Robust H-infinity sliding mode control for nonlinear stochastic systems with multiple data packet losses

This is the post-print version of this Article. The official published version can be accessed from the link below - Copyright @ 2012 John Wiley & SonsIn this paper, an ∞ sliding mode control (SMC) problem is studied for a class of discrete-time nonlinear stochastic systems with multiple data packet losses. The phenomenon of data packet losses, which is assumed to occur in a random way, is taken into consideration in the process of data transmission through both the state-feedback loop and the measurement output. The probability for the data packet loss for each individual state variable is governed by a corresponding individual random variable satisfying a certain probabilistic distribution over the interval [0 1]. The discrete-time system considered is also subject to norm-bounded parameter uncertainties and external nonlinear disturbances, which enter the system state equation in both matched and unmatched ways. A novel stochastic discrete-time switching function is proposed to facilitate the sliding mode controller design. Sufficient conditions are derived by means of the linear matrix inequality (LMI) approach. It is shown that the system dynamics in the specified sliding surface is exponentially stable in the mean square with a prescribed ∞ noise attenuation level if an LMI with an equality constraint is feasible. A discrete-time SMC controller is designed capable of guaranteeing the discrete-time sliding mode reaching condition of the specified sliding surface with probability 1. Finally, a simulation example is given to show the effectiveness of the proposed method.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Royal Society of the U.K., the National Natural Science Foundation of China under Grant 61028008 and the Alexander von Humboldt Foundation of German

Multirate input based quasi-sliding mode control for permanent magnet synchronous motor

Permanent magnet synchronous motor field oriented control system often uses dual-loop (speed and current) cascade structure, and the dynamics speeds of the two loops mismatch. The motor’s mechanical and electrical subsystems have the typical multirate characteristics. Based on the multirate control theory, this paper proposes multirate input quasi-sliding mode algorithm for the speed control loop. Under the situation of the output data loss, the proposed algorithm builds the extended input vector with the output prediction information. Due to the extended input vector, the proposed algorithm reduces the system steady state chatterring, and then improves the performance of the whole system. Simulation and experimental results demonstrate the effectiveness of the proposed algorithm

Variable-parameter double-power reaching law sliding mode control method

To solve the problem of the slow convergence rate of the reaching law and the chattering problems in the dynamic response in the sliding mode control, an improved double-power sliding mode reaching law is proposed. The reaching law is adjusted by changing the magnitude of the power terms adaptively at different stages of the system approach process, and the convergence speed of the dynamic response process is greatly improved. Its existence, accessibility and stability are proven by theory. The simulation results show that the improved double-power reaching law is faster than the double-power reaching law and the fast power reaching law. When there is uncertainty in the system, the system state and its derivatives can rapidly converge to the neighbor-hood of the equilibrium zeros. In the presence of time-varying perturbations of the two-order system, the sliding mode control system based on the improved double-power sliding mode reaching law has higher tracking precision of the given signal and differential signal and effectively reduces the high-frequency chattering phenomenon of the control input signal

Discrete-time exponentially stabilizing fuzzy sliding mode control via lyapunov's method

The exponentially stabilizing state feedback control algorithm is developed by Lyapunov's second method leading to the variable structure system with chattering free sliding modes. Linear time-invariant discrete-time second order plant is considered and the control law is obtained by using a simple fuzzy controller. The analytical structure of the proposed controller is derived and used to prove exponential stability of sliding subspace. Essentially, the control algorithm drives the system from an arbitrary initial state to a prescribed so-called sliding subspace S, in finite time and with prescribed velocity estimate. Inside the sliding subspace S, the system is switched to the sliding mode regime and stays in it forever. The proposed algorithm is tested on the real system in practice, DC servo motor, and simulation and experimental results are given

