For a class of robot arms, a proportional-derivative (PD) controller plus gravity compensation yields the global asymptotic stability for regulation tasks, and some proportional-integral-derivative (PID) controllers guarantee local regulation without gravity cancellation. However, these controllers cannot render asymptotic stability for tracking tasks. In this paper, a simple decentralized continuous sliding PID controller for tracking tasks that yields semiglobal stability of all closed-loop signals with exponential convergence of tracking errors is proposed. A dynamic sliding mode without reaching phase is enforced, and terminal attractors, as well as saturated ones, are considered. A comparative experimental study versus PD control, PID control, and adaptive control for a rigid robot arm validates our design.

Dynamic sliding PID control for tracking of robot manipulators: theory and experiments

A strategy is proposed to control Lorenz chaos, whereby a sliding surface is assigned such that a sliding mode motion occurs when the proposed control law is applied. The results show that only part of the system state can be regulated arbitrarily, due to the structure of the Lorenz system and the applied control variable. The paper also provides a further discussion on the resulting system behavior, which is not addressed in the literature.

Control of chaos in Lorenz system

The demand for high-precision stages has received great attention due to the progress of nano-technology in recent years. Systems to provide long-range and high-precision performance for positioning, tracking and contouring actions have become stringent issues. Among these systems, the ball-screw-driven systems have been widely used in industrial applications and academic researches. In such systems, the friction behavior dominates the resulting performance and is usually known as the stick-slip phenomenon. The friction dynamics can be divided into the static and the dynamic regimes according to the conventional usage. In this paper, friction models are introduced to describe the dynamic behavior of a conventional ball-screw-driven x – y stage. The coherence between the theoretical and experimental data supports the validity of these models. Two sets of controllers corresponding to the static and the dynamic friction models are proposed based on the integral type sliding mode control (SMC) law. Experimental results demonstrate that the system achieves high-precision (10 nm) and long-range (10 cm) positioning performance with repeatability and robustness by the proposed control approaches.

Modeling and high-precision control of a ball-screw-driven stage

This paper presents the analysis and control of active magnetic bearing (AMB) systems with a flexible rotor. A sliding mode controller design scheme is proposed to compensate for the nonlinear effects of the AMB system. A nonlinear model of the AMB system with an electromagnetic actuator and a flexible rotor is proposed to facilitate the present system analysis and controller design. This nonlinear model takes into account the dynamics of the flexible rotor, the characteristics of the nonlinear electromagnetic suspended system, and the contact force between the auxiliary bearing and the shaft. This study also considers the auto-centering control of the AMB system when subjected to disturbances and variations in the system parameters. The numerical results show that the system exhibits a periodic motion and demonstrates high accuracy and robustness when operating under sliding mode control.

Sliding mode control for active magnetic bearing system with flexible rotor

In this paper, a sliding mode controller is applied to control the cubic Chua’s circuit system. The sliding surface of this paper used is one dimension higher than the traditional surface and guarantees its passage through the initial states of the controlled system. Therefore, using the characteristic of this sliding mode we aim to design a controller that can meet the desired specication and use less control energy by comparing with the result in the current existing literature. The results show that the proposed controller can steer Chua’s circuit system to the desired state without the chattering phenomenon and abrupt state change.

Sliding mode control of chaos in the cubic chua's circuit system

The tracking control problem of robot manipulator is considered in this paper. A sliding mode controller design with global invariance is proposed using the concept of extended system and feedback linearization. The sliding surface is assigned such that the sliding mode motion will occur while the proposed control law is applied. This results in a system with global invariance. The stability and performance of the resulting system can be guaranteed by the proposed systematic design procedure.

Tracking Control of Robot Manipulator Using Sliding Mode Controller With Performance Robustness

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Tracking Control of Robot Manipulator Using Sliding Mode Controller With Performance Robustness