Super-twisting observer design for systems of dimension more than one

IET Control Theory & Applications

2015

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This study presents a fault-tolerant continuous super-twisting control algorithm for dynamical systems, subject to Lipshitzian and non-Lipshitzian bounded disturbances. The conditions of finite-time convergence of the entire system state to the origin are obtained. An experimental verification of the designed fault-tolerant algorithm is conducted for a DTS200 three-tank system through varying fault sources, disturbances, input conditions and inter-tank connections. IntroductionIt is well-known that the classical discontinuous sliding mode control provides finite-time convergence for a scalar system state [1]. A finite-time stabilising control for a system of dimension two is realised using the twisting algorithm [2], where the secondorder sliding mode control is also discontinuous. Both algorithms are robust with respect to bounded disturbances. On the other hand, using a continuous second-order sliding mode super-twisting algorithm [3], a scalar system state can be stabilised along with its first derivative. The super-twisting algorithm is robust with respect to unbounded disturbances satisfying a Lipschitz condition. A recent paper [4] has presented a modified super-twisting algorithm for systems of dimension more than one, which is, however, robust only against disturbances satisfying a Lipschitz condition. This paper presents a fault-tolerant homogeneous continuous super-twisting control algorithm for dynamical systems, subject to not only Lipshitzian and but non-Lipshitzian bounded disturbances as well, thus making a substantial advance with respect to existing results. The conditions of finite-time convergence of the entire system state to the origin are obtained. First, the case of dimension two is addressed. Similar results are then obtained for systems of dimension more than two. The paper concludes with an experimental verification of the designed fault-tolerant algorithm, which is conducted for a DTS200 three-tank system through varying fault sources, disturbances, input conditions and inter-tank connections. This three-tank system is a widely recognised testbed for applying performance tests and validating new control strategies [5]. Making use of its built-in fault scenarios (sensor fault, actuator fault and process fault), the three-tank system has been actively employed for research in the areas of fault detection and diagnosis [6-10] and fault-tolerant control design [7,[11][12][13][14].The paper is organised as follows. The problem statement is given in Section 2. A fault-tolerant continuous super-twisting control algorithm for dynamical systems is designed in Section 3. An experimental verification of the designed fault-tolerant algorithm is conducted for a DTS200 three-tank system in Section 5. The proofs of all theorems are given in the Appendix. 2Control problem statement for faulted systems Consider a dynamic system of dimension two in the presence of faultẋ∈ R 2 is the system state and u(t) ∈ R is the control input. The function f (x 1 (t), x 2 (t), t) satisfies the Lipschitz condition with...

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See 3 more Smart Citations

Finite‐time‐convergent fault‐tolerant control for dynamical systems and its experimental verification for DTS200 three‐tank system

Krueger

IET Control Theory & Applications

2015

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Second‐order sliding mode controller design subject to mismatched unbounded perturbations

Liu

Intl J Robust & Nonlinear

2017

Summary The dynamics of the second‐order sliding mode (SOSM) can be obtained by directly taking the second derivative on the sliding variable when it has a relative degree of 2 with respect to the control input. However, there will always appear some state‐dependent certain or uncertain terms in the first derivative of the sliding variable, and the derivative directly imposed on these terms could enlarge the uncertainties in the control channel. One method to reduce the uncertainties in the control channel is to hold this information in the dynamics of the first derivative of the sliding variable, while the original SOSM dynamics could be transformed to be a SOSM system with a mismatched unbounded perturbation. This paper focuses on the controller design problem for SOSM dynamics subject to mismatched unbounded perturbation. By using Lyapunov analysis, a novel backstepping‐like design methodology will be proposed. The rigorous mathematical proof will show that under the derived SOSM controller, the closed‐loop sliding mode dynamics is globally finite‐time stable. Meanwhile, the frequently used constant upper bound assumptions for the standard SOSM system can also be extended to the state‐dependent hypotheses in this paper. An academic example is illustrated to verify the effectiveness of the proposed method. Copyright © 2017 John Wiley & Sons, Ltd.

A new adaptive second‐order sliding mode controller design for nonlinear systems with multiple uncertainties

Intl J Robust & Nonlinear

2022

Summary This study is dedicated to solving the problem of a new adaptive second‐order sliding mode (SOSM) controller design for a type of nonlinear systems with multiple uncertainties by using adding a power integrator (API) and the parameter separation techniques. Supported by the finite‐time Lyapunov theory, the finite‐time stability of the closed‐loop system under the proposed adaptive SOSM controller has been firmly guaranteed. The significant advantages here lie in that the prior knowledge about the bounds of uncertainties is not required in the designed adaptive SOSM control approach, and the switching gain can be tuned dynamically. Finally, a numerical example is presented to indicate the notable feature and effectiveness of the designed adaptive SOSM approach.