Robotic Manipulator Control in the Presence of Uncertainty

openThis research focuses on the problem of manipulator control in the presence of uncertainty and aims to compare different approaches for handling uncertainty while developing robust and adaptive methods that can control the robot without explicit knowledge of uncertainty bounds. Uncertainty is a pervasive challenge in robotics, arising from various sources such as sensor noise, modeling errors, and external disturbances. Effectively addressing uncertainty is crucial for achieving accurate and reliable manipulator control. The research will explore and compare existing methods for uncertainty handling such as robust feedback linearization , sliding mode control and robust adaptive control. These methods provide mechanisms to model and compensate for uncertainty in the control system. Additionally, modified robust and adaptive control methods will be developed that can dynamically adjust control laws based on the observed states, without requiring explicit knowledge of uncertainty bounds. To evaluate the performance of the different approaches, comprehensive experiments will be conducted on a manipulator platform. Various manipulation tasks will be performed under different levels of uncertainty, and the performance of each control approach will be assessed in terms of accuracy, stability, and adaptability. Comparative analysis will be conducted to highlight the strengths and weaknesses of each method and identify the most effective approach for handling uncertainty in manipulator control. The outcomes of this research will contribute to the advancement of manipulator control by providing insights into the effectiveness of different approaches for uncertainty handling. The development of new robust and adaptive control methods will enable manipulators to operate in uncertain environments without requiring explicit knowledge of uncertainty bounds. Ultimately, this research will facilitate the deployment of more reliable and adaptive robotic systems capable of handling uncertainty and improving their performance in various real-world applications.This research focuses on the problem of manipulator control in the presence of uncertainty and aims to compare different approaches for handling uncertainty while developing robust and adaptive methods that can control the robot without explicit knowledge of uncertainty bounds. Uncertainty is a pervasive challenge in robotics, arising from various sources such as sensor noise, modeling errors, and external disturbances. Effectively addressing uncertainty is crucial for achieving accurate and reliable manipulator control. The research will explore and compare existing methods for uncertainty handling such as robust feedback linearization , sliding mode control and robust adaptive control. These methods provide mechanisms to model and compensate for uncertainty in the control system. Additionally, modified robust and adaptive control methods will be developed that can dynamically adjust control laws based on the observed states, without requiring explicit knowledge of uncertainty bounds. To evaluate the performance of the different approaches, comprehensive experiments will be conducted on a manipulator platform. Various manipulation tasks will be performed under different levels of uncertainty, and the performance of each control approach will be assessed in terms of accuracy, stability, and adaptability. Comparative analysis will be conducted to highlight the strengths and weaknesses of each method and identify the most effective approach for handling uncertainty in manipulator control. The outcomes of this research will contribute to the advancement of manipulator control by providing insights into the effectiveness of different approaches for uncertainty handling. The development of new robust and adaptive control methods will enable manipulators to operate in uncertain environments without requiring explicit knowledge of uncertainty bounds. Ultimately, this research will facilitate the deployment of more reliable and adaptive robotic systems capable of handling uncertainty and improving their performance in various real-world applications

Analysis of explicit and implicit discrete-time equivalent-control based sliding mode controllers

Different time-discretization methods for equivalent-control based sliding mode control (ECB-SMC) are presented. A new discrete-time sliding mode control scheme is proposed for linear time-invariant (LTI) systems. It is error-free in the discretization of the equivalent part of the control input. Results from simulations using the various discretized SMC schemes are shown, with and without perturbations. They illustrate the different behaviours that can be observed. Stability results for the proposed scheme are derived

Improved Third Order PID Sliding Mode Controller for Electrohydraulic Actuator Tracking Control

An electrohydraulic actuator (EHA) system is a combination of hydraulic systems and electrical systems which can produce a rapid response, high power-to-weight ratio, and large stiffness. Nevertheless, the EHA system has nonlinear behaviors and modeling uncertainties such as frictions, internal and external leakages, and parametric uncertainties, which lead to significant challenges in controller design for trajectory tracking. Therefore, this paper presents the design of an intelligent adaptive sliding mode proportional integral and derivative (SMCPID) controller, which is the main contribution toward the development of effective control on a third-order model of a double-acting EHA system for trajectory tracking, which significantly reduces chattering under noise disturbance. The sliding mode controller (SMC) is created by utilizing the exponential rule and the Lyapunov theorem to ensure closed-loop stability. The chattering in the SMC controller has been significantly decreased by substituting the modified sigmoid function for the signum function. Particle swarm optimization (PSO) was used to lower the total of absolute errors to adjust the controller. In order to demonstrate the efficacy of the SMCPID controller, the results for trajectory tracking and noise disturbance rejection were compared to those obtained using the proportional integral and derivative (PID), the proportional and derivative (PD), and the sliding mode proportional and derivative (SMCPD) controllers, respectively. In conclusion, the results of the extensive research given have indicated that the SMCPID controller outperforms the PD, PID, and SMCPD controllers in terms of overall performance.