Adaptive Controller Design for Overhead Cranes With Moving Sliding Surface

In this paper, we propose a Takagi-Sugeno-Kang (TSK) fuzzy model for a four-Mecanum-wheel omni-directional mobile free-base (4MW-ODMFB) with system uncertainties and external disturbances based on the model given in [12], [13], and then design an adaptive sliding-mode control (ASMC) system for trajectory tracking of 4MW-ODMFB, which combines the techniques of adaptive control and sliding-mode control. By using Lyapunov method we prove that the ASMC system is global asymptotic stable. We also conduct simulation experiments in MATLAB environment to test our TSK fuzzy model and the ASMC method. All the simulation results demonstrate the effectiveness of the proposed TSK fuzzy model and the stability and robustness of ASMC system.

This paper proposes a novel adaptive sliding mode control (ASMC) for a class of polynomial systems comprising uncertain terms and input nonlinearities. In this approach, a new polynomial sliding surface is proposed and designed based on the sum‐of‐squares (SOS) decomposition. In the proposed method, an adaptive control law is derived such that the finite‐time reachability of the state trajectories in the presence of input nonlinearity and uncertainties is guaranteed. To do this, it is assumed that the uncertain terms are bounded and the input nonlinearities belong to sectors with positive slope parameters. However, the bound of the uncertain terms is unknown and adaptation law is proposed to effectively estimate the uncertainty bounds. Furthermore, based on a novel polynomial Lyapunov function, the finite‐time convergence of the sliding surface to a pre‐chosen small neighborhood of the origin is guaranteed. To eliminate the time derivatives of the polynomial terms in the stability analysis conditions, the SOS variables of the Lyapunov matrix are optimally selected. In order to show the merits and the robust performance of the proposed controller, chaotic Chen system is provided. Numerical simulation results demonstrate chattering reduction in the proposed approach and the high accuracy in estimating the unknown parameters.

The sliding mode control (SMC) strategy is employed to a permanent magnet synchronous motor (PMSM) vector control system in this study to improve system robustness against parameter variations and load disturbance. To decrease the intrinsic chattering behavior of SMC, a speed SMC with an adaptive law and an extended state observer (ESO) is proposed. In this method, based on the Lyapunov stability theorem, adaptive estimation laws are deduced to estimate uncertainties of a PMSM caused by parameter variations and unmodeled dynamics. Online estimated uncertainties can be used to eliminate the effect caused by the real uncertainties. In addition, an ESO is applied to observe the load disturbance in real time. The load disturbance observed value is then utilized to the output side of the speed adaptive SMC controller as feed-forward compensation. Both the simulation and experiment results demonstrate that the proposed approach effectively alleviates system chattering and enhances system robustness against uncertainty and load disturbance.

We propose a novel data‐driven model‐free adaptive terminal sliding mode control (SMC) for a class of discrete nonlinear systems with perturbations in which tracking error constraints are taken into account in improving tracking accuracy. The goal of this design is that the tracking error trajectory is maintained within the prescribed convergence region which is defined by the performance function, while the disturbances exist. In explaining the advantage of this proposed control scheme, at first, by theoretical calculation, it is proved theoretically that the quasi‐sliding mode can be achieved in a limited time under the specified tracking performance. Furthermore, comparative investigation results are given to validate the effectiveness of the proposed control scheme. Simulation results show that the proposed strategy is superior to model‐free adaptive control, model‐free adaptive terminal SMC, and data‐driven adaptive SMC with prescribed performance control algorithms in terms of tracking accuracy and response speed, which demonstrates the efficiency of the proposed scheme.

In the control algorithm of digital hydraulic position tracking system, there exists many modeling assumptions and limited robustness. By the combining of the sliding mode variable structure control and model reference adaptive control, the present essay is to design a new sliding mode adaptive controller and do a simulation analysis. The simulation results indicate that the controller has high precision in controlling and fast in responding. It overcomes the problem of the control precision's decreasing when the adaptive control is applied alone and the output of the system is zero and avoids the influences of the uncertain parameters and the external disturbance, thus the robustness of the system.

This paper aims to design an adaptive fault-like model-based sliding-mode control (SMC) law for a class of vehicle platoon systems, where the follower vehicles have quantized input, unknown actuator deadzone, and distance restrictions. Using adaptive terminal sliding mode control method and barrier Lyapunov function (BLF), an adaptive controller is designed to ensure the collision avoidance and communication connection keeping. In addition, the problem of the unknown actuator deadzone and input quantization is first transformed to a fault-like problem, which will simplify the control design procedure. Finally, the effectiveness of the proposed control strategy is verified by a numerical example.

