Sliding Control Theory Research Articles

Robust Control of Uncertain Nonlinear Switched Systems: A Dissipativity-Based Integral Sliding Mode Control Redesign Approach

This paper considers the redesign control problem based on integral sliding control theory for a class of uncertain nonlinear switched systems where the primary control law is designed based on the dissipativity of the unperturbed system. Unlike the existing works, the model is considered nonlinear with different input channels and matched and unmatched perturbations. The dissipativity-based redesign strategy includes an integral sliding mode control with a common sliding surface with smooth changes in the switching instances. The sliding surface depends on the initial value of states such that the controlled system operates on the sliding mode from the initial time and the sliding dynamics are stable. Moreover, the reachability of the specified sliding surface in finite time is guaranteed, and the designed control law preserves the stability of the perturbed system with the same characteristics of the unperturbed system. In addition, these results are further extended to the cases that the initial values of states are not exactly known. By including an additive term in the sliding surface equation, the resulting sliding mode controller guarantees the dissipativity of the closed-loop system in the neighborhood of the sliding surface. This control law improves the behavior of the controlled switched system in the partial reaching phase and during the chattering. The proposed technique eliminates the restrictive design conditions on the derivative of storage functions and the switching law required in recent works. Finally, the theoretical results are applied to a nonlinear switched system to illustrate the effectiveness of the proposed method.

Analysis of the forces acting on beating cilia

Detailed analysis of the forces acting on a uniform-diameter beating cilium is carried out to determine the moment generated by the inter-doublet forces acting along the length of a cilium and the results are compared with the sliding-control theory according to which the moment is a function of the interdoublet sliding. In the central part of the cilium the inter-doublet forces are found to be proportional to the inter-doublet sliding. However, in spite of the uniformity of the diameter of the cilium, the proportionality constant, known as the dynamic stiffness, is not constant along its entire length. Significant variations are observed in the regions both near the tip of the cilium and proximal to the cell body. In the tip region the magnitude of the dynamic stiffness is found to decrease. This decrease is probably due to decrease in the number density of the molecular motors in that region and in the number of doublet microtubules. The behavior in the proximal region, on the other hand, does not appear to be well described by the sliding control theory. Our analysis therefore suggests that the dynamics of ciliary beating cannot be adequately described by a simple sliding-control theory with constant dynamic stiffness. Our analysis suggests that the cilium is differentiated into a basal region optimized for the creation of a wave and a central region optimized to support a traveling wave that provides the thrust for the cell.

Optimal sliding guidance algorithm for Mars powered descent phase

Landing on large planetary bodies (e.g. Mars) with pinpoint accuracy presents a set of new challenges that must be addressed. One such challenge is the development of new guidance algorithms that exhibit a higher degree of robustness and flexibility. In this paper, the Zero-Effort-Miss/Zero-Effort-Velocity (ZEM/ZEV) optimal sliding guidance (OSG) scheme is applied to the Mars powered descent phase. This guidance algorithm has been specifically designed to combine techniques from both optimal and sliding control theories to generate an acceleration command based purely on the current estimated spacecraft state and desired final target state. Consequently, OSG yields closed-loop trajectories that do not need a reference trajectory. The guidance algorithm has its roots in the generalized ZEM/ZEV feedback guidance and its mathematical equations are naturally derived by defining a non-linear sliding surface as a function of the terms Zero-Effort-Miss and Zero-Effort-Velocity. With the addition of the sliding mode and using Lyapunov theory for non-autonomous systems, one can formally prove that the developed OSG law is globally finite-time stable to unknown but bounded perturbations. Here, the focus is on comparing the generalized ZEM/ZEV feedback guidance with the OSG law to explicitly demonstrate the benefits of the sliding mode augmentation. Results show that the sliding guidance provides a more robust solution in off-nominal scenarios while providing similar fuel consumption when compared to the non-sliding guidance command. Further, a Monte Carlo analysis is performed to examine the performance of the OSG law under perturbed conditions.

