Optimal Sliding Mode Control Research Articles

Nearly optimal fixed time sliding mode controller for leader–follower consensus problem with partially unknown nonlinear agents

This paper presents a conceptual framework for addressing the consensus problem in multi-agent systems with unknown nonlinear dynamics using reinforcement learning (RL) based nearly optimal sliding mode controller (SMC). The agents’ dynamics are assumed to have uncertainty and mismatched disturbance. An adaptive fixed-time estimator is introduced to estimate uncertain dynamics and disturbances for each agent at a certain time. The paper proposes two control strategies. In the first strategy, a controller is designed, incorporating adaptive SMC and an optimal controller. Adaption law in SMC estimates the bound of fixed time estimator error before convergence, ultimately achieving asymptotic convergence to the sliding surface and converting the agent’s dynamics to linear. This enables solving a linear consensus problem using an RL-based adaptive optimal controller through an on-policy critic–actor method. The second control strategy enhances the adaptive SMC into a fixed-time controller, reducing the time to reach the sliding surface regardless of initial conditions. Consequently, the convergence time of the consensus error to zero is diminished. This reduction in reaching time results in faster convergence of the consensus error to zero. The effectiveness of both strategies is validated through numerical experiments on two real system models, aligning with the theoretical proofs.

Dynamic Modelling and Optimal Sliding Mode Control of the Wearable Rehabilitative Bipedal Cable Robot with 7 Degrees of Freedom

Although robot-assisted physiotherapy has gained increasing attention in recent years, the use of wearable rehabilitation robots for lower limbs has shown reduced efficiency due to additional equipment and motors located at the center of the joint, increasing complexity and load on disabled patients. This paper proposes a novel rehabilitation approach by eliminating motors and equipment from the center of joints and placing them on a fixed platform using cable-based power transmission. A proposed model of a 14 cable-driven bipedal robot with 7 degrees of freedom has been used to model a lower limb rehabilitation robot corresponding to it. The dynamic equations of the robot are derived using the Euler-Lagrange method. The sliding mode control technique is utilized to offer accurate control for tracking desired trajectories, ensuring smoothness despite disturbances, and reducing tracking errors. This approach is employed to help prevent patients from falling and support them in maintaining balance during rehabilitative exercises. To ensure that cables exert positive tension, the sliding mode controller was combined with quadratic programming optimization, minimizing path error while constraining the controller input torque to be non-negative. The performance of the proposed controller was assessed by considering several control gains resulting in K = 10 identified as the most effective one. The feasibility of this approach to rehabilitation is demonstrated by the numerical results in MATLAB simulation, which show that the RMSE amount of the right and left hip and thigh angles are 0.29, 0.37, 0.31, and 0.44, respectively which verified an improved rehabilitation process. Also, the correlation coefficient between the Adams and MATLAB simulation results for motor torque was found to be 0.98, indicating a high degree of correlation between the two simulation results.

Trajectory Tracking Control of Unmanned Underwater Vehicle Based on Projected Perpendicular Guidance Method with Disturbance Observer

Unmanned underwater vehicles (UUVs) possess impressive maneuverability and versatility, but controlling them during trajectory tracking can be challenging due to their susceptibility to external disturbances and perturbations in their model parameters. Additionally, the UUV has four degrees of freedom underwater, but only three control inputs, making it a typical underactuated system. To address these issues, this paper introduces a novel optimize sliding mode control (OPSMC) algorithm grounded in projected perpendicular guidance (PPG). The PPG algorithm transforms the three-degree-of-freedom path trajectory control into two-degree-of-freedom heading tracking control and surge velocity tracking control by designing virtual posture angles. Optimized sliding mode control, based on sliding mode control, improves control precision and reduces control input chattering by constructing optimization functions for control inputs. During trajectory tracking, UUVs are susceptible to external environmental disturbances and perturbations in system model parameters. Disturbance observers are employed to estimate these disturbances and perturbations. Finally, MATLAB/Simulink is used for numerical simulation experiments. The simulation results demonstrate that the PPG algorithm effectively enables underactuated UUVs to achieve trajectory tracking control. The designed optimized sliding mode controller and disturbance observer enhance the control precision and robustness of the system.

