Abstract
This paper considers the stabilization problem for under-actuated rotary inverted pendulum systems (RotIPS) via a fuzzy-based continuous sliding mode control approach. Various sliding mode control (SMC) methods have been proposed for stabilizing the under-actuated RotIPS. However, there are two main drawbacks of these SMC approaches. First, the existing SMCs have a discontinuous structure; therefore, their control systems suffer from the chattering problem. Second, a complete proof of closed-loop system stability has not been provided. To address these two limitations, we propose a fuzzy-based (continuous) super-twisting stabilization algorithm (FBSTSA) for the under-actuated RotIPS. We first introduce a new sliding surface, which is designed to resolve the under-actuation problem, by combining the fully-actuated (rotary arm) and the under-actuated (pendulum) variables to define one sliding surface. Then, together with the proposed sliding surface, we develop the FBSTSA, where the corresponding control gains are adjusted based on a fuzzy logic scheme. Note that the proposed FBSTSA is continuous owing to the modified super-twisting approach, which can reduce the chattering and enhance the control performance. With the proposed FBSTSA, we show that the sliding variable can reach zero in finite time and then the closed-loop system state converges to zero asymptotically. Various simulation and experimental results are provided to demonstrate the effectiveness of the proposed FBSTSA. In particular, (i) compared with the existing SMC approaches, chattering is alleviated and better stabilization is achieved; and (ii) the robustness of the closed-loop system (with the proposed FBSTSA) is guaranteed under system uncertainties and external disturbances.
Highlights
Rotary inverted pendulums were first developed by Furuta and his colleagues at the Tokyo Institute of Science and Technology [1], [2]
We note that the proposed fuzzy-based (continuous) super-twisting stabilization algorithm (FBSTSA) is continuous, whereas the existing sliding mode control (SMC)-based stabilization controllers for the under-actuated rotary inverted pendulum systems (RotIPS) are discontinuous [12]–[15]
Theorem 1 together with Theorem 2 overcome the two main drawbacks mentioned in Introduction when applying the SMC for the under-actuated RotIPS. (iii) it should be noted that the existing supertwisting algorithms in [22], [23] cannot be used directly for the stabilization control of the underactuated RotIPS because of two reasons: (i) their sliding surfaces were proposed only for fully-actuated systems; and (ii) as shown in Theorem 2, the sliding variable is required to reach zero in finite time in order to ensure the asymptotic stability of the closed-loop system, whereas the adaptive gains in [23] only ensure the finite-time convergence of the sliding variable to a small region around zero
Summary
We show that the sliding variable can reach zero in finite time in the reaching phase, and the closed-loop system state converges to zero asymptotically in the sliding phase This contribution resolves the second limitation (see the statement in (D-2)); and (iii) various simulation and experimental results are provided to demonstrate the effectiveness of the proposed FBSTSA. To the best of our knowledge, our paper is the first to consider fuzzy-based super-twisting sliding mode stabilization control for the under-actuated RotIPS, where the stability of the closed-loop system is addressed in both the reaching and the sliding phases. (iii) we generalize the results of the super-twisting algorithm (STA) in [22], [23] to the case of under-actuated systems with fuzzy-based gains; and (iv) compared with the proposed adaptive gains in [23], our proposed fuzzy-based gains ensure the finite-time convergence to zero rather than to a small region around zero of the sliding variable.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