Convergence Analysis and Tuning of a Sliding-Mode Ripple-Correlation MPPT

The development of fast maximum power point tracking (MPPT) algorithms for photovoltaic (PV) systems with high bandwidth and predictable response to irradiation transients is attractive for mobile applications and installations under fast changing weather conditions. This paper proposes the convergence analysis of a sliding-mode version of the MPPT based on ripple correlation control (RCC). The contribution of this paper is a dynamic model, useful to derive a set of design guidelines to tune the sliding-mode RCC-MPPT and achieve a desired dynamic performance under irradiation transients. The research is based on sliding control theory and it includes both the chattering phenomena analysis, and a discussion on the effects of reactive parasitic elements in the PV module. The proposed analysis and design have been validated by MATLAB simulations first, and then with experimental tests on a 35-W panel with a boost converter charging a 24-V battery. The results support the effectiveness of the proposed modeling procedure and design guidelines, showing good agreement between the model prediction and the experimental transient response.

Design of the static var compensator adaptive sliding mode controller considering model uncertainty and time-delay

Using supplementary controller of static var compensator (SVC) is an effective way for enhancing the transient stability of an interconnected power system. In conventional controller design, SVC is usually considered as a first-order inertial model with known parameters. In this paper, a nonlinear controller design method based on adaptive sliding mode control is proposed to design a SVC supplementary controller. The imprecise of the model and the external disturbances such as time-delay are taking into consideration in the SVC model, and the interconnected system with SVC is considered by the center of inertia model. Then the SVC supplementary controller is designed based on the adaptive sliding control theory to improve the transient stability of the power system. Finally, the effectiveness of the proposed controller is verified using two simple systems. Simulation results show that the designed SVC sliding mode controller is robust to the variation of operation conditions and time-delays, and it has a better performance in enhancing the system stability as compared with the conventional SVC controller.

Sliding Mode Controller Design for Global Chaos Synchronization of Coullet Systems

This paper derives new results for the design of sliding mode controller for the global chaos synchronization of identical Coullet systems (1981). The synchronizer results derived in this paper for the complete chaos synchronization of identical hyperchaotic systems are established using sliding control theory and Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the sliding mode control method is very effective and convenient to achieve global chaos synchronization of the identical Coullet systems. Numerical simulations are shown to illustrate and validate the synchronization schemes derived in this paper for the identical Coullet systems.

Drive control system design for stability and maneuverability of a 6WD/6WS vehicle

This paper describes a drive controller designed to improve the lateral vehicle stability and maneuverability of a 6-wheel drive / 6-wheel steering (6WD/6WS) vehicle. The drive controller consists of upper and lower level controllers. The upper level controller is based on sliding control theory and determines both front and middle steering angle, additional net yaw moment, and longitudinal net force according to the reference velocity and steering angle of a manual drive, remotely controlled, autonomous controller. The lower level controller takes the desired longitudinal net force, yaw moment, and tire force information as inputs and determines the additional front steering angle and distributed longitudinal tire force on each wheel. This controller is based on optimal distribution control and takes into consideration the friction circle related to the vertical tire force and friction coefficient acting on the road and tire. Distributed longitudinal/lateral tire forces are determined as proportion to the size of the friction circle according to changes in driving conditions. The response of the 6WD/6WS vehicle implemented with this drive controller has been evaluated via computer simulations conducted using the Matlab/Simulink dynamic model. Computer simulations of an open loop under turning conditions and a closed-loop driver model subjected to double lane change have been conducted to demonstrate the improved performance of the proposed drive controller over that of a conventional DYC.

Fuzzy Adaptive Variable Structure Active Attitude Control of Flexible Spacecraft

This paper presents a novel control system design method for the three-axis-rotational tracking and vibration stabilization of a spacecraft with flexible appendages. Based on the sliding control theory, a robust attitude control law is derived to control the attitude motion of spacecraft. For actively suppressing the induced vibration, both fuzzy methods and strain rate feedback (SRF) control methods are presented. Numerical simulations are performed to show the feasibility and effeteness of the proposed methods.

