Shihong Ding

Global set stabilisation of the spacecraft attitude using finite-time control technique

In this article, we revisit the classical problem of attitude stabilisation for a rigid spacecraft with external disturbances. A global set stabilisation method using finite-time control technique is proposed. In the absence of disturbances, the states of the closed loop system will be stabilised in finite time to a set consisting of two equilibria. In the presence of disturbances, the states will be stabilised to a neighbourhood of this set. By constructing a particular Lyapunov function, it is proved that the closed-loop system satisfies global set stability. The control method in this article is based on set control idea and thus is more natural and energy-efficient. Numerical simulation results show the effectiveness of the method.

A speed control for a PMSM using finite-time feedback control and disturbance compensation

The speed-regulation problem for a permanent-magnet synchronous motor (PMSM) servo system is studied in this paper. In order to improve the disturbance rejection property of the PMSM, a novel composite controller for the speed-loop is presented. First, an extended state observer (ESO) is introduced to estimate the disturbances of the system. The estimated value is used in the feed-forward compensation design. Second, a continuous feedback-based finite-time control technique is employed for the feedback design. The composite speed controller can be considered as a composition of finite-time proportional feedback plus feed-forward compensation based on ESO (FTP + ESO). Two standard proportional—integral (PI) controllers are employed for two current loops. The closed-loop system of the speed error can be regarded as a first-order finite-time control system with bounded disturbances. Rigorous analysis shows that the proposed scheme can enhance the disturbance rejection property of the closed-loop system. Simu...The speed-regulation problem for a permanent-magnet synchronous motor (PMSM) servo system is studied in this paper. In order to improve the disturbance rejection property of the PMSM, a novel composite controller for the speed-loop is presented. First, an extended state observer (ESO) is introduced to estimate the disturbances of the system. The estimated value is used in the feed-forward compensation design. Second, a continuous feedback-based finite-time control technique is employed for the feedback design. The composite speed controller can be considered as a composition of finite-time proportional feedback plus feed-forward compensation based on ESO (FTP + ESO). Two standard proportional—integral (PI) controllers are employed for two current loops. The closed-loop system of the speed error can be regarded as a first-order finite-time control system with bounded disturbances. Rigorous analysis shows that the proposed scheme can enhance the disturbance rejection property of the closed-loop system. Simulation and experimental comparisons with two other control methods, ie the composite control method with proportional feedback plus feed-forward compensation based on ESO (P + ESO), and the PI control method, are given to verify the effectiveness of the proposed method.

Global finite-time stabilisation by output feedback for a class of uncertain nonlinear systems

This article considers the problem of global finite-time stabilisation by output feedback for a class of nonlinear systems comprised of a chain of power integrators perturbed by an uncertain vector field. To solve the problem, we first construct a homogeneous observer and controller in a recursive way for the nominal system without the perturbing nonlinearities. Then, using the homogeneous domination approach, we scale the homogeneous observer and controller with an appropriate choice of gain to render the uncertain nonlinear system globally finite-time stable. Due to the use of a reduced-order observer, the proposed output feedback controller is applicable to those systems with unknown gains associated with the power integrators.

Nonsmooth stabilization of a class of nonlinear cascaded systems

A global nonsmooth stabilization scheme is presented for a class of nonlinear cascaded systems with uncontrollable linearization. A stepwise constructive control methodology is proposed for the driving subsystem by using the adding a power integrator technique. Under suitable conditions and based on homogeneous properties, it is proved that the stabilization of the driving subsystem implies the stabilization of the overall cascaded system. Due to the versatility of the adding a power integrator technique and homogeneous properties, the proposed controller not only can be used to stabilize the cascaded system asymptotically, but also is able to lead to an interesting result of finite-time stabilization under appropriate conditions.

Global Stabilization of a Class of Feedforward Systems with Lower-Order Nonlinearities

This note considers the problem of global stabilization for a class of feedforward systems whose nonlinearities are allowed to be lower-order growing, instead of higher-order or linear growing as required by many existing results. To solve the problem, a domination approach is developed to design the stabilizer with a new structure, which is also integrated with the adding a power integrator and nested saturation methods. The use of a locally homogeneous stabilizer enables us to relax the growth condition imposed on the nonlinearities and hence enlarges the class of feedforward systems which are globally stabilizable.

Second-Order Sliding Mode Control for Nonlinear Uncertain Systems Bounded by Positive Functions

This paper considers the second-order sliding (2-sliding) mode control design problem for nonlinear systems with uncertainties bounded by positive functions. Two different 2-sliding mode control algorithms are proposed, including a discontinuous one and a quasi-continuous one. The discontinuous algorithm is built based upon the Lyapunov method, and the global finite-time Lyapunov stability rather than the global finite-time convergence is established for the resulting closed-loop system by using the modified adding a power integrator technique. On this basis, a quasi-continuous 2-sliding mode algorithm is further developed, and the chattering problem can be considerably reduced. Simulation results show that the control strategies proposed in this paper are effective.

Simple homogeneous sliding-mode controller

High-order sliding mode (HOSM) control is known to provide for finite-time-exact output regulation of uncertain systems with known relative degrees. Yet the corresponding universal HOSM controllers are typically constructed by special recursive procedures and have complicated form. We propose two new families of homogeneous HOSM controllers of a very simple form. Lyapunov functions are provided for a significant part of the first-family controllers. The second family consists of quasi-continuous controllers, which can be done arbitrarily smooth everywhere outside of the HOSM manifold. A regularization procedure ensures high-accuracy output regulation by means of control with required smoothness level. Output-feedback controllers are constructed. Controllers of the orders 3-5 are demonstrated.

Second-order sliding mode controller design subject to mismatched term

Abstract This communique proposes a novel second-order sliding mode (SOSM) control method to handle sliding mode dynamics with mismatched term, so as to reduce the terms in the control channel. Meanwhile, it is shown that the proposed control approach can be used to design SOSM controllers under disturbances bounded by positive functions rather than conventional constant upper bounds. The finite-time stability of the sliding variables has been shown by using finite-time Lyapunov theory. The validity of the proposed approach is verified by controlling a Buck converter.

Nested saturation control for overhead crane systems

This paper presents a new control strategy for overhead crane systems. First, by utilizing a coordinate change, the underactuated overhead crane dynamical model can be transformed into an upper-triangular form. Second, a finite-time controller is designed based on the nonlinear nested saturation and adding a power integrator technique. Rigorous proof shows that the controller can guarantee finite-time stability of the closed-loop system. Simulations show the effectiveness of the proposed method.

Sliding Mode Direct Yaw-Moment Control Design for In-Wheel Electric Vehicles

The direct yaw-moment control system can significantly enhance vehicle stability in critical situations. In this paper, the direct yaw-moment control strategies are proposed for in-wheel electric vehicles by using sliding mode (SM) and nonlinear disturbance observer (NDOB) techniques. The ideal sideslip angle at the center of gravity and the yaw rate are first calculated based on a linear two degree of freedom vehicle model. Then, the actual sideslip angle is identified and estimated by constructing a state observer. On this basis, a traditional discontinuous SM direct yaw-moment controller is designed to guarantee that the sideslip angle and the yaw rate will approach the ideal ones as closely as possible. To tackle the chattering problem existing in the traditional SM controller, a second-order sliding mode (SOSM) controller is further designed by taking the derivative of the controller as the new control, which implies that the actual control can be an integration of the SOSM controller. Finally, to avoid the large gains in the derived controllers, by combining the NDOB with the derived controllers, the composite control schemes are also proposed. In comparison with the discontinuous first-order SM controller, the proposed SOSM controller is shown to be more effective.