On multi-input second order sliding mode control of nonlinear systems with uncertainty

A high order sliding mode control algorithm for uncertain nonlinear systems is presented. This problem can be considered as finite time stabilization of higher order input-output dynamic systems with bounded uncertainties. The algorithm developed is based on the concept of integral sliding mode and includes two steps. One is the controller for nominal system using geometric homogeneity. The other is one compensating for uncertainties utilizing sliding mode control. In addition, to overcome the difficulty in determining the boundaries of uncertainties, the adaptive radial basis function neural network is designed to estimate bounded uncertainties. The proposed procedure ensures establishment of high order sliding mode and provides easy implementation. An illustrative example of a car control shows feasibility of the approach.

Fixed-Time Stabilization via Second Order Sliding Mode Control

This paper presents a nonlinear disturbance observer-based finite time convergent second order sliding mode control scheme for a tailless aircraft with uncertain parameters. Command angles and angular rate commands are robustly tracked in outer and inner loops correspondingly via finite time convergent second order sliding mode controllers. Nonlinear disturbance observer is employed to retain overall high accuracy of the closed-loop tracking. An optimal control allocation algorithm is employed using nominal mathematical model of an aircraft. The control approach is applied to the innovative control effectors (ICE) fighter aircraft. Computer simulations demonstrate high accuracy tracking performance.

The design of a globally stable second order sliding mode controller for sensorless induction motors is discussed in this paper. The adaptive component of the controller enables to compensate for the variation in time of the rotor resistance value, while the use of a suitably designed sliding mode speed/flux observer avoids the necessity of including speed and flux sensors within the control loop, making this proposal suitable for sensorless applications. The use of a second order sliding mode control approach, realized by regarding the second time derivatives of the stator currents as discontinuous auxiliary control inputs, is effective in limiting the mechanical wear, making this proposal more acceptable in practical applications than those based on conventional sliding mode control.

The main purpose of this paper is to design a robust second order sliding mode controller that can deal with uncertain nonlinear systems. This controller can keep the main advantages of the first order sliding mode controller, such as the ability to make the system asymptotically stable by forcing the error and its derivatives to have a zero value, the simplicity in the operation, and the robustness in the existence of perturbations. In spite of the features that characterize the first order sliding mode controller (1 SMC), it still suffers from the unwanted phenomenon “chattering”, which originates from a discontinuous control part (sign function). In this context, saturation function can be used instead of sign function to reduce this problematic chattering. Different from the saturation function method, the second order sliding mode controller can be used to overcome the chattering; suffered by the first order sliding mode controller and to retain the stability and performance of the system. In this paper, the twisting and the super twisting second-order algorithms of the sliding mode controller were used, and their results were compared with the first order sliding mode controller. So, this subject focused on the chattering problem who suffers from it the 1 SMC and try to reduce it by using the 2 SMC, the uncertain pendulum system was adopted in this work for the purpose of checking the three controllers. The simulations results showed that the second order sliding mode controller has the ability to reduce both the chattering magnitude and the steady state error and achieve an asymptotically stable system. The results were obtained by using MATLAB programming.

This paper deals with the design of a third order Sliding Mode Control (SMC) algorithm for a perturbed chain of integrators with box constraints on state variables. The proposed strategy takes into account a robust generalization of the so-called Fuller's Problem, which is a standard optimal control problem for a chain of integrators under critical uncertainty condition, and proves to steer the system trajectories to the origin of the state space in finite time, while satisfying the imposed constraints. The proposed algorithm is tested in simulation to solve a trajectory-tracking problem for a nonholonomic car.

This paper presents a novel second order sliding mode control strategy for a robust tracking controller of a quad-rotor helicopter by utilizing a nonlinear sliding surface. The nonlinear sliding surface enables the closed loop dynamics to have a variable damping ratio, and therefore the transient time to reach the sliding mode can be shorten. The effectiveness of the proposed control strategy is proven experimentally.

