Finite-time Convergent Control Research Articles

Nonsingular Finite-Time Convergent Control for Spacecraft Rendezvous and Docking

This paper deals with the problem of relative position control of the chaser spacecraft during rendezvous using sliding mode control, wherein the time of operation plays a critical role in the success of mission. Conventional sliding mode controller ensures only asymptotic convergence. We propose the application of a controller based on terminal sliding mode that guarantees the finite time convergence of controlled variable to achieve the mission successfully. The proposed controller may encounter a singularity for some scenarios in real applications. To achieve finite time convergent controller enabling the spacecraft for rendezvous mission while avoiding any singularities, we also propose a controller based on nonsingular terminal sliding mode control. We validated the proposed techniques using numerical simulations and found them to be satisfactory.

Robust Composite Finite-Time Convergent Speed Control of Induction Machine Based on Multiple Sources Disturbance Estimation Technology Generalized Proportional Integral Observer

To improve the robustness of the conventional finite-time convergent speed controller (FTCSC) against unpredictable disturbances, a finite-time generalized proportional integral observer (FT-GPIO) is proposed based on the state observer to achieve finite-time convergence of the closed-loop control system. First, an FTCSC is devised to improve the speed convergence performance of the induction machine (IM) control system. However, the system will inevitably be affected by multiple sources disturbances, such as friction, load disturbance, parameter mismatch, and torque current tracking error, resulting in performance degradation. To improve the disturbance rejection ability of the IM control system, an FT-GPIO based on multiple sources disturbance estimation technology is designed. Finally, a 1.1-kW IM is used as a case study, and the experimental results are provided to verify the effectiveness of the proposed robust composite finite-time convergent speed controller.

Adaptive sliding-mode trajectory tracking control for state constraint master–slave manipulator systems

This study aims to propose an adaptive state-dependent gain finite-time convergent controller (using the fundamentals of the sliding mode theory) that solves the trajectory tracking for a class of state constraint master–slave robotic system (M-SRS) formed by two manipulators with the same number of articulations. The control design considers the effect of state constraints by implementing a state dependent adaptive gain. A Lyapunov-stability analysis leads to design the gain variation laws yielding proving the finite-time convergence of the sliding surface as well as the asymptotic convergence of the tracking error. The state constraints of the slave system motivate the characterization of the convergence-time as a function of the bounded uncertainties affecting the M-SRS dynamics. The forward-complete setting of the M-SRS justified the application of a robust and exact differentiator which estimated the articulation velocities for the slave robot. The estimated velocities are used as part of the realization of the output feedback controller. Numerical simulations demonstrate that the proposed control scheme provides a smaller quadratic norm of the tracking error compared with the obtained with other controllers (proportional–derivative and conventional sliding modes). The proposed control approach satisfies the state constraints while the sliding manifold converges to the origin in finite-time as justified by the theoretical stability analysis.

Three-dimensional impact angle constrained distributed cooperative guidance law for anti-ship missiles

This paper investigates the problem of distributed co-operative guidance law design for multiple anti-ship missiles in the three-dimensional (3-D) space hitting simultaneously the same target with considering the desired terminal impact angle constraint. To address this issue, the problem formulation including 3-D nonlinear mathematical model description, and communication topology are built firstly. Then the consensus variable is constructed using the available information and can reach consensus under the proposed acceleration command along the line-of-sight (LOS) which satisfies the impact time constraint. However, the normal accelerations are designed to guarantee the convergence of the LOS angular rate. Furthermore, consider the terminal impact angle constraints, a nonsingular terminal sliding mode (NTSM) control is introduced, and a finite time convergent control law of normal acceleration is proposed. The convergence of the proposed guidance law is proved by using the second Lyapunov stability method, and numerical simulations are also conducted to verify its effectiveness. The results indicate that the proposed cooperative guidance law can regulate the impact time error and impact angle error in finite time if the connecting time of the communication topology is longer than the required convergent time.

