Continuous Robust Control Research Articles

Continuous robust controller with fixed convergence time for synchronization of perturbed nonlinear transducers

The synchronization of two chaotic electrostatic and electromechanical transducers is addressed via a continuous terminal sliding-mode control (SMC) strategy. Recently, fixed-time convergence has received increased attention among scholars. The convergence time with this type of controller has an upper bound independent of the initial conditions. In this regard, two fixed-time sliding variables are proposed to design a robust continuous controller having a fixed-time convergence feature. Then, a robust SMC control is formulated to steer the error states onto the sliding surfaces despite the external disturbances and model uncertainties. Due to the continuous structure of the designed strategy, the proposed controller is chattering-free, which is essential in many practical applications. The convergence proof for the continuous robust controller based on the Lyapunov stability theory has been presented. Finally, a comparison of the proposed approach with existing methods has been illustrated through simulation results to demonstrate its superiority.

Continuous Robust Control Based on Fixed-Time Super-Twisting Disturbance Observer

Continuous Robust Control Based on Fixed-Time Super-Twisting Disturbance Observer

Output-Feedback Stabilization of the Reaction Wheel Pendulum Via Active Disturbance Rejection Control

This work presents a continuous robust control method for stabilizing the reaction wheel pendulum, despite the effect of external perturbations and using only output information. To achieve this, first, an extended high-order sliding-modes observer estimates the states and identifies the perturbations, theoretically, in finite time. Then, an active disturbance rejection scheme considers the estimated states and the identified perturbation. As a result, the closed-loop system is robust against external perturbations, and the system trajectories converge to the origin. Experimental results illustrate the performance and advantages of the presented algorithm.

Robust adaptive regulation of magnetic levitation systems with input quantization and external disturbances

This paper investigates two intricate problems in magnetic levitation systems: the loss of the information during the transmission over a limited communication network channel and the chattering caused by external disturbances. By combining input quantization technique with two infinitesimal smooth functions, we successfully construct a continuous robust adaptive feedback controller which stabilizes the position of the levitated electromagnet at the equilibrium point. Compared with the existing methods, the proposed quantized control strategy not only guarantees the global stability with asymptotic state regulation of the system even if there are external disturbances, but also exhibits better performance than that of traditional PID control. The simulation validates the robustness and effectiveness of the proposed scheme.

LESO-Based Nonlinear Continuous Robust Stabilization Control of Underactuated TORA Systems

In this paper, we consider the robust stabilization control problem of underactuated translational oscillator with a rotating actuator (TORA) system in the presence of unknown matched disturbances by employing continuous control inputs. A nonlinear continuous robust control approach is proposed by integrating the techniques of backstepping and linear extended state observer (LESO). Specifically, based on the backstepping design methodology, a hyperbolic tangent virtual control law is designed for the first subsystem of the cascaded TORA model, via which an integral chain error subsystem is subsequently constructed and the well-known LESO technique is easy to implement. Then, an LEO is designed to estimate the lumped matched disturbances in real-time, and the influence of the disturbances is compensated by augmenting the feedback controller with the disturbance estimation. The convergence and stability of the entire control system are rigorously proved by utilizing Lyapunov theory and LaSalle’s invariance principle. Unlike some existing methods, the proposed controller is capable of generating robust and continuous control inputs, which guarantee that both the rotation and translation of TORA systems are stabilized at the origin simultaneously and smoothly, attenuating the influence of disturbances. Comparative simulation results are presented to demonstrate the effectiveness and superior control performance of the proposed method.

Robust adaptive trajectory tracking for wheeled mobile robots based on Gaussian process regression

In this paper, we propose a novel learning-based robust adaptive trajectory tracking controller for wheeled mobile robots (WMR) subject to velocity input uncertainties. Gaussian process regression (GPR) is employed in view of its powerful estimation ability and wide scope of applications as a nonparametric regression method. The velocity uncertainties are estimated online using the real-time measured data. The prediction mean and variance of the GPR are used to counteract the effect of the uncertainties and to design the robust control term, respectively. A continuous robust controller is proposed which has the advantage of achieving asymptotic convergence of the trajectory tracking error instead of uniformly ultimately boundedness. Comparisons with the neural network based adaptive controller and a state of the art GPR-based design demonstrate the effectiveness of the proposed control strategy.

