Higher Order Sliding Mode Research Articles

A strong robust DC-DC converter of all-digital high-order sliding mode control for fuel cell power applications

In the fuel cell power applications, the output voltage and load power are variable which highly depends on the operating conditions. Thus, DC/DC power converters are usually utilized to obtain a constant voltage to match the subsequent power bus. Due to the non-linear characteristics of the fuel cell and load profiles, a stronger robustness design of power converters is required. In order to resolve the above issues, this paper designs a strong robust isolated flyback DC/DC converter for the fuel cell power applications. An all-digital controller based on high-order sliding mode (HSM) control is developed. The super-twisting algorithm of HSM is applied with a digital signal processor (DSP) TMS320F28035 that is used as the control chip. In the experiments, the designed digital HSM controller can achieve a fast convergence with a settling time of less than 0.1 ms and an overshoot of less than 0.1%. A typical incremental PI controller is also designed as the benchmark control method. The effectiveness of the proposed digital HSM controller is demonstrated through several different experiments conducted under large disturbances of load and input voltage.

Closing Gaps for Aircraft Attitude Higher Order Sliding Mode Control Certification via Practical Stability Margins Identification

In this paper, the conventional aircraft control system certification approach based on phase margin (PM) and gain margin (GM) is extended to higher order sliding mode (HOSM) controllers. The proposed practical stability PM (PSPM) and the practical stability GM (PSGM) are used to quantify the HOSM control system robustness to unmodeled dynamics. The tools/algorithms for the identification of PSPM and PSGM are developed using describing function-harmonic balance method. A design algorithm of a cascade dynamic compensator for a dynamically perturbed HOSM control system is presented and can be used to satisfy required practical stability margins. The theoretical developments are illustrated and validated on controlling the attitude of an F-16 aircraft.

Quasi-Continuous MIMO Sliding-Mode Control

High-order sliding-mode (HOSM) control is called quasi-continuous (QC), if it remains continuous everywhere except the HOSM set, where the sliding variables and their derivatives vanish. Such sliding-mode (SM) control features less chattering. Homogeneous QC SM control is designed for the general uncertain multi-input multi-output case and provides any predefined control smoothness level outside of the HOSM set.

Approximation-Free Output-Feedback Control of Uncertain Nonlinear Systems Using Higher-Order Sliding Mode Observer

A novel output-feedback controller for uncertain single-input single-output (SISO) nonaffine nonlinear systems is proposed using high-order sliding mode (HOSM) observer, which is a robust exact finite-time convergent differentiator. The proposed controller utilizes (n + 1)th-order HOSM observer to cancel the uncertainty and disturbance where n is the relative degree of the controlled system. As a result, the control law has an extremely simple form of linear in the differentiator states. It is required no separate sliding-mode controller or universal approximators such as neural networks (NNs) or fuzzy logic systems (FLSs) that are adaptively tuned online. The proposed controller guarantees finite time stability of the output tracking error.

Event-Triggered Adaptive Integral Higher-Order Sliding Mode Control for Load Frequency Problems in Multi-area Power Systems

The study proposes a method to design continuous-time event-triggered adaptive integral higher-order sliding mode control for load frequency problems in multi-area power system under load disturbances and parameter uncertainties. Event-triggered strategy reduces the communication burden and lowers the control updating frequency while ensuring high-performance system stability. Event-triggered integral higher-order sliding mode control is used to attain need-based chattering-free control signal compared to event-triggered integral sliding mode control which assures its easy practical implementation. Adaptive estimation of switching gain is used with higher-order integral sliding mode control that eliminates the need of prior knowledge about the system uncertainties. Nonlinear uncertainties in power system like generation rate constraints (GRC) and governor deadband lead to load disturbance that results in deviation of frequency from its nominal value. Robustness of the controller is tested for plant considered with such nonlinearities. System performance without GRC is better; however, proposed controller still ensures finite time convergence of change in frequency under GRC and governor deadband. Proposed controller also guarantees finite time convergence of change in frequency under random varying load disturbances. We have also integrated renewable energy resources in the system and tried to handle relevant output power uncertainty in load frequency problem.