Performance analysis of different methods for optimal sliding mode control of DC/DC buck converter

Performance analysis of different methods for optimal sliding mode control of DC/DC buck converter

Optimization‐based design of sliding sector control for active seismic protection of structures

SummaryThe active tuned mass damper (ATMD) is a reliable energy‐dissipating device to effectively protect structures from serious damages due to earthquake excitations. This study proposes the optimal design of sliding sector control (SSC) for the seismic protection of an 11‐story shear building structure equipped with ATMD. First, the SSC controller is optimally designed for the seismic control of the structure subjected to an artificial earthquake. Then, the effectiveness of the optimized SSC (OSSC) is assessed in reducing the seismic responses of the structure subjected to four near‐ and far‐fault earthquake excitations. The efficient performance of the OSSC technique is also validated and compared with that of a number of the control techniques such as linear quadratic regulator (LQR), fuzzy logic control (FLC), proportional‐integral‐derivative (PID), and optimal sliding mode control (OSMC). Comparative results demonstrate the efficiency and robustness of the proposed OSSC in comparison with those of the other controllers.

Adaptive optimal sliding mode control for three-phase voltage source inverter: Reinforcement learning approach

The operation of the three-phase standalone inverter is affected by many factors, such as heavy changes in load, unbalanced loads, nonlinear loads, system uncertainties and external disturbances. These are critical weaknesses for the control system of the three-phase inverter to reach robust optimal performance. This paper proposes an adaptive optimal sliding mode control (AOSMC) scheme for a three-phase nonlinear uncertain inverter. This AOSMC strategy solves the problems of nonlinear optimization by adaptive dynamic programming, one of the techniques of reinforcement learning, and overcomes the uncertainties and disturbance effects by a disturbance observer–based sliding mode controller. This algorithm uses only one neural network to approximate the critic; therefore, the burden of computation is significantly reduced. Both the weight matrix of the critic network and the disturbance observer are asymptotically stable. The overall system is guaranteed to be ultimately uniformly bounded stable via Lyapunov stable theory. The simulation is conducted to validate the insensitivity of the proposed AOSMC algorithm to working conditions. Also, the competitive results are presented to demonstrate the improvement of the proposed AOSMC scheme in comparison to some other existing controllers.

NN-based reinforcement-learning optimal sliding mode control for drag-free and attitude of spacecraft with state constraints

This paper investigates a tracking control issue for a class of drag-free spacecraft with state constraints caused by the optical assembly. Firstly, a nonlinear kinematics and dynamics relative equation of coupling system of position and attitude is devised by a 6-degree of freedom (DOF) model of rigid body. Secondly, an optimal control method with a terminal functional is designed to meet state constraints. To solve the Hamilton-Jacobi-Bellman (HJB) equation generated by the optimal control of the nonlinear model, a policy iteration ideal is presented and the final numerical solution of the iteration is obtained by a critic neural network (NN). Thirdly, to enhance the robustness of the closed-loop system, an optimal sliding mode control is proposed, which can ensure the optimal and robustness performance simultaneously. At last, the simulation results demonstrate the performance of the proposed methods and the contrast of precision and robustness of two methods are showcased.

Optimized Sliding Mode Control Based on Cuckoo Search Algorithm: Application for 2DF Robot Manipulator

Robot manipulators are used in high-accuracy processes they provide flexibility, adaptability, and a large workspace. Hence, in the presence of uncertainties, disturbance, and high-performance control approaches are necessary to improve their accuracy to achieve high-tracking precision requirements and transient response under load variation. We present in this article, a novel concept of robust nonsingular fast terminal sliding mode controller (NFTSMC). In fact, the use of the NFTSMC offers a fast convergence rate, avoids singularities but still suffers from chattering. To overcome this limitation, two approaches have been developed: robust nonsingular fast terminal sliding mode controller (RNFTSMC) and robust optimized nonsingular fast terminal sliding controller (RONFTSMC). In the first one an additional term called switching signal is added to the equivalent control law. The second one is a combination of the NFTSM technique, and a cuckoo search algorithm as optimum term. Simulations show that the control strategy can overcome the chattering phenomena ensures the accuracy and stability of the joint robot position control.

