Disturbance-Resilient Position Control of Maglev Systems Using Advanced Sliding Mode Techniques

Chattering-free higher order sliding mode controller with a high-gain observer for the load following of a pressurized water reactor

A major drawback of magnetic linear micro actuators is the vertical attractive force between stator and traveler. In the case of a micro step motor, this force is typically one order of magnitude greater than the driving force itself. To compensate for this undesired vertical force and thus taking full advantage of the driving force available, a magnetic levitation system was developed and implemented as a guide. The electromagnetic field generated by the stator coils interacts with the field of permanent magnets positioned in the traveler. This way, the traveler is elevated. Since repulsive magnetic levitation systems are inherently unstable, a tribological guide was integrated on both sides of the magnetic levitation system. During motion, the combination of stationary coils in the stator and moving permanent magnets in the traveler lifts up the traveler, while the lateral tribological guide prevents the traveler from shifting sideways. Initial investigations proved the feasibility of this magnetic levitation concept (1). A complete linear micro step motor system with magnetic levitation guide consists of the micro step motor itself, the magnetic micro levitation system (including the lateral guides), and a capacitive air gap measurement system. The latter one detects the size of the air gap between stator and traveler of the micro actuator. An assembly consisting of the three components results in a linear micro actuator system with adjustable air gap. For achieving optimal working conditions of the linear micro step motor, the magnetic levitation system was designed for a nominal air gap of 8 μm at the micro step motor. While earlier work proved the feasibility of such a guide, it also indicated (i) that the levitation system has to be capable of correcting a pitch motion of the traveler and (ii) that an as high magnetic levitation force as possible is desirable. To address the first issue, the magnetic levitation system received four coils arranged in a square along the axis of motion of the micro step motor. This way, both pitch and roll may be controlled. For resolving the second issue, the number of coil layers was increased from two to four. The technology for such a four layer coil is quite challenging, particularly since every effort has to be made to minimize its building height. The challenges were resolved by creating a coil system where the lateral insulation between conductors consists of SU-8™ (a photosensitive epoxy by Micro Resist Technology), while the vertical insulation layers were formed by a thin, stress compensated Si3N4 film. This way, a very compact coil with a high conductor-to-insulator ratio and thus a great current conducting capability could be realized. Due to the thin Si3N4 insulation, it also features an excellent thermal conductivity.

Heavy disturbances caused mainly by wind and friction in the mount drive system greatly impair the pointing accuracy of the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST). To overcome this negative effect, a third order Higher Order Sliding Mode (HOSM) controller is proposed. The key part of this approach is to design an appropriate observer which obtains the acceleration state. A nonlinear adaptive observer is proposed in which a novel polynomial model is applied to estimate the internal disturbances of the mount drive system. Theoretical analysis demonstrates the stability of the proposed observer. Simulation results show that this nonlinear adaptive observer can obtain a high precision acceleration signal which completes the HOSM controller. Furthermore, the HOSM approach can easily satisfy the position tracking requirements of the LAMOST mount drive system.

This work presents a nested super-twisting second-order sliding mode speed controller for a brushless direct current motor with a high order sliding mode observer used for back electromotive force (back-EMF) estimation. Due to the trapezoidal nature of the back-EMF, a modified Park transformation is used in order to achieve proper field orientation. Such transformation requires information from the back-EMF that is not accessible. A second-order sliding mode observer is used to estimate the back electromotive forces needed in the modified transformation. Sliding mode control is known to be robust to matched uncertain disturbances and parametric variations but it is prone to unmatched perturbations that affect the performance of the system. A nested scheme is used to improve the response of the controller in presence of unmatched disturbances. Simulations performed under similar conditions to real-time experimentation show a good regulation of the rotor speed in terms of transient and steady-state responses along with a reduced torque ripple.

In this paper, we develop a strategy for lateral control of an autonomous vehicle using a higher-order sliding mode control by the super-twisting algorithm. We minimize the lateral displacement of the autonomous vehicle to a reference trajectory. And more particularly we used a Particle Swarm optimization (PSO) algorithm to optimize the Control parameters of the higher-order Sliding Mode. In the simulation, We have followed two scenarios, the first is to optimize the sliding surface parameter and the second scenario based on the optimization of the control parameters. In this system the command input is the steering angle and the output is the lateral error. The simulation show that the control results by higher-order sliding mode control with parameters optimization PSO are better than those of the control by sliding mode control random.