Simulation Study of Sliding Control for Constant Polishing Force Using an Innovative Sphere-Like Polishing Tool on a Machining Center

This study proposes an innovative sphere-like tool for polishing process in the machining center. It can be applied not only z-axis rotation but also spinning rotation so that multidirectional polishing can be performed simultaneously. One of important polishing parameters is polishing force. It should be constant to prevent over or under polishing. In this paper, sliding control theory is proposed to achieve constant polishing force. Polishing process was modeled as a single degree of freedom of mechanical system including mass, spring, and damper. Control law has been determined based on polishing process model using sliding surface equation. Based on this control law, single and multi desired polishing force simulations were conducted. From the simulation results, it can be shown that the procedure to design control law has effective performance.

Mixed [formula omitted] autopilot design of bank-to-turn missiles using fuzzy basis function networks

This paper presents a novel mixed H 2 / H ∞ autopilot design for bank-to-turn missiles. Based on sliding control theory, the proposed autopilot utilizes a fuzzy basis function network to approximate the unknown nonlinear functions of bank-to-.turn missile dynamics, enabling a mixed H 2 / H ∞ controller with weight updating laws to be applied to attenuate the effects of approximation errors and external disturbances. Moreover, the mixed H 2 / H ∞ autopilot design can minimize H 2 performance criteria under a desired H ∞ disturbance rejection constraint. Unlike general mixed H 2 / H ∞ control problems, the proposed H 2 / H ∞ autopilot with self-tuning fuzzy basis function network can avoid solving coupled Riccati equations by adequately selecting diagonal weighting matrices in the H 2 performance criterion and H ∞ constraint. Therefore, the proposed H 2 / H ∞ control approach can be implemented efficiently. Computer simulation results are presented to illustrate the effectiveness of the proposed mixed H 2 / H ∞ autopilot for BTT missiles.

Does the brain use sliding variables for the control of movements?

Delays in the transmission of sensory and motor information prevent errors from being instantaneously available to the central nervous system (CNS) and can reduce the stability of a closed-loop control strategy. On the other hand, the use of a pure feedforward control (inverse dynamics) requires a perfect knowledge of the dynamic behavior of the body and of manipulated objects. Sensory feedback is essential both to accommodate unexpected errors and events and to compensate for uncertainties about the dynamics of the body. Experimental observations concerning the control of posture, gaze and limbs have shown that the CNS certainly uses a combination of closed-loop and open-loop control. Feedforward components of movement, such as eye saccades, occur intermittently and present a stereotyped kinematic profile. In visuo-manual tracking tasks, hand movements exhibit velocity peaks that occur intermittently. When a delay or a slow dynamics are inserted in the visuo-manual control loop, intermittent step-and-hold movements appear clearly in the hand trajectory. In this study, we investigated strategies used by human subjects involved in the control of a particular dynamic system. We found strong evidence for substantial nonlinearities in the commands produced. The presence of step-and-hold movements seemed to be the major source of nonlinearities in the control loop. Furthermore, the stereotyped ballistic-like kinematics of these rapid and corrective movements suggests that they were produced in an open-loop way by the CNS. We analyzed the generation of ballistic movements in the light of sliding control theory assuming that they occurred when a sliding variable exceeded a constant threshold. In this framework, a sliding variable is defined as a composite variable (a combination of the instantaneous tracking error and its temporal derivatives) that fulfills a specific stability criterion. Based on this hypothesis and on the assumption of a constant reaction time, the tracking error and its derivatives should be correlated at a particular time lag before movement onset. A peak of correlation was found for a physiologically plausible reaction time, corresponding to a stable composite variable. The direction and amplitude of the ongoing stereotyped movements seemed also be adjusted in order to minimize this variable. These findings suggest that, during visually guided movements, human subjects attempt to minimize such a composite variable and not the instantaneous error. This minimization seems to be obtained by the execution of stereotyped corrective movements.