Robust Optimal Sliding Mode Control Research Articles

Robust optimal sliding mode control for the deployment of Coulomb spacecraft formation flying

Inter-spacecraft electrostatic force (Coulomb force) is desirable for close formation flying control because of its propellant-less and free contaminate characteristics attributed to the propellant exhaust emission. This paper presents robust optimal sliding mode control to deal with the problem of thruster saturation in tracking the formation trajectory for Coulomb spacecraft formation flying. The robust controller design is based on optimal control theory as a linear quadratic system, and it is augmented with an integral sliding mode control technique. The stability of the closed-loop system is guaranteed using the second Lyapunov method. The developed controller outperforms the existing ones, because it has a higher degree of fine-tuning to cope with the uncertainty. Numerical simulations are employed to confirm the efficiency of the developed controller.

Zero-sum differential games-based fast adaptive robust optimal sliding mode control design for uncertain missile autopilot with constrained input

This paper designs a novel adaptive robust optimal sliding mode control (SMC) strategy for constrained input missile system with uncertain input and unknown disturbance. First, a smooth function is employed to map the constrained input. Based on SMC theory, a fast adaptive SMC scheme is designed to reduce the effects of unknown input and approximate error which has two advantages. One is that the proposed scheme is independent of the uncertain information. The other is that the proposed scheme forces the states to converge with exponential rate as they are far away from the sliding mode surface, and the states move with linear rate when they are closed to the sliding mode surface. Then, a zero-sum differential games strategy-based adaptive dynamic programming (ADP) technique is employed to obtain the optimal performance of sliding mode dynamics system. The loop-system and estimation weight error can be proved stable by utilising Lyapunov theory. Finally, the missile autopilot system is used to indicate the effectiveness of the designed approach.

Metaheuristics-based Multi-objective Design of Global Robust Optimal Sliding Mode Control of Discrete Uncertain Systems

The paper introduces a new design control strategy for finite time stabilization of uncertain discrete systems. The proposed control method uses the First Order Sliding Mode Control (FOSMC), the Linear Quadratic Regulator (LQR) and Genetic Algorithms (GA). The key idea of combining two control strategies lies in the fact that a robust controller tackles the uncertainties when the optimal controller performances are unaffected. Firstly, as the performances of the Sliding Mode Control (SMC) greatly depends on the choice of the sliding surface, a novel method based on the resolution of a Sylvester equation is proposed. Secondly, to ensure the robustness in the whole space, the Integral Sliding Mode Control (ISMC) is combined with the above LQR method. Rigorous stability analysis for the closed-loop system is given and proves that the system states are always bounded even the unknown disturbances. In order to handle the problem accompanying the LQR synthesis as well as the gain of the robust compensator, a multi-objective optimization problem considering a set of competing objectives is solved using GA. For that, a novel dynamically aggregated objective function is proposed. A set of non-dominated optimal solutions are provided to the control engineer and then may select the most adequate solution among the resulting optimal Pareto set. The novel method has successfully solved the robust stabilization of two known benchmarks and the different results asserts not merely the efficiency as well as the quality of the designed controller but also its supremacy compared to some existing ones.

Multi-Objective Design of Optimal Sliding Mode Control for Trajectory Tracking of SCARA Robot Based on Genetic Algorithm

This paper focuses on robust optimal sliding mode control (SMC) law for uncertain discrete robotic systems, which are known by their highly nonlinearities, unmodeled dynamics, and uncertainties. The main results of this paper are divided into three phases. In the first phase, in order to design an optimal control law, based on the linear quadratic regulator (LQR), the robotic system is described as a linear time-varying (LTV) model. In the second phase, as the performances of the SMC greatly depend on the choice of the sliding surface, a novel method based on the resolution of a Sylvester equation is proposed. The compensation of both disturbances and uncertainties is ensured by the integral sliding mode control. Finally, to solve the problem accompanying the LQR synthesis, genetic algorithm (GA) is used as an offline tool to search the two weighting matrices. The main contribution of this paper is to consider a multi-objective optimization problem, which aims to minimize not only the chattering phenomenon but also other control performances. A novel dynamically aggregated objective function is proposed in such a way that the designer is provided, once the optimization is achieved, by a set of nondominated solutions and then he selects the most preferable alternative. To show the performance of the new controller, a selective compliance assembly robot arm robot (SCARA) is considered. The results show that the manipulator tracing performance is considerably improved with the proposed control scheme.

