Backlash Compensation in Discrete Time Nonlinear Systems Using Dynamic Inversion by Neural Networks

A dynamics inversion compensation scheme is designed for control of nonlinear discrete-time systems with input backlash. The compensator uses backstepping technique with neural networks (NN) for inverting the backlash nonlinearity in the feedforward path. The technique provides a general procedure for using NN to determine the dynamics preinverse of an invertible discrete time dynamical system. A discrete-time tuning algorithm is given for the NN weights so that the backlash compensation scheme becomes adaptive, guaranteeing bounded tracking and backlash errors, and also bounded parameter estimates. A rigorous proof of stability and performance is given and a simulation example verifies performance. Unlike standard discrete-time adaptive control techniques, no certainty equivalence (CE) assumption is needed. 1 Introduction Robotic systems often have nonlinearities in the actuator such as deadzone, backlash, saturation, etc. This includes xy-positioning tables, robot manipulators, overhead crane mechanism, and more. The deadzone characteristic is a non-smooth nonlinearity, which models diverse physical imperfections: biases to prevent inflow-outflow or heating-cooling overlaps, aggregate effects of dry friction, etc. The difference between toothspace and tooth width in mechanical system is known as backlash and it is necessary to allow two gears mesh without jamming. Any amount of backlash greater that the minimum amount necessary to ensure satisfactory meshing of gears can result in instability in dynamics situations and position errors in gear trains. In fact, there are many applications such as instrument differential gear trains and servomechanisms that require the complete elimination of backlash in order to function properly. Saturation and friction are among other nonlinearities frequently present in robotic actuator dynamics. Our main concern is backlash. In most applications the backlash parameters are unknown, which represent a challenge for the control design engineer. Proportional-derivative (PD) controllers have been observed to result in limit cycles if the actuators have deadzone or backlash. To overcome the PD controller limitations, several techniques have been applied to compensate for the actuator nonlinearities. These techniques include adaptive control, fuzzy logic and neural networks. Recently, in seminal work rigorously derived adaptive schemes have been given for actuator nonlinearity compensation [20]. Backlash compensation is addressed in [21]. For dynamic system in the Lagrangian form, deadzone compensation using neural networks is given in [18]. Many systems with actuator nonlinearities such as deadzone and backlash are modeled in discrete time. An example of deadzone in biomedical control is the functional neuromuscular stimulation for restoring motor function by directly activating paralyzed muscles [2]. Moreover, …