This paper establishes a new stochastic SIR epidemic model that incorporates telegraph noise and Lévy noise to simulate the complex environmental disturbances affecting disease transmission. Given the susceptibility of epidemic spread to environmental noise and its intricate dynamics, an adaptive sliding mode controller based on an integral sliding surface and an adaptive control law is proposed. This controller is capable of stabilizing the constructed model and effectively suppressing the spread of the disease. The main contributions of this paper include the following: establishing a comprehensive and realistic stochastic SIR model that accounts for the complex impacts of telegraph noise (symbolizing periodic environmental changes) and Lévy noise (representing sudden environmental shocks) on the dynamics of disease transmission; employing T-S fuzzy modeling, which considers the design of fuzzy rules and the symmetry of membership functions, to ensure linearization of the model; constructing an integral sliding surface and designing an adaptive sliding mode controller for the fuzzy-processed model. Finally, the effectiveness of the proposed control method is validated through numerical simulations.

This paper deals with the trajectory tracking of differential driven wheeled mobile robots (WMRs). It is widely known that parameter uncertainty and unknown external disturbances could bring adverse effects to WMRs. To achieve high-performance tracking, a control scheme is proposed in this paper, which integrates a kinematics controller and a dynamics controller. The kinematics controller is designed by the backstepping control and the dynamics controller is derived via adaptive sliding mode control. Moreover, dual radial basis function neural networks (RBFNNs) with adaptive adjust algorithms are adopted to approximate parameter alterations of system dynamics as well as external disturbances. To solve the uncertainty of wheel rolling radius, an adaptive control law is applied. In addition, a PI-type sliding mode control strategy with an exponential reaching law is designed to compensate for the approximation errors of the RBFNNs. Furthermore, the stability and global asymptotic convergence of the control system are proved by the Lyapunov stability theorem. Finally, simulations are provided to verify the effectiveness of the proposed control strategy. The results indicate that the proposed control law is effective in response to parameter uncertainty and external disturbances.

The slotless self-bearing motor (SSBM) is a motor with its self-bearing function. The mechanical structure of the motor is six symmetrical hexagonal shapes. The main control problem for this motor is disturbance and uncertainty rejection. Therefore, this paper proposes a new disturbance observer (DOB) based on an optimal fixed-time state observer (OFTSOB) and adaptive sliding mode control (SMC) for the motor. Firstly, the optimal state observer was used to construct to obtain the information of the states of the bearing-less motor system. Second, a new disturbance observer base on the fast speed reaching law is proposed for estimating the unknown dynamics and unpredicted uncertainty of the motor system. Third, the adaptive fast-reaching law-sliding mode control is designed to control the positions and rotational speed. Fourth, the proposed control system is proved via the Lyapunov theorem. Finally, the corrections of proposed method once again tested by using MATLAB simulation. The obtained results figured out that the proposed method is good at rejection disturbance and uncertainty and precision in control the movement and rotation. The novelties of the proposed method are that the gains of fixed-time observer were met by the support of optimal pole placement method, the disturbances were mostly rejected by a new reaching law of unknown input observer.

A new adaptive fuzzy sliding-mode control (FSMC) scheme was proposed, which incorporated the fuzzy logic into sliding-mode control using fuzzy logic to approximate the equivalent control and the upper bound of uncertainty which involved the disturbance and approximation error, thus the influence of modeling error was reduced and the gain of sliding-mode control part was more fitting, such that the chattering effects could be alleviated . Besides, inspired by the thought of fully tuned RBF neural networks, a fully tuned fuzzy logic was proposed which enhanced the approximating ability of fuzzy logic system. Lyapunov stability theorem was used to prove the stability of the system and the adaptive laws were deduced. Finally, simulation results of some BTT missile were included to illustrate the effectiveness of the adaptive fuzzy sliding-mode control scheme.