Optimal sliding mode control for frequency stabilization of hybrid renewable energy systems

AbstractThe constant changes in the load power lead permanently to a power mismatch between the power generation and the power consumption. So, the system frequency due to the power imbalance deviates from the nominal value. Consequently, a control loop should be implemented to stabilize the system frequency whenever a load change occurs. This paper presents a new super‐twisting sliding mode control methodology for obtaining an optimal frequency performance in a multi‐pool system. The paper presents a three‐pool system for frequency deviation problems using an optimal gain Super Twisting Sliding Mode Controller (STSMC), which regulates the frequency change and the line power change to zero in a minimal time. The extent of the excellence of the study proposed is evaluated by comparing it with three Benchmark classical controllers, which are the Tilt‐Integral‐Derivative (TID), Proportional‐Integral‐Derivative (PID), and Fractional‐Order PID (FOPID). The parameters of the four controllers are determined by a proposed physical meta‐heuristic optimization technique called Transient Search Optimizer (TSO), inspired by the dynamic behaviour in the electrical circuits comprising storage elements such as capacitors and inductors during the switching actions. The system simulation is performed, and the STSMC proved overwhelming superiority over other controllers, as it deals better with the transient interval of the system response. Renewable Energy sources (RESs) like photovoltaic and wind energy systems are established, and the STSMC is tested with industrial and residential load models. Finally, energy storage devices such as batteries and superconducting magnetic energy storage are implemented to suppress the rapid fluctuations in the system response, and it succeeded in doing that as the system oscillations are greatly damped with the energy storage devices.

Optimal sliding mode controller for lower limb rehabilitation exoskeleton in constrained environments

<p>In this article, a lower limb exoskeleton (LLE) under contacting constrained motion has been modelled using augmented Lagrange equations which include Lagrange multiplier and Jacobian vectors. A sliding mode Controller optimized by the grey Wolf optimization algorithm has been used for controlling (LLE) in the case of constrained motion with uncertainties and outside perturbation. The grey wolf optimization algorithm has been used as an optimization algorithm for finding the optimal controllers’ parameters in order to improve the performance of the system. The stability analysis of the closed-loop system has been performed using Lyapunov theory of stability. To validate the effectiveness of the proposed controller structure grey wolf optimization algorithm controller (GW-SMC), a series of comparative simulations have been carried out with other types of recently existing sliding mode control (SMC). The results of numerical simulations indicate the superiority of the sliding mode optimized by the GW-SMC over other types of recently existing controller in terms of tracking errors and robustness towards uncertainties and external disturbances.</p>

An ITAE Optimal Sliding Mode Controller for Systems with Control Signal and Velocity Limitations

Abstract In this paper, a sliding mode controller, which can be applied for second-order systems, is designed. Robustness to external disturbances, finite regulation time and a good system’s behaviour are required for a sliding mode controller. In order to achieve the first two of these three goals, a non-linear, time-varying switching curve is introduced. The representative point (state vector) belongs to this line from the very beginning of the control process, which results in elimination of the reaching phase. The stable sliding motion along the switching curve is provided. Natural limitations such as control signal and system’s velocity constraints will be taken into account. In order to satisfy them, the sliding line parameters will be properly selected. However, a good dynamical behaviour of the system has to be provided. In order to achieve that, the integral time absolute error (ITAE) quality index will be introduced and minimised. The simulation example will verify theoretical considerations.

Sliding sector–based adaptive controller for seismic control of structures equipped with active tuned mass damper

Active tuned mass damper (ATMD) as a reliable active device of structural control can protect structures subjected to earthquake excitations from the severe seismic damages. The present study focus on the design of an adaptive sliding sector controller (ASSC) employed in the ATMD system to mitigate the seismic responses of an 11–story shear building under earthquake excitations. The ASSC technique is designed based on the hyper-surface of the sliding mode which is surrounded by a sector and can consider the uncertainty of system parameters. In this study, the design of the ASSC strategy is first implemented for the structure subjected to an artificial earthquake excitation. Then, the performance of the ASSC strategy is evaluated in mitigating the seismic responses of the structure under four near– and far–fault earthquake excitations. Furthermore, the efficiency of the ASSC strategy is also compared against that of a few control techniques including proportional-integral-derivative [PID], linear-quadratic regulator [LQR], fuzzy logic control [FLC], optimal sliding mode control [OMSC]. Comparative results of the numerical simulation confirm the robustness and ability of the ASSC strategy for the reduction of the structural responses under real earthquake excitations.