Robust Trajectory Tracking for Unmanned Aircraft Systems using a Nonsingular Terminal Modified Super-Twisting Sliding Mode Controller

Precision trajectory tracking problem for Unmanned Aerial Systems (UAS) is addressed in this work. A novel algorithm that combines a Nonsingular Modified Super-Twisting Controller with a High Order Sliding Mode Observer to enable an aerial vehicle tracking a desired trajectory under the assumption that i) its translational velocities are not available and ii) there are unmodeled dynamics and external disturbances. The proposed Sliding Mode Controller is based on a nonlinear sliding mode surface that ensures that the position and velocity tracking errors of all system’s state variables converge to zero in finite time. Moreover, the proposed controller generates a continuous control signal eliminating the chattering phenomenon. Finally, simulation results and an extensive set of experiments are presented in order to illustrate the robustness and effectiveness of the proposed control strategy.

Adaptive Higher-Order Sliding Mode Control for Islanding and Grid-Connected Operation of a Microgrid

Grid-connected and islanding operations of a microgrid are often influenced by system uncertainties, such as load parameter variations and unmodeled dynamics. This paper proposes a novel adaptive higher-order sliding mode (AHOSM) control strategy to enhance system robustness and handle an unknown uncertainty upper bounds problem. Firstly, microgrid models with uncertainties are established under islanding and grid-connected modes. Then, adaptive third-order sliding mode and adaptive second-order sliding mode control schemes are respectively designed for the two modes. Microgrid models’ descriptions are divided into nominal part and uncertain part, and higher-order sliding mode (HOSM) control problems are transformed into finite time stability problems. Again, a scheduled law is proposed to increase or decrease sliding mode control gain adaptively. Real higher-order sliding modes are established, and finite time stability is proven based on the Lyapunov method. In order to achieve smooth mode transformation, an islanding mode detection algorithm is also adopted. The proposed control strategy accomplishes voltage control and current control of islanding mode and grid-connected mode. Control voltages are continuous, and uncertainty upper bounds are not required. Furthermore, adjustable control gain can further whittle control chattering. Simulation experiments verify the validity and robustness of the proposed control scheme.

Second-order sliding-mode differentiators: an experimental comparative analysis using Van der Pol oscillator

ABSTRACTThis article provides a comparative study of four different second-order sliding-mode (SOSM) differentiators proposed in the literature, namely, standard higher-order sliding-mode (HOSM) differentiator, non-homogeneous HOSM differentiator, uniform robust exact differentiator and hybrid fixed-time differentiator. Based on sliding-mode principles, these differentiators can provide robust exact differentiation with finite/fixed-time convergence. First, a comprehensive summary of the different methods is provided. Then, the differentiators are applied experimentally to estimate the states of a Van der Pol oscillator. Through experiments, it is shown that the different differentiators outperformed a Kalman-like observer, high-gain differentiator and extended Kalman filter. Finally, some suggestions are provided on the selection of SOSM differentiators for various applications.

High-Order Sliding Mode Observer Based OER Control for PEM Fuel Cell Air-Feed System

This paper presents oxygen excess ratio (OER) control methods for proton exchange membrane fuel cell systems based on high-order sliding mode (HOSM) observer. The nonlinear and strong coupling characteristics make it difficult for the nonlinear uncertain systems to realize OER closed-loop feedback control. An improved HOSM observer is developed to observe the unmeasurable system states. Even under the interference of model parametric uncertainties, external disturbances, and measurement noises, the HOSM observer can still show fast convergence and good robustness. With the output error injection feature of improved HOSM algorithm, OER can be reconstructed in finite time. The proposed two stage sliding mode based on super twisting algorithm plus feedforward (TS_SM_STW+FF) controller and TS_SM_STW plus fuzzy feedforward (TS_SM_STW+Fuzzy_FF) controller are applied to regulate the estimated OER to track optimal value, respectively. The dynamic performance of OER with proposed methods is validated through the RT-LAB hardware-in-loop platform. The experimental results have shown the feasibility and effectiveness of proposed controllers as compared with conventional strategies.

Implementation of Caterpillar Inspired Rolling Gait and Nonlinear Control Strategy in a Spherical Robot

This paper presents a novel Central Pattern Generator (CPG) based rolling gait generation in a small-sized spherical robot and its nonlinear control mechanism. A rhythmic rolling pattern mimicking Pleurotya caterpillar is produced for the spherical robot locomotion. A synergetically combined feedforward-feedback control strategy is proposed. The feedforward component is generated from centrally connected network of CPGs in conjunction with nonlinear robot dynamics. Two nonlinear feedback control methods namely integral (first order) Sliding Mode Control (SMC) and High (or second) Order Sliding Mode Control (HOSMC) are proposed to regulate robot stability and gait robustness in the presence of matched parameter uncertainties and bounded external disturbances. Design, implementation and experimental evaluation of both roll gait control strategies for the spherical robot are done on smooth (indoor) and irregular (outdoor) ground surfaces. The performance of robot control is quantified by measuring the roll angle stability, phase plane convergence and wheel velocities. Experimental results show that proposed novel strategy is efficient in producing a stable rolling gait and robust control of a spherical robot on two different types of surfaces. It further shows that proposed high HOSMC strategy is more efficient in robust rolling gait control of a spherical robot compared to an integral first-order SMC on two different ground conditions.