As typical underactuated systems, overhead cranes are widely utilized in heavy-load transportation. However, their strong nonlinear coupling and underactuated characteristics complicate precise positioning and payload swing suppression. Furthermore, model uncertainties and external disturbances in practical environments increase control complexity and degrade system performance. To address these issues, this paper develops a trajectory tracking control scheme based on time delay estimation (TDE). Specifically, some transformations are made for the dynamic model and the TDE mechanism is used to estimate unknown nonlinear dynamics and external disturbances. Then, a sliding mode trajectory tracking controller, along with the TDE mechanism, is proposed for the trajectory tracking control and uncertainties estimation of the overhead crane system. Rigorous mathematical analysis is provided to demonstrate the asymptotic stability of the closed-loop system. Finally, simulation results verify the effectiveness of the proposed method in comparison with the existing control methods.

In this chapter an adaptive sliding mode controller for the Furuta pendulum is proposed. The Furuta pendulum is a class of underactuated mechanical systems commonly used in many control systems laboratories due to its complex stabilization which allows the analysis and design of different nonlinear and multivariable controllers that are useful in some fields such as aerospace and robotics. Sliding mode control has been extensively used in the control of mechanical systems as an alternative to other nonlinear control strategies such as backstepping, passivity based control etc. The design and implementation of an adaptive sliding mode controller for this kind of system is explained in this chapter, along with other sliding mode controller variations such as second order sliding mode (SOSMC) and PD plus sliding mode control (PD \(+\) SMC) in order to compare their performance under different system conditions. These control techniques are developed using the Lyapunov stability theorem and the variable structure design procedure to obtain asymptotically stable system trajectories. In this chapter the adaptive sliding mode consist of a sliding mode control law with an adaptive gain that makes the controller more flexible and reliable than other sliding mode control (SMC) algorithms and nonlinear control strategies. The adaptive sliding mode control (ASMC) of the Furuta pendulum, and the other SMC strategies shown in this chapter, are derived according to the Furuta’s pendulum dynamic equations making the sliding variables, position errors and velocity errors reach the zero value in a specified reaching time. The main reason of deriving two well known sliding mode control strategy apart from the proposed control strategy of this chapter (adaptive sliding mode control) is for comparison purposes and to evince the advantages and disadvantages of adaptive sliding mode control over other sliding mode control strategies for the stabilization of the Furuta pendulum. A chattering analysis of the three SMC variations is done, to examine the response of the system, and to test the performance of the ASMC in comparison with the other control strategies explained in this chapter.

Electro-hydraulic servo system is often affected by parameter uncertainties and mismatched random disturbances, which are two major obstacles to achieving high-performance servo control. In this article, a sliding mode adaptive controller is proposed to solve these two problems. The proposed controller employs sliding mode control method to eliminate unknown mismatched disturbances, adaptive design to deal with parametric uncertainties. A new smooth and continuous sliding mode control law is proposed to solve the design conflicts between sliding mode control technology and back-stepping adaptive control technology. The stability of the algorithm is proved based on the Lyapunov theory. Theoretically, the algorithm can make the position tracking error arbitrarily small. Through the co-simulation platform of AMESim and MATLAB/Simulink, the control performance of the developed control algorithm is verified. The results show that the developed sliding mode adaptive controller scheme can achieve high-performance tracking under the condition of parametric uncertainties and unknown mismatched disturbances.

This paper presents a sliding mode control for the motion control of tethered space robot. The input saturation of tension and thrusters is well taken into account, which is dealt with by a modified adaptive law to aid the expression of ideal control input in Lyapunov-based stability analysis. The adaptive law is designed to be naturally bounded such that the boundary of adaptive law is calculable and fixed to make the ideal input bounded, which satisfies the condition of the partial expression of the ideal input. For reducing the effect from disturbance and uncertainties, the relay-type control law combined with the adaptive law is used to drive the system states onto the sliding surface although the saturation occurs. Numerical simulation illustrate the results of deployment process to verify the effectiveness of the stability analysis.

An effective method, adaptive fuzzy sliding-mode (SM) PI Control to design full-bridge inverter is proposed in this paper. For practical applications, sliding mode control (SMC) with chattering phenomenon is a large hindrance. The modified model of the PI controller is built by the plant extension scheme, in order to relieve the chattering. Also, the fuzzy logic is applied to find the appropriate parameter values of the PI controller, and can adapt to plant parameter variations and external load disturbances. The proposed method has been realized for the actual full-bridge inverters controlled by DSP and CPLD. Simulation and experimental results of the closed-loop system show that the proposed method yields system performance improvement, such as low total harmonic distortion (THD), fast dynamic response, reduced steady-state error, and reduced chattering.