High-gain Feedback Control Research Articles

Exact output tracking in prescribed finite time via funnel control

Output reference tracking of unknown nonlinear systems is considered. The control objective is exact tracking in predefined finite time, while in the transient phase the tracking error evolves within a prescribed boundary. To achieve this, a novel high-gain feedback controller is developed that is similar to, but extends, existing high-gain feedback controllers. Feasibility and functioning of the proposed controller is proven rigorously. Examples for the particular control objective under consideration are, for instance, linking up two train sections, or docking of spaceships.

Low-power high-gain homogeneous feedback control for chain of integrators with disturbances

We present a new high-gain feedback control design ensuring finite-time input-to-state stabilization of chains of integrators of dimension n subject to additive disturbances. The proposed high-gain homogeneous controller involves only control gains of power limited to 2 regardless of the dimension of the chains of integrators in contrast to the classical high-gain controllers involving gains with powers up to n + 1 which grows with the growth of the chain of integrators. The stability analysis of the closed-loop system is achieved by means of classical Lyapunov-based tools and homogeneity-based concepts. This result can be seen as the dual design of low-power high-gain observers recently extended to the homogeneous context.

Prescribed-time control of perturbed nonholonomic systems by time-varying feedback

This paper studies the prescribed-time control problem of nonholonomic systems. By using some properties of a class of parametric Lyapunov equations and constructing time-varying Lyapunov-like functions, a time-varying high-gain feedback controller is firstly proposed for the chained nonholonomic system such that the state of the closed-loop system converges to zero at any prescribed time. The advantage of time-varying feedback is revealed by comparison with time-invariant feedback. Then time-varying high-gain feedback controllers for a class of perturbed nonholonomic systems are designed to achieve prescribed time convergence of the states. Both state feedback and observer-based output feedback are considered and the controls are proved to be bounded in all the cases. The effectiveness of the proposed methods are verified by numerical examples.

Advanced sensorless nonlinear control strategy for grid connected photovoltaic systems via the two-time scale singular perturbation technique

This paper presents a new control strategy for grid connected photovoltaic (PV) system. The system consists of a solar panel, a boost converter, and a full-bridge inverter with L-filter connected to the grid. The control objectives are threefold: 1) tracking the maximum power point of the PV panel; 2) balancing the power exchange by regulating the DC link voltage; 3) ensuring a unity power factor in the grid. To achieve these objectives, a multi-loop controller is synthesised using a high-gain output feedback controller and the singular perturbation technique. The addressed control problem involves several difficulties including the existence of a number of state variables that are inaccessible to measurement. To address this problem, two-time-scale sliding mode observers are added which allow estimating, simultaneously, the solar panel current and the grid voltage. It is formally shown that all control objectives are asymptotically accomplished. This theoretical result is confirmed by numerical simulation tests.

High-gain observer-based output feedback control with sensor dynamic governed by parabolic PDE

In this paper it is proposed to extend the result described in Khalil and Praly (2014) and the references therein, regarding the high-gain observer-based nonlinear control to the case of systems with diffusion sensor dynamic. Based on some usual hypotheses, we provide sufficient conditions involving the high-gain parameter and the length on the PDE sensor. In fact it is brought into light an explicit trade off between them: the larger the observer gain, the smaller the length of the PDE sensor needs to be. The stability analysis of the closed loop system is based on a Lyapunov functional.

High-Stiffness Control of Series Elastic Actuators Using a Noise Reduction Disturbance Observer

Rendering a high impedance on a series elastic actuator (SEA) can improve motion control performance while retaining collision safety by a lower physical stiffness. The safe impedance range can be increased with high-gain velocity feedback control, but, in practice, this is limited by noise. This article applies the noise reduction disturbance observer to inner-loop velocity control of an SEA, attenuating noise and allowing higher safe rendered stiffness compared with standard torque and torque/velocity hierarchical control. Closed-form expressions for maximum passive stiffness and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Z$</tex-math></inline-formula> -region are found, shown to depend strongly on the high-frequency noise gain, and used to optimize the control gains. Performance is experimentally verified on a reaction-force SEA, validating the passivity of the high-stiffness control in impact (free space and stiff environment) while rendering a safe stiffness 3.0 times the intrinsic stiffness.

