PID Sliding Surface Research Articles

The Synchronization of a Class of Time-Delayed Chaotic Systems Using Sliding Mode Control Based on a Fractional-Order Nonlinear PID Sliding Surface and Its Application in Secure Communication

A novel approach for the synchronization of a class of chaotic systems with uncertainty, unknown time delays, and external disturbances is presented. The control method given here is expressed by combining sliding mode control approaches with adaptive rules. A sliding surface of fractional order has been developed to construct the control strategy of the abovementioned sliding mode by employing the structure of nonlinear fractional PID (NLPID) controllers. The suggested control mechanism using Lyapunov’s theorem developed robust adaptive rules in such a way that the estimation error of the system’s unknown parameters and time delays tends to be zero. Furthermore, the proposed robust control approach’s stability has been demonstrated using Lyapunov stability criteria and Lipschitz conditions. Then, in order to assess the performance of the proposed mechanism, the presented control approach was used to simulate the synchronization of two chaotic jerk systems with uncertainty, unknown time delays, and external distortion. The results of the simulation confirm the robust and desirable synchronization performance. Finally, a secure communications mechanism based on the proposed technique is shown as a practical implementation of the introduced control strategy, in which the message signal is disguised in the transmitter with high security and well recovered in the receiver with high quality, according to the mean squared error (MES) criteria.

A Lyapunov Stability Analysis of Modified HOSM Controllers Using a PID-Sliding Surface Applied to an ABS Laboratory Setup

The antilock braking system (ABS) is a mechatronic system that helps a driver maintain the maneuverability of a vehicle while braking by preventing wheel lock-ups. However, the design of high-performance controllers for this type of system is complicated because of its highly nonlinear dynamics. The problem becomes even more difficult to resolve when uncertainties in the parameters appear in its dynamics. In this paper, an ABS laboratory setup mimicking a quarter car model is considered. A modified high-order sliding mode (HOSM) controller using a proportional-integral-differential (PID) control as a sliding surface was designed. This controller provides a reference value of a tire slip. The proposed controller uses a tracking error to define the slip surface through the PID controller structure, and the modified HOSM controller holds the system on the previously designed slip surface. The closed-loop system stability has been proven in the sense of Lyapunov. Finally, the ABS laboratory setup allows for experimentally checking the performance of the modified HOSM controller using a PID-sliding surface, showing a considerable increase in the efficiency of the control system compared with a PID-like controller.

Sliding Mode Control With PID Sliding Surface for Active Vibration Damping of Pneumatically Actuated Soft Robots

This paper proposes a novel active vibration damping mechanism for soft robots. In recent years, soft robots have gained increasing research attention for robotic researchers and industrial developers alike. Soft robots offer a significant number of advantages when it comes to the handling of fragile objects, clinical rehabilitation tasks, and human-machine interaction. Soft robots demonstrate a high degree of compliance and safety because of their inherent softness, achieving the same with rigid robots will require intricate controller design and sensing mechanisms. However, the most commonly used soft robots use pneumatic systems for actuation. These pneumatic soft robots undergo large amplitude vibrations when deactuated suddenly. These vibrations not only decrease the accuracy of these soft robots but also compromise their structural integrity, which results in a decrease in their useable lifespan. An active vibration damping mechanism is very much needed to increase the utility of soft robots in industrial applications. To accurately control the dynamic behavior of soft robots, we propose a sliding mode based controller with PID sliding surface. The proposed controller uses feedback error to define a PID sliding surface, and a nonlinear sliding mode controller works to keep the system attached to the sliding surface. The coefficients of the PID sliding surface determine the dynamic behavior of the soft robot. The performance of the proposed controller is verified by using a multi-chambered parallel soft robot. The experimental results demonstrate that the proposed controller can suppress vibration amplitude to a decidedly smaller range.

A Sliding Mode Control with Nonlinear Fractional Order PID Sliding Surface for the Speed Operation of Surface‐Mounted PMSM Drives Based on an Extended State Observer

A novel sliding mode controller (SMC) with nonlinear fractional order PID sliding surface based on a novel extended state observer for the speed operation of a surface‐mounted permanent magnet synchronous motor (SPMSM) is proposed in this paper. First, a new smooth and derivable nonlinear function with improved continuity and derivative is designed to replace the traditional nonderivable nonlinear function of the nonlinear state error feedback control law. Then, a nonlinear fractional order PID sliding mode controller is proposed on the basis of the fractional order PID sliding surface with the combination of the novel nonlinear state error feedback control law to improve dynamic performance, static performance, and robustness of the system. Furthermore, a novel extended state observer is designed based on the new nonlinear function to achieve dynamic feedback compensation for external disturbances. Stability of the system is proved based on the Lyapunov stability theorem. The corresponding comparative simulation results demonstrate that the proposed composite control algorithm displays good stability, dynamic properties, and strong robustness against external disturbances.