Design of Output-Based Finite-Time Convergent Composite Controller for a Class of Perturbed Second-Order Nonlinear Systems

This article is concerned with the problem of global finite-time output stabilization for a class of second-order nonlinear systems with both uncertain nonlinear dynamics and unknown external disturbance. Specifically, at the first step, without considering the external disturbance, a global finite-time state feedback controller is proposed to dominate uncertain nonlinear dynamics of the second-order system. To address the more challenging case where only the system output is available, a novel design idea of the nonseparation principle is employed. By treating the unknown external disturbance as a generalized state, a finite-time convergent extended state observer is constructed to estimate the unmeasured state and the unknown external disturbance. Based on this observer, an output-based composite controller with finite-time convergence is developed. The global uniform finite-time stability of the overall closed-loop system is proven based on the Lyapunov method. Simulation results of the inverted pendulum system demonstrate the superiority of the proposed control method in terms of both convergence performance and disturbance rejection performance.

Finite-Time Convergent Control of Electrohydraulic Velocity Servo System Under Uncertain Parameter and External Load

The disturbances suppression is one common control problem in electrohydraulic systems (EHSs) since both unknown external load and hydraulic parametric uncertainty often obviously degrade the tracking performance and bias the load pressure of EHS. In this paper, a finite-time convergent controller (FTCC) is tried to use in EHS to address this problem. Different from the asymptotic convergent controller, this FTCC not only improve the dynamic and steady tracking performance of the velocity servo system but also guarantee the system state error convergent to zero in a finite time. According to the finite-time stable principle, the FTCC is derived by backstepping and fractional-type Lyapunov techniques. The effectiveness of the proposed controller is verified by comparative simulation and experimental results with the other traditional and advanced controllers.

Three-dimensional terminal angle constrained robust guidance law with autopilot lag consideration

Based on sliding mode control theory and back stepping design technique, this paper proposes a robust guidance law considering autopilot dynamics for maneuvering target interception in three-dimensional environment and terminal angle constraints. The proposed guidance law is summarized as an “observer–controller” system. More specifically, to estimate the knowledge of target maneuvers, an adaptive second-order sliding mode observer is presented whose design parameters can be adjusted autonomously according to the estimation error, and a nonsingular switchable sliding manifold based finite time convergent controller is proposed to drive the line-of-sight angle error and angular rate to a small region around zero, further, enable the missile accurately intercept the target in finite time. Finally, by formulating the autopilot lag as a first-order or second-order dynamics, the higher-order comprehensive model is built and complex guidance laws are presented. The simulation results demonstrated the proposed properties.

Robust finite-time tracking control for Euler–Lagrange systems with obstacle avoidance

This paper addresses the tracking control problem of Euler–Lagrange systems with external disturbances in an environment containing obstacles. Based on a novel sliding manifold, a new asymptotic tracking controller is proposed to ensure the tracking errors converge to zero as time goes to infinity. Moreover, based on a modified nonsingular terminal sliding manifold, a finite-time convergent control algorithm is also developed to make sure the tracking errors converge to a small bounded area near the origin in finite time. Through introducing collision avoidance functions into the sliding manifolds, both controllers can guarantee the obstacle avoidance. Moreover, the stability of the closed-loop systems and approaches free of local minima have been rigorously analyzed. Finally, numerical simulations are carried out to demonstrate the effectiveness of the proposed strategies.

Application of Single- and Multi-Objective Evolutionary Algorithms for Optimal Nonlinear Controller Design in Boiler–Turbine System

This paper presents an application of evolutionary algorithm techniques for optimal nonlinear controller design in drum-type boiler–turbine system. Designing of controller for third-order boiler–turbine system is always a complicated task due to the presence of highly interactive nonlinearities. The present work is the first one which attempts to design and implement recently developed finite time convergent controller in third-order boiler–turbine dynamics, and it is described as multi-input–multi-output (MIMO) nonlinear system. The present work explores the possibility of application of single-objective and multi-objective evolutionary algorithm techniques toward optimal tuning of finite time convergent controller to achieve the desired performance for third-order boiler–turbine system. The single-objective evolutionary algorithm techniques such as real-coded genetic algorithm (RGA), modified particle swarm optimization (MPSO), differential evolution (DE), and self-adaptive differential evolution (SADE) are implemented with the minimization of integral square error (ISE) as an objective to obtain optimal tuning parameters. Also, the present paper explores the possibility of simultaneous minimization of conflicting objectives such as ISE and computational cost of the proposed controller using multi-objective evolutionary algorithms such as non-dominated sorting genetic algorithm (NSGA) and modified non-dominated sorting genetic algorithm-II (MNSGA-II). The performance of the proposed optimal finite time convergent controller is validated by simulating different kinds of set point changes, and the obtained results are presented as various case studies. The adaptability of the proposed controller during parameter variations is also examined. The performance of the single-objective and multi-objective evolutionary algorithms has been statistically analyzed, and the results are reported. The results reveal that among the four single-objective EA techniques, SADE offers better performance due to its inherit self-adaptive capability. Also, during multi-objective optimization, MNSGA-II has provided better solution due the presence of dynamic crowding distance (DCD) and control elitism (CE) strategies.