We consider single-input nonlinear systems with unknown unmodelled time-varying parameters or disturbances which are bounded. The main goal is to identify classes of uncertain systems for which the control exist and to provide design procedures. Assuming that the undisturbed nominal system (f,g) is partially state feedback linearizable, that a strict triangularity condition, a linear parametrization condition, and f/spl isin/G/sub r-1/ hold for the uncertain terms, and that some condition is satisfied in the transformed partially linear system, we design an adaptive regulating dynamic control. First, we identify classes of nonlinear uncertain systems and give a systematic procedure for the design of a robust regulation for the nonlinear systems.

The paper proposes an approach to second order sliding mode control for multi-input multi-output (MIMO) nonlinear uncertain systems. Second order sliding mode techniques for single-input single-output (SISO) systems show, with respect to standard sliding mode control, the same properties of robustness and precision, feature a higher order accuracy and can be exploited to eliminate the chattering effect. The application of second order sliding mode control to MIMO nonlinear systems is a challenging matter. The presented MIMO control method applies to a quite large class of nonlinear processes affected by uncertainties of general nature; the control design is simple; the conditions of existence on the controllers are weak. The proposed procedure represents a general approach to the second order sliding mode control of MIMO systems

Based on the working principle of a ship with a controllable pitch propeller (CPP), a mathematical model of the ship-propeller subsystem, the engine-propeller subsystem, and the ship main engine subsystem was established. The model was represented by a set of differential equations, in which the ship speed, the rotational speed of the propeller, and the rotational speed of the main engine were used as the state variables, and the angle of pitch and the fuel injection quantity were used as the control input. The equation set was a multi-input nonlinear speed control system with the characteristics of coupling and nonlinearity. In order to design a sliding mode variable structure (SMVS) controller, appropriate coordinates were selected for the nonlinear state transformation, and the multi-input nonlinear system was decomposed into two single-input systems to solve the equivalent control through the manifold calculation. MATLAB simulation results showed that under the control of the angle of pitch and the fuel injection quantity, the ship speed, the rotational speed of the propeller, and the rotational speed of the main engine could quickly approach the given values, verifying the advantages of the SMVS control for complex multi-input nonlinear systems.

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This paper deals with the hybrid position/force control of constrained manipulators subject to uncertainties and disturbances of various nature. A solution is proposed based on the sliding mode control theory, which revealed to be highly effective in counteracting uncertainties and disturbances for some class of uncertain nonlinear systems. Specific problems connected to this technique are the chattering elimination and the algebraic coupling between constraint forces and possibly discontinuous control signals. The solution proposed in this paper overcomes these problems by applying a new second order sliding mode control algorithm.

This paper proposes a robust supertwisting algorithm (STA) design for nonlinear systems where both matched and unmatched uncertainties are considered. The main contributions reside primarily to conceive a novel structure of STA, in order to ensure the desired performance of the uncertain nonlinear system. The modified algorithm is formed of double closed-loop feedback, in which two linear terms are added to the classical STA. In addition, an integral sliding mode switching surface is proposed to construct the attractiveness and reachability of sliding mode. Sufficient conditions are derived to guarantee the exact differentiation stability in finite time based on Lyapunov function theory. Finally, a comparative study for a variable-length pendulum system illustrates the robustness and the effectiveness of the proposed approach compared to other STA schemes.

Fuzzy sliding mode control as a robust and intelligent nonlinear control technique is proposed to control processes with severe nonlinearity and unknown models. This paper proposes a new adaptive tracking fuzzy sliding mode controller for nonlinear systems in the presence of fuzzy compensation. The main contribution of the proposed method is that the fuzzy system is used to realize the adaptive approximation of the unknown part of the model, and the fuzzy gain can be reduced effectively. The fuzzy self-adaptive rate is derived through the Lyapunov method, and the stability and convergence of the whole closed-loop system are guaranteed by adjusting the adaptive weight value. The performance of the proposed approach is evaluated for double joint rigid manipulator problems. The simulation results illustrate the effectiveness of our proposed controller.

Neural network-based H∞ sliding mode control for nonlinear systems with actuator faults and unmatched disturbances