Robust Sensors-Fault-Tolerance With Sliding Mode Estimation and Control for PMSM Drives

In general, permanent magnet synchronous motor (PMSM) drives require four sensors (one position, one dc-link voltage, and at least two current sensors) to obtain good dynamic control performance. If an unpredictable fault occurs in any of these sensors, the performance of the drive deteriorates or even becomes unstable. Most of the existing works are limited to fault diagnosis of one or two sensors due to complexity. Therefore, to provide a continuous drive operation regardless of any of the sensor faults, an advanced fault-tolerant control (FTC) scheme that comprises of higher order sliding mode (HOSM) based observers and controllers is proposed. Two HOSM observers and one Luenberger observer are designed to generate the respective residuals and provide the detection of all sensor faults. Moreover, HOSM controllers are developed to ensure finite-time convergence of the error trajectories after the fault reconfiguration. The proposed FTC scheme reduces the existing chattering phenomenon with good performance in terms of convergence speed and steady-state error. Evaluation results on a three-phase PMSM are presented to validate the effectiveness of the proposed FTC approach.

Continuous higher order sliding mode control for a class of uncertain MIMO nonlinear systems: An ISS approach

In this article, we propose a new approach towards the design of higher order sliding mode (HOSM) control, for a class of multiple input multiple output (MIMO) uncertain nonlinear systems subject to matched and unmatched uncertainties. In the proposed method, nonlinear sliding surfaces incorporating the system initial conditions and exponential functions, which guarantee the existence of sliding mode from an initial state are utilized and appropriate control inputs are designed. The control inputs are designed to enforce second order sliding mode w.r.t the sliding variables via the use of multivariable super-twisting algorithm (STA) in finite time. The resulting sliding motion is in turn proved to be input-to-state-stable (ISS) with respect to the perturbations and unmatched uncertainties. The developed sliding mode control strategy is applied for the posture stabilization of a unicycle mobile robot. The proposed method is illustrated through simulations.

Robust synchronization of master-slave chaotic systems using approximate model: An experimental study

Robust synchronization of master slave chaotic systems are considered in this work. First an approximate model of the error system is obtained using the ultra-local model concept. Then a Continuous Singular Terminal Sliding-Mode (CSTSM) Controller is designed for the purpose of synchronization. The proposed approach is output feedback-based and uses fixed-time higher order sliding-mode (HOSM) differentiator for state estimation. Numerical simulation and experimental results are given to show the effectiveness of the proposed technique.

High Order Sliding Mode Control and Observation for DP Systems

Sliding Mode Controllers (SMC) are a robust and simple strategy suitable to mechanical systems subject to structured disturbances. Such characteristics make them an interest solution as control algorithms for Dynamic Positioning Systems, providing enhanced trajectory tracking capacities even during transients. The trade-off is usually a limit in accuracy, due to smoothing methods required to reduce control chattering. This work proposes the usage of a Second Order SMC method, named Super-Twisting control as an alternative for the application of SMC in DP Systems. This algorithm provides high accuracy and robustness while eliminating chattering. The solution is completed with the introduction of a High Order Sliding Mode Observer, which performs wave-filtering, velocity and drift estimation. The controller-observer structure is tested in a high fidelity marine simulation environment, producing results that confirm the performance of the system.

Hypersonic Missile Adaptive Sliding Mode Control Using Finite- and Fixed-Time Observers

Finite- and fixed-settling time differentiators utilizing a nonrecursive higher order sliding mode (HOSM) observer are studied. Fixed convergence time estimation is achieved independent of initial conditions of the differentiation errors. The corresponding convergence/settling times are estimated. The finite- and fixed-time HOSM differentiators’ performance is compared against the Levant recursive one via a hypersonic missile control simulation case study during the missile's terminal phase of flight. A continuous adaptive HOSM control is utilized. The double-layer adaptive algorithm is based on an equivalent control concept and does not allow overestimation of the control gains that mitigates control chattering. The robustness and high-accuracy output tracking in the presence of matched and unmatched external disturbances and missile model uncertainties is demonstrated for both the differentiators and the controller.