Super-twisting sliding mode control of grid-side inverters for wind power generation systems with parameter perturbation

This paper presents roll stabilization of three axis gimbal system (TAGS) using higher order sliding mode control (HOSMC). TAGS under consideration has mass imbalance due to it's structural design. To achieve robust performance in presence of mass imbalance, robust control is sought. A mathematical model which includes cross coupling effect is used. HOSMC is proposed for roll stabilization and to encounter mass imbalance, different sets of gains are used. Simulated results of HOSMC are compared with PI controller. Performance of HOSMC is tested experimentally.

A survey on High-Order Sliding-Mode control design using Lyapunov functions

Permanent Magnet Synchronous Motors (PMSMs) exhibit inherent symmetry in their electromagnetic structure yet behave as nonlinear and strongly coupled systems that are susceptible to internal parameter perturbations and external disturbances, posing challenges to effective control under dynamic operating conditions. To address these issues, this paper proposes a sliding mode control strategy for PMSMs that integrates a Novel Adaptive Reaching Law (NARL) and an Improved Terminal Fuzzy Sliding Mode Disturbance Observer (IFTSMDO), denoted as SMC-NARL-IFTSMDO. The NARL is designed with a state-dependent dynamic gain adjustment mechanism and terminal attractive factor characteristics: it increases the gain to ensure fast convergence when the system state is far from the sliding mode surface, and adaptively attenuates the gain to suppress chattering when approaching the sliding mode surface, thereby balancing the contradiction between convergence speed and chattering in traditional sliding mode control. The IFTSMDO constructs a composite sliding mode surface incorporating error derivatives, terminal power terms, and saturation functions, which enhances the sensitivity of disturbance estimation in the small-error stage, avoids high-frequency chattering caused by sign functions, and provides accurate feedforward compensation for the speed loop controller to improve the system’s anti-disturbance capability. Additionally, the asymptotic stability of the proposed control strategy is strictly proven using the Lyapunov stability theory, laying a solid theoretical foundation for its application. Experiments are conducted on a TMS320F28379D DSP-based platform, and quantitative results show that compared with the traditional sliding mode control (SMC-TRL), the proposed strategy reduces the no-load startup response time by 60%, the steady-state speed fluctuation by 60%, and the speed fluctuation under load disturbance by 81.5%, fully demonstrating its superiority in dynamic response and anti-disturbance performance.

This paper presents a Radial Basis Function neural network based higher-order Sliding Mode Control for robust control of a dynamical system. A conventional sliding mode controller is suffering from a chattering problem, and the Super Twisting Algorithm is a special kind of higher-order Sliding Mode Control that has the capability of minimizing the chattering problem. There are also unknown model parameters and external disturbances that exert a negative influence on the control performance. To address the issues of model uncertainties and chattering, a Radial Basis Function (RBF) neural network based Super Twisting Algorithm is designed. The RBF neural network evaluates the model parameters and uncertainties, while the Super Twisting approach mitigates chattering, hence improving the controller’s overall performance. Lyapunov stability based adaptive laws are derived for online updating of the parameters of the neural network. The proposed control algorithm was tested on a 2-degree-of-freedom serial flexible joint robotic arm to investigate its efficacy. The controller has a lower control chattering amplitude, lower control energy consumption, and a good tracking response, when compared to the RBF based conventional Sliding Mode controller and simple STA controller, as shown by the results.

In this paper we present a nonlinear control using super twisting high order sliding mode for a vertical axis wind turbine (VAWT) with direct attack based on doubly-fed induction generator (DFIG) supplied by an AC-AC converter. In the first place, we carried out briefly a study of modeling on the whole system (H-darrieus wind turbine). In order to control the power flowing between the stator of the DFIG and the grid, a proposed control design uses high order sliding mode technique is applied for implementing to remove completely the chattering phenomenon on a conventional sliding mode control. The use of this method provides very satisfactory performance for the DFIG control, and the chattering effect is also reduced by this technique. The machine is tested in association with a wind turbine. Simulations results are presented and discussed for the whole system.

