خود تنظیمی عصبی – فازی کنترل متناسب انتگرال مشتق شده (پی ای دی) برای مسیریابی نمایی بازوهای روباتیک Neuro-fuzzy self-tuning of PID control for semiglobal exponential tracking of robot arms

Effectiveness and simple model-free control structure are the principal characteristics that make PID controller be useful in several applications. Based only on state feedback, the PID control has been developed for regulation tasks principally, [1–۵]. The regulation of robotic arms, without linearization scheme, stands out from the overwhelming contributions in the literature on PID control. In particular, it has become the preferred option in the industrial floor for control of robot manipulators, [6]. To overcome the intrinsic uncertainties of the model commonly encountered in the robotic tasks, [7], some studies have provided the fundamentals for regulation without using the regressor nor any robot parameter, [8]. However, stability for the tracking case with a pure PID structure of non-linear plants, in particular for robotic arms, remains largely elusive in the literature. Additionally, to simplify the complex procedure of tuning constant feedback gains in the time domain for robotic arms, explicit rules rely onadvancedstability grounds [9], or in view of the lack of simple procedures knowledge-based schemes have been proposed as an alternative to tuning feedback gains on-line [10]. In this paper, we explore a novel idea to design a self-tuning PID controller for robotic arms to obtain exponentially semiglobal tracking, in the sense of Lyapuonov [11], even under affine unmodeled bounded exogenous disturbance and smooth joint friction. Using a typical passivity-based robot control approach [12,13], it is shown that the error equation can be stabilized in the extended error manifold in the sense of Lyapunov, where the nonlinear integral control term yields a smaller stable domain of attraction. In order to drive the error manifold to zero to ensure the tracking, a neuro-fuzzy network is proposed to extract the knowledge and tune a gain, avoiding any knowledge of robot dynamics, in contrast to [14,15], nor attempting to approximate inverse dynamics, [12]. This gain is used together a PID controller of constant gains, resulting in a self-tuning PID control based on a single feedback gain using a neuro-fuzzy scheme. This self-tuning gain in fact expands or contracts the domain of attraction where passivity is enforced to yield Global Uniformly Ultimately Bounded, GUUB. Once tracking errors are trapped in this domain of attraction,the tuning scheme is synthesized and an exponential convergence to the desired trajectory is enforced, as long as initial conditions belong to the compact set in the neighbourhood of the time-varying desired trajectory. In this sense our proposal extends, by simplifying, the involved neuro-fuzzy structure of [16–۱۸] such that the neuro-fuzzy tuning scheme enforces a dissipative mapping in terms of the error manifold by shaping the dissipation rate function to dominate the robot dynamics. This shows that a simple and intuitive fuzzy-based tuning rules keeps a model-free PID control structure to get tracking. This paper is organized as follows. A short background on self-tuning PID is presented in Section 2 to contextualize our contribution. Then, the proposal is given in Section 3, with the self-tuning policy presented in Section 4. Section 5 shows the main result and its stability analysis, with discussions and remarks in Section 6. Comparative experimental results are presented in Section 7, which highlights the viability and potential of the proposed approach in real robotic arms applications. Final conclusions are provided in Section 8.