Prescribed-time control of high-order nonholonomic systems in chained form by time-varying feedback

In this paper, the prescribed-time control problem for a class of high-order nonholonomic systems is investigated. With the aid of a novel state transformation, the nonholonomic systems are decoupled. Further, a time-varying high-gain feedback controller is constructed by backstepping. It is shown that the proposed control law can achieve the prescribed-time convergence for high-order nonholonomic systems and the controller is bounded. Numerical examples verify the effectiveness of the method proposed in this paper.

Approach to calibrate actual cavity forward and reflected signals for continuous wave-operated cavities

Precise measurement of the cavity forward (Vf) and reflected signals (Vr) are crucial for calibrating other key parameters such as cavity detuning and forward power. In practice, the accuracy of these measurements is impacted by the crosstalk between the forward and reflected channels. For a pulsed radio-frequency (RF) system, DESY has proposed an algorithm to calibrate the actual Vf and Vr based on the cavity differential equation. This method requires the value of cavity voltage (Vc) changing over time to establish a complete differential equation. However, for a continuous wave (CW)-operated RF system, the signal Vc is almost constant over time thanks to the high gain feedback control of the low-level RF system. As a result, it is difficult to locate the optimal calibration factors using the DESY’s algorithm. Therefore, we offer an alternative algorithm to determine the calibration factors using the CW RF waveforms during a nominal RF shutdown event (RF power source is forced to shut down while the cavity remains working appropriately without any RF-related faults). The validity of the proposed algorithm was demonstrated on a Chinese ADS front-end demo superconducting linac (CAFe) facility that operated in CW mode. Using the calibrated Vf signal, we successfully estimated the beam current and beam phase during the CAFe beam commissioning, and we confirmed the accuracy of these estimations with the measurement result.

PID-type sliding mode-based adaptive motion control of a 2-DOF piezoelectric ultrasonic motor driven stage

This paper presents a new scheme of adaptive sliding mode control (ASMC) for a piezoelectric ultrasonic motor driven X–Y stage to meet the demand of precision motion tracking while addressing the problems of unknown nonlinear friction and model uncertainties. The system model with Coulomb friction and unilateral coupling effect is first investigated. Then the controller is designed with adaptive laws synthesized to obtain the unknown model parameters for handling parametric uncertainties and offsetting friction force. The robust control term acts as a high gain feedback control to make the output track the desired trajectory fast for guaranteed robust performance. Based on a PID-type sliding mode, the control scheme has a simple structure to be implemented and the control parameters can be easily tuned. Theoretical stability analysis of the proposed novel ASMC is accomplished using a Lyapunov framework. Furthermore, the proposed control scheme is applied to an X–Y stage and the results prove that the proposed control method is effective in achieving excellent tracking performance.

Output-feedback control of precision motion systems with uncertain nonlinearities

We propose output-feedback tracking control with an extended high-gain observer-based feedback control for a class of precision motion systems that include unknown rate-dependent hysteresis nonlinearities with linear dynamics. The proposed control system has a number of features; namely, (i) it can guarantee ultimate boundedness of the tracking error, where the ultimate bound can be made arbitrarily small, for any given initial conditions and for bounded unknown exogenous inputs and modeling parameters, (ii) it provides the possibility of shaping the transient response of the closed-loop system as desired, and (iii) the proposed technique is non-adaptive inversion free technique. To verify the effectiveness of these results, first simulation results are provided for an iron pendulum in a magnetic field system. Then, the output-feedback approach is also applied experimentally to a piezotube micropositioning actuator for a precision motion control.