This paper proposes a nonsingular fast terminal sliding mode approach integrated with finite-time disturbance observer (DO-NFTSMC) for a magnetic levitation system exposed to uncertainties and external disturbances. A finite-time disturbance observer is first proposed to handle disturbances and modeling uncertainties. Then a nonsingular fast terminal sliding mode control (NFTSMC) approach is formulated relying on a newly constructed sliding surface to ensure fast transient convergence to the equilibrium. Overall stability and finite-time estimation were verified using the Lyapunov stability theory. Computer experiments using a highly nonlinear magnetic levitation (maglev) system showed promising results in terms of finite-time attainability, disturbance rejection and effective continuous control with reduced chattering. Additionally, performance comparison to that of a dynamic sliding mode control (DSMC) design was carried over and showed that the proposed controller outperformed the DSMC in all aspects.

A novel analogue circuit environment to implement higher order sliding mode (HOSM) and continuous finite time (CFT) stabilising controllers is proposed in this paper. The novelty lies in the ability of the circuit to capture the underlying theoretical features by producing non-Lipschtiz controller implementations. The circuit can be built using readily available off-the-shelf components. Since the environment is based on an analogue circuit, the development matches the mathematics of a class of non-Lipschitz differential equations more closely than its digital counterparts thereby narrowing the theory-practice gap. The key contribution is the implementation of a class of non-Lipschitz controllers using analogue components thereby nullifying steady-state tracking errors without the need for integral action, a key concept of both HOSM and CFT philosophies with the former being more robust. The circuit has plug-and-play functionality similar to the ubiquitous PID controllers, where recent results on the tuning of HOSM controller parameters give the potential to replicate the classical PID controller tuning approach. The functionality is demonstrated by the closed-loop speed control of a dc motor, although the results are applicable to other engineering problems which are also discussed.

Due to the advantages of high stiffness, high precision, high load capacity and large workspace, hybrid robots are applicable to drilling and milling of complicated components with large sizes, for instance car panels. However, the difficulty in establishing an exact dynamic model and external disturbances affect the high accuracy control directly, which will decrease the machining accuracy and thereby affect the machining quality and efficiency of the system. Sliding mode control is an effective approach for high-order nonlinear dynamic systems since that it is very insensitive to disturbances and parameter variations. However, chattering may exist in traditional sliding mode control with fixed parameters, which results from a constant approaching speed. Besides, the approaching speed will affect the chattering strength directly. To solve these problems, a modified sliding mode controller with self-adaptive parameters is proposed to enhance the trajectory-tracking performance of a 5-degree-of-freedom hybrid robot. Firstly, the kinematic model of the robot is established. Then adopting the principle of virtual work, a rigid dynamic model of the robot is built. Based on the built dynamic model, a modified sliding mode control method is developed, of which the approaching speed is dependent on the system state. Finally, the sliding mode controller with self-adaptive parameters is created for a hybrid robot. The proposed sliding mode controller can achieve a rapid approaching speed and suppress chattering simultaneously. Simulation results demonstrate that the proposed modified sliding mode controller can achieve a comparatively accurate and smooth trajectory, which owns good robustness to external disturbances.

The paper aims to discuss the issues of actuator saturation and external disturbance in the magnetic levitation (maglev) system. The proposed technique is composed of composite nonlinear feedback (CNF) and super-twisting algorithm (STA)-based integral sliding mode (ISM) control to tackle the problem of actuator saturation and external disturbances simultaneously. The composite nonlinear feedback scheme comprises of linear feedback law which provides stability and fast response whereas the nonlinear feedback law takes care of input saturation and reduces the overshoot. The super-twisting algorithm (STA)-based integral sliding mode (ISM) controller is designed for disturbance rejection. A super-twisting algorithm-based approach is applied on ISM scheme to eliminate the chattering effect and make it continuous in nature for its direct implementation to the physical maglev system. The designed scheme is successfully tested on real-time feedback instruments model of the maglev system.