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In order to minimize steady-state error with respect to uncertainties in robot control, proportional-integral-derivative (PID) control needs a big integral gain, or a neural compensator is added to the classical proportional-derivative (PD) control with a large derivative gain. Both of them deteriorate transient performances of the robot control. In this paper, we extend the popular neural PD control into neural PID control. This novel control is a natural combination of industrial linear PID control and neural compensation. The main contributions of this paper are semiglobal asymptotic stability of the neural PID control and local asymptotic stability of the neural PID control with a velocity observer which are proved with standard weight training algorithms. These conditions give explicit selection methods for the gains of the linear PID control. An experimental study on an upper limb exoskeleton with this neural PID control is addressed.
Yu et al. (2012) studied this question.