Adaptive Sliding Mode Control Based on Uncertainty and Disturbance Estimator

This paper presents an original adaptive sliding mode control strategy for a class of nonlinear systems on the basis of uncertainty and disturbance estimator. The nonlinear systems can be with parametric uncertainties as well as unmatched uncertainties and external disturbances. The novel adaptive sliding mode control has several advantages over traditional sliding mode control method. Firstly, discontinuous sign function does not exist in the proposed adaptive sliding mode controller, and it is not replaced by saturation function or similar approximation functions as well. Therefore, chattering is avoided in essence, and the chattering avoidance is not at the cost of reducing the robustness of the closed-loop systems. Secondly, the uncertainties do not need to satisfy matching condition and the bounds of uncertainties are not required to be unknown. Thirdly, it is proved that the closed-loop systems have robustness to parameter uncertainties as well as unmatched model uncertainties and external disturbances. The robust stability is analyzed from a second-order linear time invariant system to a nonlinear system gradually. Simulation on a pendulum system with motor dynamics verifies the effectiveness of the proposed method

Adaptive Sliding Mode Control Based on Uncertainty and Disturbance Estimator

This paper presents an original adaptive sliding mode control strategy for a class of nonlinear systems on the basis of uncertainty and disturbance estimator. The nonlinear systems can be with parametric uncertainties as well as unmatched uncertainties and external disturbances. The novel adaptive sliding mode control has several advantages over traditional sliding mode control method. Firstly, discontinuous sign function does not exist in the proposed adaptive sliding mode controller, and it is not replaced by saturation function or similar approximation functions as well. Therefore, chattering is avoided in essence, and the chattering avoidance is not at the cost of reducing the robustness of the closed-loop systems. Secondly, the uncertainties do not need to satisfy matching condition and the bounds of uncertainties are not required to be unknown. Thirdly, it is proved that the closed-loop systems have robustness to parameter uncertainties as well as unmatched model uncertainties and external disturbances. The robust stability is analyzed from a second-order linear time invariant system to a nonlinear system gradually. Simulation on a pendulum system with motor dynamics verifies the effectiveness of the proposed method

Robust nonlinear generalised predictive control for a class of uncertain nonlinear systems via an integral sliding mode approach

In this paper, a robust nonlinear generalised predictive control (GPC) method is proposed by combining an integral sliding mode approach. The composite controller can guarantee zero steady-state error for a class of uncertain nonlinear systems in the presence of both matched and unmatched disturbances. Indeed, it is well known that the traditional GPC based on Taylor series expansion cannot completely reject unknown disturbance and achieve offset-free tracking performance. To deal with this problem, the existing approaches are enhanced by avoiding the use of the disturbance observer and modifying the gain function of the nonlinear integral sliding surface. This modified strategy appears to be more capable of achieving both the disturbance rejection and the nominal prescribed specifications for matched disturbance. Simulation results demonstrate the effectiveness of the proposed approach

Dynamic output feedback sliding mode control for uncertain linear systems

In this paper, a class of uncertain linear systems with unmatched disturbances is considered, where the nominal system representation is allowed to be non-minimum phase. A sliding surface is designed which is dependent on the system output, observed state, and estimated uncertain parameters. A linear coordinate transformation is introduced so that the stability analysis of the reduced-order sliding mode dynamics can be conveniently performed. A robust output feedback sliding mode control (OFSMC) is then designed to drive the considered system state to reach the sliding surface in finite time and maintain a sliding motion thereafter. A simulation example for a high incidence research model (HIRM) aircraft is used to demonstrate the effectiveness of the proposed method

Consensus Control for a Class of Linear Multiagent Systems using a Distributed Integral Sliding Mode Strategy

In this paper, a consensus framework is proposed for a class of linear multiagent systems subject to matched and unmatched uncertainties in an undirected topology. A linear coordinate transformation is derived so that the consensus protocol design can be conveniently performed. The distributed consensus protocol is developed by using an integral sliding mode strategy. Consensus is achieved asymptotically and all subsystem states are bounded. By using an integral sliding mode control, the subsystems lie on the sliding surface from the initial time, which avoids any sensitivity to uncertainties during the reaching phase. By use of an appropriate projection matrix, the size of the equivalent control required to maintain sliding is reduced which reduces the conservatism of the design. MATLAB simulations validate the effectiveness and superiority of the proposed method

Output tracking via sliding modes in causal systems with time delay modeled by higher order pade approximations

Output tracking in a SISO causal uncertain nonlinear system with an output subject to a time delay is considered using sliding mode control. A higher order Pade approximation to a delay function with a known time delay is used to construct a model of a transformed system without a time delayed output and is employed in a feedback sliding mode control. This model functions as a predictor of the plant states and the plant output, but is of nonminimum phase due to the application of the Pade approximation. The method of the stable system center is used to stabilize the internal dynamics of this plant model, and a control is developed using a sliding surface to allow the plant to track an arbitrary reference profile given by an exogenous system with a known characteristic equation. Simulations of the system are performed for the plant model using a first, second and third order Pade approximations and a controller in plant feedback mode. Numerical examples for Pade approximations of increasing order are considered and compare

Hierarchical Model Predictive/Sliding Mode control of nonlinear constrained uncertain systems

This paper presents an overview of some hierarchical control schemes composed by a high level Model Predictive Control (MPC) and a low level Sliding Mode Control (SMC). The latter is realized by using the so-called Integral Sliding Mode (ISM) control approach and is meant to reject the matched disturbances affecting the plant, thus providing a system with reduced uncertainty for the MPC design. Both continuous and discrete-time solutions are discussed in the paper. Moreover, assuming the presence of a network in the control loop, a networked version of the control scheme is presented. It is a model-based event-triggered MPC/ISM control scheme aimed at minimizing the packets transmission. The input-to-state (practical) stability properties of the proposed approaches are also addressed in the paper

Integral sliding mode fault tolerant control allocation for a class of affine nonlinear system

This is the author accepted manuscript. The final version is available from Wiley via the DOI in this record.This paper develops novel fault tolerant integral sliding mode control allocation schemes for a class of over-actuated affine nonlinear system. The proposed schemes rely on an existing baseline controller and the objective is to retain the nominal (fault-free) closed-loop performance in the face of actuator faults/failures by effectively utilizing actuator redundancy. The online control allocation reroutes the control effort to the healthy actuators using knowledge of the actuator effectiveness level estimates. One of the proposed schemes is tested in simulation using a well known high fidelity model of a large civil transport aircraft (B747) from the literature. Good simulation results show the efficacy of the scheme

Kuhn-Tucker-based stability conditions for systems with saturation

This paper presents a new approach to deriving stability conditions for continuous-time linear systems interconnected with a saturation. The method presented can be extended to handle a dead-zone, or in general, nonlinearities in the form of piecewise linear functions. By representing the saturation as a constrained optimization problem, the necessary (Kuhn-Tucker) conditions for optimality are used to derive linear and quadratic constraints which characterize the saturation. After selecting a candidate Lyapunov function, we pose the question of whether the Lyapunov function is decreasing along trajectories of the system as an implication between the necessary conditions derived from the saturation optimization, and the time derivative of the Lyapunov function. This leads to stability conditions in terms of linear matrix inequalities, which are obtained by an application of the S-procedure to the implication. An example is provided where the proposed technique is compared and contrasted with previous analysis methods