Overcome uncertainties of vertical take-off and landing aircraft based on optimal sliding mode control

<span>This study aims to design a robust and optimal controller to overcome the problems related to the existence of disturbances and uncertainties during takeoff and landing operations of vertical take-off and landing (VTOL) aircraft. The dynamics are decomposed into two phase’s parts which are the minimum phase and the non-minimum phase. These two-part are controlled by proposing a robust nonlinear controller represented by sliding mode control (SMC). Also, the chattering effect due to the fast-switching surface in SMC is eliminated by utilizing a proposed sigmoid function which acts as the sigmoid function. The controller's main parameters are tuned optimally based on the particle swarm optimization (PSO) algorithm. In addition, the controller guaranteed the system stability based on the Lyapunov and Routh theories. The main output parameter responses represented by the positioning of the centre of mass and angle of rolling are determined with bounded control inputs. The performance of the proposed controller is tested by tracking VTOL parameters to the desired trajectories. The simulated results not only showed a significant tracking trajectory but also system stability guaranteed. In addition, the results showed an improved rate of 72% and 84% compared with those results obtained from the literature.</span>

Trajectory tracking control of upper limb rehabilitation robot based on optimal discrete sliding mode control

In this paper, an optimal sliding mode control method for trajectory tracking of discrete-time systems based on linear quadratic regulator is proposed to improve the trajectory tracking control accuracy and robustness of upper limb rehabilitation robot under the condition of highly nonlinearities, external disturbances, and unmodeled dynamics. Firstly, considering the uncertainty of the mass and moment of inertia of the connecting rod arm of the upper limb rehabilitation robot and the uncertainty of external interference, the dynamic model of the upper limb rehabilitation robot is established by using the Euler Lagrange method, and the linear time-varying state equation of the rehabilitation robot system under the influence of both nonlinear and uncertain factors is derived. Secondly, directing at the chattering problem in sliding mode control, a sliding mode control method based on a new discrete time reaching law is designed to reduce the amplitude of chattering in the control input signal of the upper limb rehabilitation robot system and improve the tracking speed. Furthermore, combined with linear quadratic optimal control, the optimal discrete integral sliding mode control law (LQRSMC) is finally obtained. Meanwhile, for the sake of reducing the influence of the uncertain signal on the system, a robust control law is adopted to estimate and compensate the uncertain interference. The stability of the upper limb rehabilitation robot system is verified by the sliding mode approach condition of the discrete system. Finally, the genetic algorithm is used to further optimize the weighted value, and MATLAB/Simulink is used to simulate the state trajectory of the upper limb rehabilitation robot under various weighted values. The control strategy can not only effectively weaken the trajectory tracking oscillation problem of the upper limb rehabilitation robot, but also overcome the external disturbance and modeling uncertainty, while ensuring the robustness of the rehabilitation robot system.

Multi-Level Coordinated Yaw Stability Control Based on Sliding Mode Predictive Control for Distributed Drive Electric Vehicles Under Extreme Conditions

It is an undeniable fact that the instant sideslip of the vehicle in case of high-speed obstacle avoidance will cause vehicles to lose stability. Current yaw moment control methods for distributed drive electric vehicles (DDEVs) does not fully consider the relationship between the vehicle instability degree and the optimal yaw moment control center, which greatly restricts the attitude correction ability of the four-wheel drive torque. To solve this problem, this article proposes a novel multi-level coordinated yaw stability control method based on robust sliding mode predictive control (SMPC) for DDEVs to improve the maneuverability and lateral stability. Firstly, a novel multi-scale vehicle dynamic model of yaw motion is constructed with the consideration that the vehicle instability center is time-varying under various sideslip conditions. Then, an online sliding mode prediction model of dynamics nonlinear system of DDEVs is established according to the local modeling method based on just-in-time learning. In addition, the linear time-varying model predictive control algorithm (LTV-MPC) with less predictive horizon is used to obtain the optimal sliding mode control law. Besides, an adaptive weighted soft switching function based on data driven hierarchical predictive proportional-integral-derivative (PID) control is put forward to determine the optimal weight value of the three yaw moment control modes in real time. Finally, the simulation and experimental results have verified that the proposed control method has strong vehicle attitude correction ability which can improve the trajectory tracking accuracy and the handling stability for DDEVs under extreme conditions.