Extended filtered high-gain output feedback controller for a class of uncertain nonlinear systems subject to external disturbances

ABSTRACT In this paper, an extended filtered high-gain output feedback controller is developed for a class of uncertain nonlinear systems subject to external disturbances. The design philosophy of the extended filtered high-gain output feedback controller is that the extended state observer (ESO), high-gain and low-pass filter are integrated together. The ESO can not only estimate the unknown internal state, but also deliver a good property of disturbance rejection simultaneously due to the presence of high gain. Since the high gain deteriorates the robustness of the system, a low-pass filtering mechanism is added in the control law to filter away aggressive signals and recover the robustness. The filtered control law is designed to compensate the nonlinear uncertainties and deliver a good tracking performance with guaranteed robustness. The uniform performance bounds are derived for the states and control signals via comparison with the virtual reference system.

Control of a nonlinear flexure-jointed X-Y positioning stage using LTV-FIR command prefiltering for finite-time error cancellation

This paper presents a new command input prefilter that achieves exact residual vibration cancellation for a single degree-of-freedom oscillator with linear time-varying (LTV) dynamics. The prefilter has a time-varying finite impulse response (FIR) function that is constructed using a time-warping technique and can be convolved with any command input signal to achieve finite settling time. Numerical results confirm that a discrete-time implementation of the prefilter can suppress vibration more effectively than robust linear time-invariant prefilter designs. The LTV-FIR prefilter was applied to a flexure-based X-Y micro-positioning platform having nonlinear dynamics and cross-coupling between motion axes. A configuration-dependent LTV model was constructed by using polynomial interpolation of a set of experimentally identified LTI models. Prefiltering was applied separately to X and Y axis command variables and a cross-coupling compensation technique used to minimize dynamic interaction between the motion axes. The LTV-FIR prefilter is shown to be effective for settling-time reduction in point-to-point motions (reduced from >6 to ≈0.4 seconds). Moreover, improved motion performance could be achieved over a large operating space without the use of high-gain feedback control, which is inappropriate in this case due to noise excitation and the risk of instability.

High-gain Observer-based Output Feedback Control with Sensor Dynamic Governed by Parabolic PDE

In this paper it is proposed to extend the result described in Khalil and Praly (2014) and the references therein, regarding the high-gain observer-based nonlinear control to the case of systems with diffusion sensor dynamic. Based on some usual hypotheses, we provide sufficient conditions involving the high-gain parameter and the length on the PDE sensor. In fact it is brought into light an explicit trade off between them: the larger the observer gain, the smaller the length of the PDE sensor needs to be. The stability analysis of the closed loop is based on a Lyapunov functional.

Asymptotic tracking with funnel control

AbstractFunnel control is a strikingly simple control technique to ensure model free practical tracking for quite general nonlinear systems. It has its origin in the adaptive control theory, in particular, it is based on the principle of high gain feedback control. The key idea of funnel control is to chose the feedback gain large when the tracking error approaches the prespecified error tolerance (the funnel boundary). It was long believed that it is a theoretical limitation of funnel control not being able to achieve asymptotic tracking, however, in this contribution it will be shown that this is not the case.

Event-Based Synchronization of Heterogeneous Complex Networks Subject to Transmission Delays

In this paper, the problem of event-based synchronization of heterogeneous complex networks is investigated. Specifically, the influence of transmission delays on event-based synchronization is considered. The designed distributed controller for each nonidentical node in heterogeneous network includes reference generator (RG) and robust regulator. Event-based communication protocol is utilized to ensure the synchronization among the identical RGs and target leader. Meanwhile, the interevent intervals are lower bounded by a positive constant. Furthermore, the proposed high-gain output feedback and adaptive control law guarantee that all nonidentical nodes converge to their RGs. Based on these two steps, which are coincided with the separation principle, nonidentical nodes can track the target leader. In addition, theoretical results are demonstrated by a numerical example.