Exponential Stability With RISE Controllers

A class of continuous robust controllers termed Robust Integral of the Sign of the Error (RISE) have been published over the past two decades as a means to yield asymptotic tracking error convergence and asymptotic identification of time-varying uncertainties, for classes of nonlinear systems that are subject to sufficiently smooth bounded exogenous disturbances and/or modeling uncertainties. Despite the wide application of RISE-based techniques, an open question that has eluded researchers during this time-span is whether the asymptotic tracking error convergence is also uniform or exponential. This question has remained open due to certain limitations in the traditional construction of a Lyapunov function for RISE-based error systems. In this letter, new insights on the construction of a Lyapunov function are used that result in an exponential stability result for RISE-based controllers. As an outcome of this breakthrough, the inherent learning capability of RISE-based controllers is shown to yield exponential identification of state-dependent disturbances/uncertainty.

Autonomous Precision Control of Satellite Formation Flight under Unknown Time-Varying Model and Environmental Uncertainties

This paper presents a new methodology for autonomous precision control of satellite formations in the presence of uncertainties and external disturbances. The methodology is developed in two steps. First, using a nominal system model that provides the best assessment of real-life uncertainties, a nonlinear controller that satisfies the formation configuration requirements is developed without making any linearizations/approximations. This closed-form control strategy is inspired by results from analytical dynamics and uses the fundamental equation of constrained motion. In the second step, an adaptive continuous robust controller is developed to compensate for model uncertainties and field disturbances to which the satellite formation may be subjected. This controller is based on a generalization of the concept of sliding mode control, and produces no chattering. The control gain is automatically updated in real time and the norm of the trajectory error is guaranteed to lie within user-provided desired bounds without a priori knowledge of the uncertainty/disturbance bounds. Since the control force is explicitly obtained, the approach is not computationally intensive, thereby making the approach ideal for on-orbit autonomous real-time satellite formation control. Numerical simulations demonstrate the effectiveness of the proposed control methodology, in which a desired formation configuration is required to be precisely and autonomously maintained despite large initial trajectory errors in the presence of uncertain satellite mass and environmental disturbances.

Continuous robust fixed-time control for double integrator system with matched disturbance

This paper investigates the continuous robust fixed-time control for the double integrator system with matched disturbance. A new integral-type sliding mode (ISM) fixed-time controller is proposed that can significantly alleviate the chattering phenomenon and ensure the states of double integrator system to converge to the origin within a fixed settling time. Continuous Lyapunov functions are given and a valid proof for the closed loop system is presented based on the bi-limit homogeneous theorem. An output feedback ISM fixed-time controller is also developed for the disturbed double integrator system based on a fixed-time observer. Numerical simulations are provided to demonstrate the performance of proposed continuous robust fixed-time algorithms.

Robust Control of Robotic Manipulators in the Task-Space Using an Adaptive Observer Based on Chebyshev Polynomials

In this paper, an adaptive observer for robust control of robotic manipulators is proposed. The lumped uncertainty is estimated using Chebyshev polynomials. Usually, the uncertainty upper bound is required in designing observer-controller structures. However, obtaining this bound is a challenging task. To solve this problem, many uncertainty estimation techniques have been proposed in the literature based on neuro-fuzzy systems. As an alternative, in this paper, Chebyshev polynomials have been applied to uncertainty estimation due to their simpler structure and less computational load. Based on strictly-positive-real (SPR) Lyapunov theory, the stability of the closed-loop system can be verified. The Chebyshev coefficients are tuned based on the adaptation rules obtained in the stability analysis. Also, to compensate the truncation error of the Chebyshev polynomials, a continuous robust control term is designed while in previous related works, usually a discontinuous term is used. An SCARA manipulator actuated by permanent magnet DC motors is used for computer simulations. Simulation results reveal the superiority of the designed method.

Augmented fixed‐time observer‐based continuous robust control for hypersonic vehicles with measurement noises

This study is concerned with the augmented fixed-time observer based adaptive super-twisting cruise control for flexible air-breathing hypersonic vehicles (FAHVs). First, the input–output linearisation technique is employed to derive a control oriented FAHV dynamic model. Then, a super-twisting controller is designed to track the reference velocity and altitude commands when faced with various uncertainties and disturbances. In addition, a novel gain adaptation law is constructed as a supplement of the super-twisting controller to avoid overestimating the values of controller gains. The adaptation law keeps the controller gains adapting dynamically to guarantee the finite-time convergence of sliding variables in the presence of disturbances with unknown boundaries. Moreover, augmented fixed-time observers are designed to estimate the true values of measured states and filter out high-frequency sensor noises. Thus, the fixed convergence time of these observers is achieved independently of initial estimation errors. Finally, the augmented fixed-time observers and adaptive super-twisting controller are combined together to ensure the superior tracking performances of FAHVs under the effects of uncertainties, disturbances, and measurement noises.

