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In this paper we propose a robust control scheme for a piezo-actuated nanopositioner to track arbitrary references. The positioner is represented as a linear system preceded by hysteresis, which is modeled with a Prandtl-Ishlinskii (PI) operator. In order to reduce the hysteresis effect, an approximate operator is used as a feedforward compensator. A sliding mode controller is then used to mitigate the effect of inversion error. In existing work on sliding mode control of piezo-actuated systems, the coefficient of the switching component of the control is typically chosen by trial and error. In contrast, in this work we analytically derive an upper bound on the inversion error using the hysteresis model. This bound is a function of the state and time, which is much less conservative than constant bounds. The stability of the closed-loop system is established by Lyapnuov analysis. Simulation and experimental results are presented to demonstrate the effectiveness of the proposed method.

The performance of the nonlinear control system that is subjected to uncertainty, can be enhanced by implementing an adaptive approach by using the robust output-feedback control and the artificial intelligence neural network. This paper seeks to utilize output feedback control for nonlinear system using artificial intelligence employing neural network. The Two Wheel Mobile Robot (TWMR) is treated as a multi-body dynamic system. The nonlinear swing-up problem is handled by designing an adaptive neural network, which is trained using a modified conventional controller called Linear Quadratic Optimal State Estimator with Integral Control (LQOSEIC). In this paper, the nonlinear system TWMR is stabilized utilizing a robust output feedback control called LQOSEIC. This controller allows a linearized model to emulate a model reference for the original nonlinear system. However, it works for a limited range of operations and will fail if the plant characteristics are unknown or uncertain. An adaptive neural network is used to overcome this problem. The adaptive neural controller is trained offline using LQOSEIC to obtain the initial weights of neurons for the network's hidden layers. After finishing the training, the LQOSEIC will be replaced by the adaptive neural controller. The main advantage of a neuro-controller is its ability to update the weights online depending on the error signal. If there are any disturbances or uncertainties that arises within the concerned nonlinear system, the neuro-controller will be able to handle it because of online learning that compensates for the effect of unpredictable conditions. The proposed adaptive neural network improves control performance and ensures the robust stability of the closed-loop control system. Finally, numerical simulations are used to demonstrate the efficacy of the proposed controllers.

Abstract-In this paper we introduce a new method for analyzing the closed-loop control system that involves a singularly perturbed plant preceded by hysteresis nonlinearity with piecewise linear characteristics, an example of which is a piezoactuated nanopositioners. Different methods are compared to quantify the tracking error and examine how the change in slopes from one segment to another interacts with the controller parameters and hence affects the tracking error. These methods all involve the combination of inverse hysteresis compensation and feedback control, but the points of insertion for the hysteresis inverse vary. A proportional-integral feedback controller is used throughout this comparison. The presented analysis is important because it provides an explicit expression for the tracking error, where the feedback controller parameters can be adjusted for the desired performance. Simulation and experimental results are presented for tracking control of a piezo-actuated nanopositioner, where the hysteresis is modeled with a Prandtl-Ishlinskii (PI) operator. The analysis carried out in this paper is applicable to other operators, such as the modified PI-operator and the Krasnoselskii-Porkovskii (KP) operator among others, since they all demonstrate piecewise linear hysteresis characteristics.

Analysis of closed-loop systems involving hysteresis is important to both the understanding of these systems and the synthesis of control schemes. However, such analysis is challenging due to the nonsmooth nature of hysteresis nonlinearities. In this paper, singular perturbation techniques are employed to derive an analytical approximation to the tracking error for a system consisting of fast linear dynamics preceded by a piecewise linear hysteresis nonlinearity, which is motivated by applications such as piezo-actuated nanopositioning. The control architecture considered combines hysteresis inversion and proportional-integral feedback, with and without a constant feedforward control. The analysis incorporates the effect of uncertainty in the hysteresis model, and offers insight into how the tracking performance depends on the system parameters and the references, thereby offering guidance in the controller design. Simulation and experimental results on a piezo-actuated nanopositioning system are presented to support the analysis. In particular, the control scheme incorporating the feedforward element consistently outperforms the classical PI controller in tracking a variety of references.