of vibration. These include the development of computed torque based on a dynamic model of the system (Moulin and Bayo, 1991), utilisation of single and multiple-switch bang–bang control functions (Onsay and Okay, 1991), construction of input functions from ramped sinusoids or versine functions (Meckl and Seering, 1990). Moreover, feedforward control schemes with command shaping techniques have also been investigated in reducing system vibration. These include filtering techniques based on low-pass, band-stop and notch filters (Singhose et al, 1995; Tokhi and Azad, 1996) and input shaping (Mohamed and Tokhi, 2002; Singer and Seering, 1990). To reduce the delay in the system response, negative amplitude input shapers have been introduced and investigated in vibration control. By allowing the shaper to contain negative impulses, the shaper duration can be shortened, while satisfying the same robustness constraint. A significant number of negative shapers for vibration control have also been proposed. These include negative unity-magnitude (UM) shaper, specified- negative-amplitude (SNA) shaper, negative zero-vibration (ZV) shaper, negative zero-vibration-derivative (ZVD) shaper, negative zero-vibration-derivative-derivative (ZVDD) shaper and time-optimal negative shaper (Mohamed et al, 2006; Rappole et al, 1993). On the other hand, feedback control techniques use measurements and estimates of the system states and changes the actuator input accordingly for control of rigid body motion and vibration suppression of the system. Several approaches utilizing closed-loop control strategies have been reported for control of flexible manipulators. These include linear state feedback control (Hasting and Book, 1990), adaptive control (Yang et al, 1992), robust control techniques based on H-infinity (Moser, 1993), variable structure control (Moallem et al, 1998) and intelligent control based on neural networks (Gutierrez et al, 1998) and fuzzy logic control schemes (Moudgal et al, 1994). This paper presents investigations into the development of hybrid control schemes for input tracking and vibration control of a single-link flexible manipulator. A constrained planar single-link flexible manipulator is considered. Hybrid control schemes based on feedforward with PD controllers are investigated. In this work, feedforward controls based on ZVDD input shapers with positive and modified SNA shapers are considered. To demonstrate the effectiveness of the proposed control schemes, initially a PD controller is developed for control of rigid body motion of the manipulator. This is then extended to incorporate the proposed input shapers for control of vibration of the manipulator. In terms of robustness, the hybrid control schemes are assessed with up to 30% error tolerance in vibration frequencies. This paper provides a comparative assessment of the performance of hybrid control schemes with different polarities of input shapers. 2. THE FLEXIBLE MANIPULATOR SYSTEM The single-link flexible manipulator system considered in this work is shown in Fig. 1, where X o OY o and XOY represent the stationary and moving coordinates frames respectively, τ represents the applied torque at the hub. E, I, Proceedings of the 17th World Congress The International Federation of Automatic Control Seoul, Korea, July 6-11, 2008 978-1-1234-7890-2/08/$20.00 © 2008 IFAC 11714 10.3182/20080706-5-KR-1001.1008