Robust Optimal Output-Tracking Control of Constrained Mechanical Systems With Application to Autonomous Rovers

This article presents a robust optimal output-tracking control strategy for underactuated mechanical systems whose motion is restricted by mixed holonomic and nonholonomic constraints. Autonomous rovers/cars and unmanned underwater/aerial vehicles are a few examples of such systems that must often operate in harsh environments and under uncertain conditions. We present a comprehensive control analysis of this large class of nonlinear systems, including the existing studies on local reachability and static state feedback linearization. We also propose a local observability analysis of the feedback transformed input–output linearized systems. Based on the input–output linearization of the holonomically restricted nominal system, we develop a sliding mode control strategy that is robust against the projected effects of uncertainties and disturbances on the system’s output. Asymptotic stability of the output toward a bounded desired trajectory is proven using Lyapunov’s direct method, while the system’s internal stability (in the sense of boundedness) is investigated based on the notion of tracking-error zero dynamics. Time-dependent bounded matched uncertainties in the inertia parameters and disturbance forces arising in the unrestricted system are considered in this study. We propose an optimal sliding manifold according to the finite-horizon linear-quadratic regulator design problem with split boundary value conditions. The developed control strategy is implemented on a six-wheel autonomous Lunar rover in a simulation environment and its performance is compared with that of an optimal proportional–integral–derivative feedback, feedforward controller. The optimal sliding mode controller shows superior performance in trajectory tracking with acceptable control actions.

Enhancing the performance of the vehicle active suspension system by an Optimal Sliding Mode Control algorithm.

The suspension system determines riding comfort. This item utilizes an active suspension system to absorb vehicle vibration. A quarter-dynamics model with five state variables simulates the oscillations of a vehicle. This model incorporates the hydraulic actuator effect into linear differential equations. This is an entirely original design. In addition, the OSMC (Optimal Sliding Mode Control) algorithm is proposed for active suspension system operation control. The in-loop algorithm optimizes the controller's parameters. According to the findings of the study, when the OSMC algorithm was implemented, the maximum and average displacement values of the sprung mass were dramatically lowered under normal oscillation conditions. If a vehicle employs only a passive suspension system or an active suspension system with a standard linear control algorithm, the wheel is fully detached from the road surface in hazardous conditions. When the OSMC algorithm is utilized to control the operation of the active suspension system, the wheel-to-road interaction is always maintained. This algorithm provides a great degree of efficiency.

Design of Optimal Sliding Mode Control based on Linear Matrix Inequality for Fractional Time-Varying Delay Systems

Design of Optimal Sliding Mode Control based on Linear Matrix Inequality for Fractional Time-Varying Delay Systems

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.

Continuous-Thrust Station-Keeping of Cis-Lunar Orbits Using Optimal Sliding Mode Control with Practical Constraints

The cis-lunar space has been more and more attractive for human beings, and different kinds of missions have been proposed. For cis-lunar missions with long durations, the stationing-keeping is a pivotal problem. In this paper, the station-keeping problem with continuous thrust for different cis-lunar orbits, including distant retrograde orbits (DROs), near rectilinear halo orbits (NRHOs), and halo orbits, are investigated in the ephemeris model. The optimal sliding mode control (OSMC) based on the linear quadrant regulator (LQR) control is designed for the station-keeping problem. Simulations only considering the initial insertion error are conducted first to show performances of the OSMC controller, and the Jupiter gravity and solar radiation pressure (SRP) are then included as unknown perturbations to test the controller’s robustness. Then, with considerations of more practical constraints caused by the navigation and propulsion systems, Monte-Carlo simulations are carried out to provide more realistic results, and station-keeping performances are compared and analyzed for different nominal orbits. The results can provide useful references for the selection of station-keeping strategy in future long-term lunar missions.