Class Of Second-order Underactuated Systems Research Articles

Observer-Based Sliding Mode Control for a Class of Noncommensurate Fractional-Order Systems

This paper investigates an application of fractional theory for control and state estimation for a class of noncommensurate systems. A single-link flexible manipulator is considered as a representative example of this class of second-order underactuated systems. A fractional model is proposed and validated experimentally. The fractional-order sliding mode control is synthesized using a novel stable fractional surface. A fractional sliding mode observer is designed for state estimation necessary for implementing the control. The proposed method is validated through simulation and experimentation both.

Comment: Design of a stable sliding-mode controller for a class of second-order underactuated systems

In the above paper [1], additional conditions are required for the sliding-mode parameters to avoid the singularity, and some of simulation results do not match up to the theoretical one. In the following remark, the conditions for the controller in [1] to avoid singularity are given.

Adaptive hierarchical sliding mode control for ball-beam systems

Ball-beam system is one of the most enduringly popular and important laboratory models for teaching control systems engineering. It is very simple to understand as a system, but there exist strong non-linearities and dynamic couplings to illustrate control methods and control concepts. It belongs to a class of second-order under-actuated systems with gravity term and two degrees of freedom. The methodology of hierarchical sliding mode control (SMC) is developed for the class. But it excludes the ball-beam system due to its special dynamic model. In this paper, an adaptive hierarchical SMC law is addressed for the class. By modifying the expression of the hierarchical SMC, the presented method is able to cover the special case. The adaptive law and the control law are deduced from Lyapunov direct method. The asymptotic stability of all the sliding surfaces is proven by Barbalat’s lemma and Lasalle’s invariance principle. Simulation results show the feasibility of this method by stabilisation control of a b...

Reply: Comment on Design of a stable sliding-mode controller for a class of second-order under-actuated systems

Reply: Comment on Design of a stable sliding-mode controller for a class of second-order under-actuated systems

Comment: Design of a stable sliding-mode controller for a class of second-order underactuated systems

The fallacies of a paper by Wang et al. concerning the stabilisation of a class of second-order underactuated systems are pointed out.

Design of a stable sliding-mode controller for a class of second-order underactuated systems

A stable hierarchical sliding-mode control method for a class of second-order underactuated systems is presented. The ideas behind the method are as follows. First, the underactuated system is divided into two subsystems. For each part a first-level sliding surface is defined. For these two first-level sliding surfaces, a second-level sliding surface is defined. The sliding-mode control law is derived using Lyapunov law. The control law can drive the subsystems toward their sliding surfaces and attain their desired values, and implement antidisturbance control. The asymptotic stability of all the sliding surfaces is proved theoretically, and simulation results show the controller's validity and its adaptive abilities for all kinds of extraneous disturbances.