An Optimized Nonlinear Controller Design for Boiler–Turbine System Using Evolutionary Algorithms

ABSTRACTThis paper investigates an optimized design of newly developed nonlinear controller called finite-time convergent controller to a third-order boiler–turbine dynamics. The third-order boiler–turbine dynamics only includes highly nonlinear and critical parameters of thermal plant like drum pressure, electric power and drum level; the design of controller is always a complicated task. The present work explores the possibility of application of newly developed finite-time convergent controller to a third-order boiler–turbine dynamics. The novelty of the newly developed finite-time convergent controller is complete utilization of system nonlinearities instead of cancelling or linearizing them. Also, the finite-time convergent controller ensures robustness and fast convergence. To achieve optimal performance, the tuning parameters involved in finite-time convergent controller have been optimized using evolutionary algorithm techniques. To validate the control performance of an optimized nonlinear controller design, simulations have been conducted using various evolutionary algorithm techniques and the results are reported as various case studies. To compare the performance of proposed optimized finite-time convergent controller, the fuzzy logic controller has also been designed using ANFIS for boiler–turbine system and the results are reported.

Energy Storage System Control for Energy Management in Advanced Aeronautic Applications

In this paper an issue related to electric energy management on board an aircraft is considered. A battery pack is connected to a high-voltage bus through a controlled Battery Charge/Discharge Unit (BCDU) that makes the overall behaviour of the battery “intelligent.” Specifically, when the aeronautic generator feeding the high-voltage bus has enough energy the battery is kept under charge, while if more loads are connected to the bus, so that the overload capacity of the generator is exceeded, the battery “helps” the generator by releasing its stored energy. The core of the application is a robust, supervised control strategy for the BCDU that automatically reverts the flow of power in the battery, when needed. Robustness is guaranteed by a low-level high gain control strategy. Switching from full-charge mode (i.e., when the battery absorbs power from the generator) to generator mode (i.e., when the battery pumps energy on the high-voltage bus) is imposed by a high-level supervisor. Different from previous approaches, mathematical proofs of stability are given for the controlled system. A switching implementation using a finite-time convergent controller is also proposed. The effectiveness of the proposed strategy is shown by detailed simulations in Matlab/Stateflow/SimPowerSystem.

Continuous finite- and fixed-time high-order regulators

The contribution of this paper is twofold. First, an upper estimate of the convergence (settling) time is calculated for the finite-time convergent control algorithm that drives the state of a series of integrators to the origin. To the best of our knowledge, such an estimate is obtained for the first time. Second, a novel fixed-time continuous control law is proposed for a chain of integrators of an arbitrary dimension. Its fixed-time convergence is established and the uniform upper bound of the settling time is computed. The theoretical developments are applied to a case study of controlling a DC motor.

Attitude control using higher order sliding mode

This paper proposes a chattering-free global finite-time convergent robust control method for the attitude control of a rigid spacecraft. The control method is formulated using higher order sliding mode control in integral sliding mode. The sliding mode order is higher than the system relative degree and therefore, chattering elimination is ensured. In the control design process, unmeasured sliding vector derivative is estimated using a robust exact differentiator. To verify the effectiveness of the proposed control method, simulations are performed in the presence of external disturbances and inertia uncertainty. The proposed controller successfully negates the effect of external disturbances and inertia uncertainty and attitude states attain the desired accuracy with good steady state precision and high convergence speed.