Robust optimal motion planning approach to cooperative grasping and transporting using multiple UAVs based on SDRE

In this paper, we consider the problem of controlling a team of Quadrotors that cooperatively grasp and transport a common payload in three dimensions in the presence of external disturbances and parametric uncertainties such as wind field effects. The main contribution of this work is to propose a cooperative control algorithm based on a decentralized strategy. This algorithm consists of two main parts: first calculating the control vectors for each Quadrotor using Moore–Penrose theory and second combining these control vectors with individual control vectors, which are obtained from a closed-loop non-linear robust optimal controller. In this regard, a robust optimal sliding mode controller (ROSMC), which incorporates the state-dependent Riccati equation (SDRE) method with sliding mode control (SMC) technique, is designed. It also has the capability of maximum dynamic load carrying capacity (DLCC) to increase the carrying capacity and the efficiency of the group of Quadrotors. The proposed method inherits the advantages of both approaches including robustness against model uncertainties and high flexibility in designing the control parameters to provide an optimal solution for the non-linear dynamic of the system. The control algorithm is based on the Lyapunov technique, which is able to provide the stability of the end-effecter during tracking of the desired trajectory with acceptable precision. Finally, the simulation results demonstrate the effectiveness of the control strategy for the cooperative Quadrotors to grasp and transport a common payload in various manoeuvres.

A Stability Guaranteed Robust Fault Tolerant Control Design for Vehicle Suspension Systems Subject to Actuator Faults and Disturbances

A fault tolerant control approach based on a novel sliding mode method is proposed in this brief for a full vehicle suspension system. The proposed approach aims at retaining system stability in the presence of model uncertainties, actuator faults, parameter variations, and neglected nonlinear effects. The design is based on a realistic model that includes road uncertainties, disturbances, and faults. The design begins by dividing the system into two subsystems: a first subsystem with 3 degrees-of-freedom (DoF) representing the chassis and a second subsystem with 4 DoF representing the wheels, electrohydraulic actuators, and effect of road disturbances and actuator faults. Based on the analysis of the system performance, the first subsystem is considered as the internal dynamic of the whole system for control design purposes. The proposed algorithm is implemented in two stages to provide a stability guaranteed approach. A robust optimal sliding mode controller is designed first for the uncertain internal dynamics of the system to mitigate the effect of road disturbances. Then, a robust sliding mode controller is proposed to handle actuator faults and ensure overall stability of the whole system. The proposed approach has been tested on a 7-DoF full car model subject to uncertainties and actuator faults. The results are compared with the ones obtained using $H_\infty $ approach. The proposed approach optimizes riding comfort and road holding ability even in the presence of actuator faults and parameter variations.

A Simulation of an Electrical Servo Drive Based on Optimal Control

In paper, the problem of robustify LQR for a class of uncertain linear systems is considered. An optimal controller is designed for the nominal system and an integral sliding surface is constructed. The ideal sliding motion can minimize a given quadratic performance index, and the reaching phase, which is inherent in conventional sliding mode control, is completely eliminated. Then the sliding mode control law is synthesized to guarantee the reachability of the specified sliding surface. The system dynamics is global robust to uncertainties which satisfy matching conditions. A GROSMC is realized. To verify the effectiveness of the proposed scheme, a robust optimal sliding mode controller is developed for rotor position control of an electrical servo drive system.

Robust Optimal Sliding-Mode Tracking Control for a Class of Uncertain Nonlinear MIMO Systems

This paper addresses the problem of tracking a reference trajectory asymptotically given by a linear time-varying exosystem for a class of uncertain nonlinear MIMO systems based on the robust optimal sliding-mode control. The nonlinear MIMO system is transformed into a linear one by the input-output linearization technique, and at the same time the input-output decoupling is realized. Thus, the tracking error equation is established in a linear form, and the original nonlinear tracking problem is transformed into an optimal linear quadratic regulator (LQR) tracking problem. A LQR tracking controller (LQRTC) is designed for the corresponding nominal system, and the integral sliding-mode strategy is used to robustify the LQRTC. As a result, the original system exhibits global robustness to the uncertainties, and the tracking dynamics is the same as that of LQRTC for the nominal system. So a robust optimal sliding-mode tracking controller (ROSMTC) is realized. The proposed controller is applied to a two-link robot system, and simulation results show its effectiveness and superiority.

Robust Optimal Sliding Mode Control for Attitude Synchronization of Autonomous Docking to a Tumbling Target

This paper investigates the control problem of attitude synchronization for an on-orbit servicing spacecraft autonomously docking to a freely tumbling target in space. An optimal sliding surface is designed based on optimal control theory, followed by a robust optimal sliding mode control law designed for attitude synchronization in accordance. Meanwhile, the unknown but bounded external disturbances, parameter variations, model uncertainties, and measurement errors are all considered during the control algorithm design. The salient feature of this control law is that the relative attitude variables will converge to the origin in the sense of optimality with respect to a quadratic cost function once the sliding surface is reached. The simulation results validate the effectiveness and robustness of the designed robust optimal sliding mode control law.