Generation of stable oscillations in uncertain nonlinear systems with matched and unmatched uncertainties

ABSTRACTIn this paper, a robust limit cycle control technique is proposed for generation of stable oscillations in a class of uncertain nonlinear systems with both matched and unmatched uncertainties. For this purpose, first, the modified Lyapunov function is introduced which is appropriate for stability analysis of invariant sets (instead of equilibrium points). The structure of the proposed Lyapunov function is related to the shape of the desirable limit cycle. Next, in order to design the robust limit cycle control input, the backstepping and Lyapunov redesign methods are employed, simultaneously. The The classical Lyapunov redesign controller is discontinuous and robust with respect to matched uncertainties. To overcome unmatched uncertainties, a modified version of the Lyapunov redesign controller is suggested in each step of backstepping which results in a continuous robust control law. Furthermore, the convergence of the phase trajectories of the uncertain closed-loop system to the target limit cycle is proved using the extended Lyapunov stability theorem. Finally, computer simulations are performed to show the applicability of the given approach. In this regard, two uncertain nonlinear practical systems are considered and robust stable oscillations are generated in these systems via the proposed controller. Simulation results confirm the effectiveness of the proposed technique.

Compensating of added mass terms in dynamically positioned surface vehicles: A continuous robust control approach

In this work, we provide a tracking controller formulation for dynamically positioned surface vessels with an asymmetric added mass terms that affects the overall system dynamics at the acceleration level. Specifically a novel continuous robust controller is proposed for surface vessels that in addition to unstructured uncertainties in its dynamics, contains added mass effects in its inertia matrix. The proposed controller compensates the overall system uncertainties while ensuring asymptotic tracking by utilizing the knowledge of the leading principal minors of the input gain matrix. Stability of the closed–loop system and asymptotic convergence are proven via Lyapunov based approaches. Simulation studies are also presented to illustrate the viability of the proposed method.

Output Feedback Finite-Time Stabilization of Systems Subject to Hölder Disturbances via Continuous Fractional Sliding Modes

The problem of designing a continuous control to guarantee finite-time tracking based on output feedback for a system subject to a Hölder disturbance has remained elusive. The main difficulty stems from the fact that such disturbance stands for a function that is continuous but not necessarily differentiable in any integer-order sense, yet it is fractional-order differentiable. This problem imposes a formidable challenge of practical interest in engineering because (i) it is common that only partial access to the state is available and, then, output feedback is needed; (ii) such disturbances are present in more realistic applications, suggesting a fractional-order controller; and (iii) continuous robust control is a must in several control applications. Consequently, these stringent requirements demand a sound mathematical framework for designing a solution to this control problem. To estimate the full state in finite-time, a high-order sliding mode-based differentiator is considered. Then, a continuous fractional differintegral sliding mode is proposed to reject Hölder disturbances, as well as for uncertainties and unmodeled dynamics. Finally, a homogeneous closed-loop system is enforced by means of a continuous nominal control, assuring finite-time convergence. Numerical simulations are presented to show the reliability of the proposed method.

Continuous robust control for series elastic actuator with unknown payload parameters and external disturbances

In this paper, the torque tracking control problem for a class of series elastic actuators U+0028 SEAs U+0029 in the presence of unknown payload parameters and external disturbances is investigated. The uncertainties U+002F disturbances rejection problem for SEAs is addressed from the view of a continuous nonlinear robust control development. Specifically, based on the analysis of a nonlinear SEA, the generic dynamics of SEA systems is described and a novel nonlinear control framework for SEAs is constructed. Then a RISE U+0028 robust integral of the sign of the error U+0028 -based second-order filter is introduced to synthesize the control law. Moreover, the control performance is theoretically ensured by Lyapunov analysis. Finally, some experimental results are included to demonstrate the superior performance of the proposed control method, in terms of transient response and robustness.

Adaptive robust stabilisation of uncertain nonlinear dynamical systems: an improved backstepping approach

ABSTRACTThe main purpose of this paper is to propose a design approach by which some simple adaptive robust controllers can be synthesised for a class of uncertain nonlinear dynamical systems which can be transformed into uncertain strict-feedback nonlinear systems. In this paper, an improved backstepping design approach is presented to synthesising a class of continuous adaptive robust state-feedback controllers with a rather simple structure. The improved backstepping design approach can avoid the repeated differentiation problem which appears in using the conventional backstepping algorithm. In particular, it is not required to know the nonlinear upper bound functions of uncertainties. In the light of the presented approach, the state-feedback controllers can be constructed to be linear in the state, with the time-varying control gains which can be self-tuned by the adaptive laws. Similar to the conventional backstepping algorithm, the improved backstepping approach can be extended to a rather large class of uncertain nonlinear systems, and by combining the improved backstepping approach with other control methods, it may be expected to obtain a number of interesting results.

