Chattering-Free Reference Sliding Variable-Based SMC

The paper addresses the problem of chattering elimination in sliding mode control for sampled data dynamical systems and proposes an innovative control scheme. The key to the proposed control method is utilizing a pregenerated nonswitching type reference sliding variable profile to control the disturbed plant. As sampled data systems contain sample-and-hold devices in their input and output channels, we carry out a discrete time analysis. We consider the discretization effects on the controller in two aspects: the pace of convergence of the system and the ultimate band width. Consequently, in the reference sliding variable generator, we analyse two reaching laws, differently adapting to changes of the controller’s frequency. We prove that this approach not only minimizes the chattering phenomenon but also provides a reduction of the quasi-sliding mode band width, which in general case remains of O(T) order. Furthermore, the proposed control method incorporates a disturbance compensation algorithm, which results in the ultimate band width of O(T2) order. Finally, we also show that a certain selection of the sliding plane guarantees limitation of all the state variables’ errors to O(T2) order as well. Therefore, the proposed control algorithm significantly improves the system’s robustness.

Adaptive Super-Twisting Control for Mobile Wheeled Inverted Pendulum Systems

Recently, the mobile wheeled inverted pendulum (MWIP) has gained an increasing interest in the field of robotics due to traffic and environmental protection problems. However, the MWIP system is characterized by its nonlinearity, underactuation, time-varying parameters, and natural instability, which make its modeling and control challenging. Traditionally, sliding mode control is a typical method for such systems, but it has the main shortcoming of a “chattering” phenomenon. To solve this problem, a super-twisting algorithm (STA)-based controller is proposed for the self-balancing and velocity tracking control of the MWIP system. Since the STA is essentially a second-order sliding mode control, it not only contains the merits of sliding mode control (SMC) in dealing with the uncertainties and disturbances but can also be effective in chattering elimination. Based on the STA, we develop an adaptive gain that helps to learn the upper bound of the disturbance by applying an adaptive law, called an adaptive super-twisting control algorithm (ASTA). The stability of the closed-loop system is ensured according to the Lyapunov theorem. Both nominal experiments and experiments with uncertainties are conducted to verify the superior performance of the proposed method.

An Adaptive Interval Type-2 Fuzzy Sliding Mode Control Scheme for Fractional Chaotic Systems Synchronization With Chattering Elimination

This chapter presents a fractional adaptive interval type-2 fuzzy logic control strategy based on active fractional sliding mode controller (FAIT2FSMC) to synchronize tow chaotic fractional-order systems. The interval type-2 fuzzy logic systems (IT2FLS) are used to approximate the plant dynamics represented by unknown functions of the system, and the IT2F adaptation law adjusts the consequent parameters of the rules based on a Lyapunov synthesis approach. One of the main contributions in this work is the use of an IT2F and an adaptive fractional order PIλ control law to eliminate the chattering action in the control signal. Based on fractional order Lyapunov stability criterion, stability analysis is performed for the proposed method for an acceptable synchronization error level. The performance of the proposed scheme is demonstrated through the synchronization of two different fractional order chaotic gyro systems. Simulations are implemented using a numerical method based on Grünwald-Letnikov approach to solve the fractional differential equations.

Chattering-free adaptive fast convergent terminal sliding mode controllers for position tracking of robotic manipulators

The paper documents a new continuous adaptive fast terminal sliding mode control approach for position tracking of robotic manipulators. Combining linear sliding mode and terminal sliding mode, a fast nonsingular terminal sliding mode manifold is presented. Considering the discontinuous property of the sign function, which is often used in traditional sliding mode controller and will result in high-freqsency chattering in the control channel, the proposed controller adopts the continuous saturation function for chattering elimination. Besides the continuous property, convergence to the origin asymptotically and in finite time can be guaranteed in theory with the proposed controller, which is quite different from traditional boundary layer technique, where only bounded motion around the sliding manifold can be ensured. For asymptotic stability, it is only required that the lumped uncertainty is bounded, but the upper bound may be unknown by virtue of the designed adaptive methodology. The obtained results are applied to the problem of position tracking for robotic manipulators. Detailed simulations with some comparisons under various conditions demonstrate the effectiveness of the proposed method.