A_New_Compensation_Technique_for_Backlash_in_Position_Control_Systems_with_Elasticity

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k from the motor side, combined with a load torque observer, has been suggested to prevent limit cycles [7,1 1]. A different approach [12] treats the nonlinear element as a linear gain plus a bounded worst-case disturbance, thereby reducing the problem to one of a linear plant with disturbance. QFT design method [8] is then applied to determine a controller. Since load side feedback is not used in both the approaches outlined above, load performance is limited by the amount of backlash in the system. As pointed out by Boneh and Yaniv [13], feedback from the load shaft is necessary to improve the tracking and disturbance rejection performance of the load. Since feedback from the load side tends to destabilize the system and cause oscillations, they suggest a nonlinear controller, which switches between two modes, depending on whether the backlash is active or not. Friedland [14] investigates a different switched mode controller, whose design is based on the state dependent algebraic Riccati equation (SDARE). Implementation of either of the switched controllers requires knowledge of the backlash dead zone width. The motion
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of a position control system represented by the two mass elastic model. The motor position feedback loop ensures good transient response, and an additional exponentially delayed load position feedback loop ensures steady state accuracy. Simulations are presented to demonstrate the performance of the new controller. A preliminary exploration of a similar controller in the context of nonelastic systems with backlash was first reported recently by the present author [10].
The presence of backlash causes steady state accuracy and stability problems in position and speed control systems. Switched and inverse nonlinear controllers have been suggested in the past to deal with these problems. The present paper proposes a simple linear controller to compensate for backlash in a two-mass elastic system. The efficacy of the new controller is demonstrated by simulations using the exact mathematical model of backlash recently proposed in the literature.
Abstract
1. Introduction
wherein the first mass represents the motor, the second mass represents the load, and the shaft is considered to be inertia-free, but can have finite stiffness and damping. Examples include robot arms [3] and rolling mills [4]. Both linear and nonlinear controllers have been proposed in the past to control position and speed in the presence of backlash. The describing function method, discussed in detail in classical nonlinear control textbooks [5,6], uses a quasi-linear approximation, and gives necessary conditions for the existence of limit cycles. Design of linear controllers by this method emphasizes the avoidance of limit cycles. Nordin and Gutman [1] compare three linear speed control designs based on the describing function method: standard PI control, PI control with load torque observer [7] and a controller designed by QFT (quantitative feedback technique) [8]. When system parameters are unknown, model reference adaptive control (MRAC) has been suggested [9] the approach here is to combine MRAC of the backlash-free (linear) case with a backlash inverse compensator, in an attempt to cancel the nonlinearity. In the present paper, a simple new linear control scheme is proposed which ensures good transient and steady state
M. Anand Mohan, Senior Member IEEE Electrical Engineering Department, Tuskegee University Tuskegee, AL 36088, USA
Keywords: Backlash compensation, nonlinear systems, position control
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39th Southeastern Symposium on System Theory Mercer University Macon, GA, 31207, March 4-6, 2007
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A NEW COMPENSATION TECHNIQUE FOR BACKLASH IN POSITION CONTROL SYSTEMS WITH ELASTICITY
2. Proposed Control Scheme
control industry practice in the USA is reported by Taal [15] to be the use of a special PID controller split into two loops, comprising of a proportionalderivative (PD) loop around the motor and an integrator (I) in the load position error path, to obtain zero steady state error to a step command input (provided the system retains its stability). This scheme is referred to as the 'modified dual loop PID controller'. The introduction of the integrator, of course, adds a phase lag of 90 degrees in the loop, and tends to cause oscillations / instability. The basic idea underlying the new controller being proposed in this paper is as follows. Feedback of motor position and speed (or equivalent) helps greatly in controlling the transient response. Steady state control of load position can be achieved by exponentially delayed introduction of load position feedback. The proposed scheme is depicted in the block diagram of Fig. 1, in which 'C' represents a cascade controller, 'M' represents the motor 'L' represents the load. The motor position (xm) feedback loop is designed to meet the transient response specifications (e.g., % overshoot and settling time). By passing the difference angle signal Xd =x - x1 through a timeconstant block, the feedback in the steady state is effectively equal to - Xm + If the time constant T = 0, (xm -xi) = it is as if the feedback were only On the other hand, as T tends to infinity, it is as if the feedback signal were only xm. Therefore, by choosing an appropriate finite value of the time-constant 'T' in the time-constant block, we should be able to achieve a desired trade-off between transient and steady state performances. The examples and simulations presented below will