Motion and force control with a nonlinear force error filter for underwater vehicle-manipulator systems

This paper deals with a control scheme for autonomous underwater robots equipped with manipulators. Several motion and force controllers have been developed. Most of them were designed in disregard of the dynamics of marine thrusters to develop a controller with a simple structure. However, the robot body propelled by thrusters generally has a considerably slower time response than the manipulator driven by electrical motors. Therefore, it may be difficult to construct a high-gain feedback control system to achieve a good control performance, because the high gain may excite the slow thruster dynamics ignored in the controller design, and the excitation will degrade the control performance. In this paper, we develop a motion and force controller for mathematical models with the dynamics of thrusters. It includes a nonlinear force error filter which allows us to construct a stable motion and force control system. To investigate its control performance, we conducted numerical simulations for comparing the proposed control scheme with an existing control scheme designed in disregard of the thruster dynamics. Simulation results demonstrate the usefulness of the proposed controller.

Minimal-Order Observer with a Function of Estimating Unmeasurable Inputs by High-Gain Feedback Control

Minimal-Order Observer with a Function of Estimating Unmeasurable Inputs by High-Gain Feedback Control

Aeroservoelastic modeling and analysis of a six-DOF hypersonic flight vehicle

By using light-weighted material in hypersonic flight vehicle, the vehicle body can be easily deformed. The mutual couplings in aerodynamics, flexible structure and control system will result in aeroservoelasticity problem. Based on the six-DOF geometry of a hypersonic flight vehicle, this paper uses assumed modes method, Shock-Expansion theory and Piston theory to develop the structural elastic model and the aerodynamic model, with actuator incorporated, the open-loop aeroservoelastic model of a six-DOF HFV is established. In open-loop analysis, the response of the elastic coordinates to the tail rudder deflection and the frequency characteristic of the transfer function of the tail rudder deflection to the first elastic coordinate are studied. A high gain feedback controller is designed for the aeroservoelastic model, and closed-loop analysis is conducted based on this model. The simulations show the influence of the elastic motion on the aerodynamic forces and moments.

High-speed and precision control of a piezoelectric positioner with hysteresis, resonance and disturbance compensation

A novel composite control strategy is developed in this paper to compensate hysteresis, resonance and disturbances in a piezo-actuated nanopositioner. The control objective of the piezoelectric positioner is to achieve high tracking performance in terms of accuracy and speed. For this purpose, a Bouc---Wen model based hysteresis compensator is first applied to mitigate the hysteresis nonlinearity without the complex inverse hysteresis calculation. And then, the linear dynamic of the hysteresis compensated system is identified and inverted to account for the resonance. A model-based inversion feed-forward controller is designed to achieve high speed tracking. Afterwards, a high-gain feedback controller is designed based on a notch filter to handle the modeling inaccuracy and all kinds of disturbances. So, the feed-forward controller can be augmented to the feedback controller to realize high speed and precision tracking. The enhancement of tracking performance is demonstrated through several comparative experiments. The performance of 70 Hz bandwidth and 0.281 μm precision can be achieved, which validated the effectiveness of the proposed composite control scheme.

Leader-following rendezvous with connectivity preservation and disturbance rejection via internal model approach

Most of the recent results on the leader-following rendezvous problem focus only on the deterministic multi-agent systems without external disturbances and plant uncertainties. In this paper, we will present a novel distributed internal model approach to further study the leader-following rendezvous problem for double-integrator multi-agent systems subject to both external disturbances and plant uncertainties. We provide both the distributed full state feedback control and the distributed partial state feedback control without velocity measurement. In both control schemes, we will give the suitable distributed internal model to convert the rendezvous problem into the stabilization problem with connectivity preserving for their augmented systems. We stabilize the corresponding augmented systems by the high gain feedback control based on a new potential function. Comparing with some recent results, our design can handle a large class of reference signals, external disturbances, and plant uncertainties.