Continuous Finite-Time Higher-Order Output Regulators for Systems with Unmatched Unbounded Disturbances

This paper presents two continuous finite-time convergent control algorithms driving an output (the highest relative degree state) of an $n$ -dimensional integrator to zero for a finite time using a scalar input in the presence of both matched and unmatched unbounded disturbances. No knowledge of all system states is required: only the output should be available for the control design. No knowledge or reconstruction of individual disturbances is assumed as well. This paper concludes with a case study of controlling an industrial benchmark DC motor, whose third-order mathematical model is perturbed by matched and unmatched disturbances.

Rigid spacecraft attitude control using adaptive integral second order sliding mode

The aim of this paper is to design a globally robust and globally finite-time convergent attitude controller for a rigid spacecraft. Second order sliding mode control in integral sliding mode is proposed to design the controller. To eliminate the need of advance information about uncertainty and external disturbance bounds, the gains of the proposed controller are calculated using the adaptive laws. The second order sliding mode controller applied is based on geometric homogeneity approach. The finite-time stability is proved by using both the Lyapunov stability and negative homogeneity approach. Simulations are conducted for the attitude tracking and attitude stabilization under the effect of spacecraft mass inertia uncertainty and external disturbances; and the outcomes reveal the effectiveness of the proposed control method.

Finite-time convergent continuous control design based on sliding mode algorithms with application to a hydraulic drive

Sliding modes impose strong robustness toward parametric plant uncertainties and disturbances and provide for accurate tracking performance in control systems. However, in physical systems the application of sliding modes may give rise to undesirable chattering of the control signal due to actuator dynamics, possible excitation of unmodelled dynamics and structural resonant modes of load systems, etc. This may be avoided by application of smoothing functions imposing boundary layers on the control constraint, or by carrying out the design in relation to the control derivative. However, such boundary layers introduce additional design parameters and actuator dynamics may not allow the desired control accuracy to be reached. In this paper continuous controllers are proposed, with the designs taking their offset in some well-known sliding controllers. The proposed controllers preserve the finite-time convergence properties known from sliding control while at the same time avoiding control chattering, however, on the cost of robustness. Experimental results confirm the announced properties when applied to a hydraulic valve-cylinder drive, and demonstrates superior performance over conventional linear controllers.

Sliding Mode Control in Finite Time Stabilization for Synchronization of Chaotic Systems

An adaptive sliding mode control for chaotic systems synchronization is considered. The design of robust finite time convergent controller is based on geometric homogeneity and integral sliding mode manifold. The knowledge of the upper bound of the system uncertainties is not prior required. The chaos synchronization is presented to system stability based on the Lyapunov stability theory. The simulation results show the effectiveness of the proposed method.

Sliding Mode Control in Finite Time Stabilization for Synchronization of Chaotic Systems

An adaptive sliding mode control for chaotic systems synchronization is considered. The design of robust finite time convergent controller is based on geometric homogeneity and integral sliding mode manifold. The knowledge of the upper bound of the system uncertainties is not prior required. System stability is proven by Lyapunov theory. The simulation results show the effectiveness of the proposed method.

A genuine nonlinear approach for controller design of a boiler–turbine system

This paper proposes a genuine nonlinear approach for controller design of a drum-type boiler–turbine system. Based on a second order nonlinear model, a finite-time convergent controller is first designed to drive the states to their setpoints in a finite time. In the case when the state variables are unmeasurable, the system will be regulated using a constant controller or an output feedback controller. An adaptive controller is also designed to stabilize the system since the model parameters may vary under different operating points. The novelty of the proposed controller design approach lies in fully utilizing the system nonlinearities instead of linearizing or canceling them. In addition, the newly developed techniques for finite-time convergent controller are used to guarantee fast convergence of the system. Simulations are conducted under different cases and the results are presented to illustrate the performance of the proposed controllers.

Fast convergent observer design for output feedback stabilisation of a planar vertical takeoff and landing aircraft

This paper explores the solution of using output feedback to stabilise a planar nonlinear model of a vertical take-off and landing (PVTOL) aircraft. We first construct a state feedback stabiliser by utilising the technique of finite-time convergent control. To address the lack of full state measurement, we design a fast convergent observer which recovers the unknown states in a finite time and thus enables the output feedback controller to stabilise the system. The finite-time convergent observer proposed in this paper is unique due to the fact that the estimated states converge rapidly to the real states regardless of the distances between them.