Sci.Int.(Lahore),27(6),5059-5064,2015 ISSN 1013-5316; CODEN: SINTE 8 5059 Nov.-Dec H INFINITY CONTROL OF A MECHANICAL SYSTEM WITH BACKLASH Musayyab Ali, Muhammad Abdullah Adnan Farooqi, Fahad Mumtaz Malik National University of Science and Technology Islamabad, Pakistan ( musayyabali@ymail.com x4xnation@yahoo.com malikfahadmumtaz@yahoo.com ) ABSTRACT—Backlash is a nonlinearity that occurs in a mechanical or a hydraulic system when two parts of that system are supposed to move together and there is an amount of space between the parts i.e.: Motor and Load Side. This non linearity is known to cause oscillations, inaccuracy and delays in the system. The performance of speed and position control is being affected by this non linearity. In this paper H infinity control approach has been selected to control the discretized model of the system with Backlash non linearity. Mechanical System operating in two modes, i.e. Contact Mode and Backlash mode. H infinity control design has been suggested to control the effect of this non linearity in the system. The robustness and good performance of the suggested control design has been compared with the performance of standard PID controller. By the comparison of results it has been found that the proposed controller is better and superior to PID controllers and other comparable linear controllers. Keywords - Backlash, H infinity control, Contact & Backlash Mode I INTRODUCTION Backlash is a common problem which occurs whenever the transmission link is disconnected between the driving and driven side.e.g; the drive train in cars, robot Arm and printing presses. The full control of a load in the presence of backlash is a tough task when better and error free results are desired. The control of systems with backlash has been the subject of study since 1940s.The importance of taking the backlash into consideration in the power train model is identified by (De La Salle et al.1999). Mechanical solutions are also been proposed for the system with backlash such as spring loaded split gear assemblies and dual motor systems.Both are much capable to handle the problem mechanically, but they are expensive, energy consuming and more importantly increase the weight of the system. So the best approach is to achieve backlash compensation without such mechanical devices. The H infinity control theory introduced by Zames is one of the advanced technique and with very wide and useful application in controls. H infinity control theory made a strong impact in the development of control systems in the decades of 1980 and 1990. H infinity techniques are of greater importance to deal with the multi variable systems. Whenever there is a need to minimize the closed loop impact of the disturbances, the H infinity control techniques used. The research made on the H infinity control is classified for the state feedback system and for the output feedback system as well. At first, it is noted that in the H infinity control of a discrete time system , although the suitable controller exist for it but cannot be called as strictly suitable controller. The main reason of focusing on the proper strict controller is because in the non-strict controller, there is a possibility of lack of robustness. Research is also being made on the continuous plant with a discrete H infinity controller or the discrete plant with the discrete time controller. In this paper, a discrete time H infinity state Feedback controller has been designed for the discrete plant with the help of stabilizing solution of Discrete Algebraic Ricatti equation. The Discrete time H infinity control problem with strictly proper measurement feedback is discussed in [1]. Robust H2 and H∞ infinity controller of Discrete Time systems with polytopic uncertainties via Dynamic Output Feedback [2]. Previously, continuous time or Sampled PI controller was known to be the most suitable especially in case of two mass systems [3]. Low order H infinity Controller design (By an LMI Approach) for the compensation of backlash non linearity in [4]. Design and Analysis of Robust H infinity controller discussed in [5]. Switched Hybrid Speed Control of Elastic Systems with Backlash discussed in [6]. Estimation of Backlash with application to Automotive Power trains is described in [7], but in this methodology the control requires estimation of backlash size. An Adaptive Control Approach for Improving Control Systems with Unknown Backlash is presented in [8]. A Benchmark on Hybrid Control of a Mechanical System with Backlash is proposed in [9]. Speed Control of Torsional Drive Systems with Backlash described in [10]. A structure Doubling Algorithm for Discrete Time Algebraic Ricatti Equation suggested in [11]. Particle swarm optimization based proportional integral and derivative (PID) controller design for linear discrete time system using reduced order model is described in [12]. Tuning P-PI and PI- PI controllers for electrical servos in [13].Design Method for control system are described in [14].Newton Method for DARE when a close loop system has eigen values on the unit circle suggested in [15]. Generalized Ricatti Equation for the full and reduced order mixed norm H2/H∞ standard problem discussed in [16] As compared to the strategies proposed above ([1]-[8]) and also with the performance of standard PID controller in the presence of disturbance and external noises, we designed the H infinity control for the system which guarantees the robustness and good performance. The advantages achieved by using this technique are, unaffected system output stability in the presence of external noises and disturbances, system achieved the preferred trajectory in quick time, high disturbance rejection, best transient response, absence of any limit cycle and steady state errors. The arrangement of rest of the paper is as follows, Section II presents the system Model equations and a state space model of both modes. Section III presents discretization of System. In Section IV H infinity control is introduced. In Section V the proposed control strategy is described. Section VI shows the graphs through simulations. Section VII the result has been discussed on the basis of simulation graphs. Finally in Section VIII the conclusion has been illustrated with the future work. II SYSTEM MODEL & EQUATIONS The Mechanical system is operating in two modes