Quadcopter Robust Adaptive Second Order Sliding Mode Control Based on PID Sliding Surface

We present a robust adaptive second-order sliding mode controller that rejects external disturbances and uncertainties to improve the tracking performance of attitude and altitude in a quadcopter based on a Proportional–Integral–Derivative sliding surface. The algorithm provides a rapid adaptation and strict robustness of the flight control for the vehicle under the effect of perturbations. The proposed controller design is based on the theory of second order sliding mode technique that eliminates the chattering phenomenon present in first-order sliding mode controllers. In addition, we derive an adaptive law from the Lyapunov stability to ensure the robust control for the quadcopter even without knowing the upper bound for disturbances. Applying the same external disturbances, we use a numerical simulation to compare our algorithm to recent alternatives, such as normal adaptive sliding mode control, super-twisting sliding mode control, modified super-twisting sliding mode control, and nonsingular terminal sliding mode control. The results demonstrate the effectiveness of our proposed algorithm.

PID-Sliding Surface Based Sliding Mode Controller for Anti-Lock Braking System of Electric Vehicle

Anti-lock Braking System (ABS) is a crucial part in electric vehicle. It is an uncertain and nonlinear system. In this paper a Sliding Mode Control (SMC) technique with PID sliding surface is used to maintain the slip ratio, at 0.2 of ABS system. The mathematical representation of a quarter vehicle model that emphasizes essential characteristics of the whole vehicle was implemented in this research. The model was developed using Simulink and the proposed SMC technique was tested and validated. In addition, the sliding mode enforcement was ensured via stability analysis. The simulation results have shown good agreement and acceptable response of the ABS system

SMC Controlled Chaotic Trajectory Tracking of Two-Link Flexible Manipulator with PID Sliding Surface

The objective of the paper is to design a controller for two-link flexible manipulator to track the chaotic signal in presence of bounded disturbances and to regulate the tip deflection to its desired value close to zero. The Genesio-Tesi chaotic system is used to generate the desired trajectory for the flexible manipulator. A sliding mode controller is designed with PID sliding surface to achieve the objective. The designed sliding mode controller works satisfactorily with low chattering in presence of bounded disturbances. The lumped parameter method is used to model the dynamics of the manipulator. The stability of the PID sliding surface is guaranteed using Lyapunov stability theory. The sliding surface is designed in terms of tracking error dynamics and tip deflection error dynamics. A chaotic trajectory tracking of angular position and regulation of tip deflection using the PID sliding mode controller for the two-link flexible manipulator is the novelty of the paper.

Sliding Mode Control with Predictive PID Sliding Surface for Improved Performance

In this paper, a sliding mode control system with a predictive proportional-integral-derivative (PPID-SMC) sliding surface is proposed. A robust sliding mode controller is suggested to track the desired trajectory despite uncertainty, set point variations, and external disturbances. The proposed sliding mode controller is chosen to ensure the stability of overall dynamics during the reaching phase and sliding phase. The chattering problem is overcome using a hyperbolic tangent function for the sliding surface. Simulation example is given to illustrate the use of the proposed structure for better performance in terms of time domain specifications over some existing design methods.

A High Order Sliding Mode Control with PID Sliding Surface: Simulation on a Torpedo

Position and speed control of the torpedo present a real problem for the actuators because of the high level of the system non linearity and because of the external disturbances. The non linear systems control is based on several different approaches, among it the sliding mode control. The sliding mode control has proved its effectiveness through the different studies. The advantage that makes such an important approach is its robustness versus the disturbances and the model uncertainties. However, this approach implies a disadvantage which is the chattering phenomenon caused by the discontinuous part of this control and which can have a harmful effect on the actuators. This paper deals with the basic concepts, mathematics, and design aspects of a control for nonlinear systems that make the chattering effect lower. As solution to this problem we will adopt as a starting point the high order sliding mode approaches then the PID sliding surface. Simulation results show that this control strategy can attain excellent control performance with no chattering problem.

A new variable structure PID-controller design for robot manipulators

In this brief, a new variable structure proportional-integral-derivative (PID) controller design approach is considered for the tracking stabilization of robot motion. The work corroborates the utility of a certain PID sliding mode controller with PID sliding surface for tracking control of a robotic manipulator. Different from the general approach, the conventional equivalent control term is not used in this controller because that needs to use the matching conditions and exact full robot dynamics knowledge, which involves unavailable parameter uncertainties. Though the sliding surface includes also the integral error term, which makes the robot tracking control problem complicated, the existence of a sliding mode and gain selection guideline are clearly investigated. Moreover, different from uniformly ultimately boundedness, the global asymptotic stability of the robot system with proposed controller is analyzed. The sliding and global stability conditions are formulated in terms of Lyapunov full quadratic form and upper and lower matrix norm inequalities. Reduced design is also discussed. The proposed control algorithm is applied to a two-link direct drive robot arm through simulations. The simulation results indicate that the control performance of the robot system is satisfactory. The chattering phenomenon is handled by the use of a saturation function replaced with a pure signum function in the control law. The saturation function results in a smooth transient performance. The proposed approach is compared with the existing alternative sliding mode controllers for robot manipulators in terms of advantages and control performances. A comparative analysis with a plenty of simulation results soundly confirmed that the performance of developed variable structure PID controller is better under than those of both classical PID controller and an existing variable structure controller with PID-sliding surface.