Sliding-Mode-Based Observer–Controller Structure for Fault-Resilient Control in DC Servomotors

This paper presents a robust observer–controller scheme for sensor fault-resilient control in dc servomotor drive-based applications (such as antennae control for satellite tracking, radio telescopes, and conveyor belt systems). In contrast to the earlier works on abrupt faults, this paper considers incipient sensor faults and detects using the higher order sliding mode (HOSM) observer, followed by a tracking controller, which maintains the acceptable drive performance. A robust output tracking controller based on fractional integral terminal sliding mode surface with HOSM terms is developed to ensure faster and finite-time convergence of the error trajectory. Moreover, various slopes of incipient faults are considered to analyze the detection delay, and switching strategy reconfigures the system with the estimated speed whenever the residual crosses the threshold. The closed-loop performance in the presence of most common faults (abrupt, incipient, and intermittent) is experimentally validated on a dc motor-based industrial mechatronic drives unit with belt-drive inertial load (which exhibits nonlinear friction, torque variations, and other disturbances).

Indirect Adaptive Control for Higher Order Sliding Mode

This contribution deals with the combination of higher-order sliding-mode with indirect adaptive control for single-input systems. Sliding-mode controllers are well-suited for bounded uncertainties whereas adaptive controllers may handle parametric uncertainties very well. The idea is to join both methods in order to obtain a new state-feedback controller design with improved robustness for both classes of uncertainties. Extending previous results on this combination, a recently found Lyapunov function allows to extend the approach also to higher-order sliding-mode systems. This way we may provide an adaptation law for the whole system dynamics without requirements on the relative degree of the sliding variable. Some advantages of the proposed extension are demonstrated in numerical simulations.

Nested High Order Sliding Mode Controller Applied to a Brushless Direct Current Motor

A nested high order sliding mode controller is proposed for speed control of a brushless direct current motor using an extended park transformation. Conventional park transformation applied to non sinusoidal back electromotive force motors results in non constant values in the (d, q) reference frame, a modified park transformation is used to obtain constant variables after transformation. Sliding mode control is robust in the presence of matched parametric variations and uncertain disturbances but unmatched variations have a negative effect in the system’s performance. A nested high order sliding mode scheme is presented to improve controller robustness to unmatched perturbations. Simulations are used to show the performance of the proposed controller with load torque and resistance variations.

Improved Hybrid Fireworks Algorithm-Based Parameter Optimization in High-Order Sliding Mode Control of Hypersonic Vehicles

With respect to the nonlinear hypersonic vehicle (HV) dynamics, achieving a satisfactory tracking control performance under uncertainties is always a challenge. The high-order sliding mode control (HOSMC) method with strong robustness has been applied to HVs. However, there are few methods for determining suitable HOSMC parameters for an efficacious control of HV, given that the uncertainties are randomly distributed. In this study, we introduce a hybrid fireworks algorithm- (FWA-) based parameter optimization into HV control design to satisfy the design requirements with high probability. First, the complex relation between design parameters and the cost function that evaluates the likelihood of system instability and violation of design requirements is modeled via stochastic robustness analysis. Subsequently, we propose an efficient hybrid FWA to solve the complex optimization problem concerning the uncertainties. The efficiency of the proposed hybrid FWA-based optimization method is demonstrated in the search of the optimal HV controller, in which the proposed method exhibits a better performance when compared with other algorithms.

Controlling the building model using high order sliding mode control optimized by multi objective genetic algorithm

High Order Sliding mode control (HOSMC) has been used in many mechanical systems and structural system due to its accuracy, chattering attenuation and high control performance. However, choosing controller parameters for systems is still an important research area. This study, presents a numerical analysis to decrease the effect of earthquake vibrations on building model having Active Tuned Mass Damper (ATMD). The system is excited by an earthquake and a linear motor is used as the control device. ATMD is installed on top floor of building model. Tuning of High Order Sliding Mode Controller (HOSMC) using Super Twisting Algorithm with Multi Objective Genetic Algorithm (MOGA) is designed for a three storey building model with ATMD. HOSMC parameters have been chosen by MOGA with multiple objective functions. Then, simulation results of uncontrolled and controlled model are compared. The results show that building model with HOSMC tuned by MOGA is effective to decrease the effects of vibrations.