Robust Task Space Finite-Time Chattering-Free Control of Robotic Manipulators

This work deals with the problem of the accurate task space control subject to finite-time convergence. Kinematic and dynamic equations of a rigid robotic manipulator are assumed to be uncertain. Moreover, unbounded disturbances, i.e., such structures of the modelling functions that are generally not bounded by construction, are allowed to act on the manipulator when tracking the trajectory by the end-effector. Based on suitably defined task space non-singular terminal sliding vector variable and the Lyapunov stability theory, we derive a class of absolutely continuous (chattering-free) robust controllers based on the estimation of a Jacobian transpose matrix, which seem to be effective in counteracting uncertain both kinematics and dynamics, unbounded disturbances and (possible) kinematic and/or algorithmic singularities met on the robot trajectory. The numerical simulations carried out for a 2DOF robotic manipulator with two revolute kinematic pairs and operating in a two-dimensional task space, illustrate performance of the proposed controllers.

A novel adaptive finite-time tracking control for robotic manipulators using nonsingular terminal sliding mode and RBF neural networks

This paper presents a novel adaptive terminal sliding mode controller for the trajectory tracking of robotic manipulators using radial basis function neural networks (RBFNNs). First, a modified terminal sliding mode (TSM) surface is approached to avoid the singularity problem of conventional TSM. Then, a nonsingular TSM control is designed for joint position tracking of a robotic manipulator. In the control scheme, fully tuned RBFNNs are adopted to approximate the nonlinear unknown dynamics of the robotic manipulator. Adaptive learning algorithms are derived to allow online adjustment of the output weights, the centers and the variances in the RBFNNs. Meanwhile, a continuous robust control term is added to eliminate chattering efforts in the sliding mode control (SMC) system. The stability and finite-time convergence of the closed-loop system are established by using Lyapunov theory. Finally, the simulation results of a two-link robotic manipulator are presented to demonstrate the effectiveness of the proposed control method.

A Continuous Robust Antiswing Tracking Control Scheme for Underactuated Crane Systems With Experimental Verification

Disturbances and uncertainties are unfavorable elements that always accompany industrial mechatronic systems including cranes. If not fully considered or properly dealt with, they would badly influence the control system performance and degrade the working efficiency. Though traditional sliding mode control (SMC) methods are powerful to address these issues, they are discontinuous and might bring potential damages to the actuating devices. In addition, most existing methods cannot involve such practical constraints as permitted swing amplitudes, maximum velocity, etc. To resolve these problems, we suggest a novel composite antiswing crane control scheme, which involves time-suboptimal analytical trajectory planning and continuous robust tracking control. More precisely, a new analytical suboptimal trajectory planning algorithm is presented, which can generate analytical swing-free smooth trajectories guaranteeing practical constraints. Then, we design a new nonlinear control law to make the crane follow the planned trajectories with continuous control efforts, ensuring stable asymptotic tracking in the presence of perturbations/uncertainties. As far as we know, this is the first crane control scheme that simultaneously achieves state-constrained time-suboptimal trajectory planning and robust control with continuous control efforts. We implement experiments to examine its practical control performance and robustness as well.

Continuous Robust Tracking Control for Magnetic Levitation System With Unidirectional Input Constraint

In this paper, the exponentially tracking control problem for a magnetic levitation system (MLS) in the presence of parameter uncertainties and external disturbances is investigated. The disturbance/uncertainties-rejecting problem for the MLS is addressed from the view of a continuous nonlinear robust control development. Another problem of the concern is the common unidirectional input constraint in the MLS (i.e., the control input, often referring to the square of the electric current, should be nonnegative during the operation of the system). By utilizing an input transformation and augmented dynamics, a virtual control input, which removes the unidirectional constraint, is affinely emerged in the dynamics. A second-order filter is introduced to provide feedback signals for the control development. A novel Lyapunov function guarantees the exponentially tracking stability of the close-loop dynamics. Finally, some numerical simulation and real-time experimental results for tracking of time-varying trajectories are presented to validate the performance of the proposed control design.