Observer-based Boundary Control Research Articles

Prescribed-time and output feedback stabilization of heat equation with an intermediate-point heat source and boundary control

This paper addresses the problem of prescribed-time stabilization for the heat equation with an interior point heat source under output feedback. The study employs a two-step backstepping approach along with time-varying feedback techniques. A prescribed-time state observer and an observer-based boundary control law are developed. The proposed method extends the applicability of the prescribed time-stabilizing algorithm to heat equations with non-strict feedback terms. Numerical simulations validate its effectiveness.

Disturbance Observer-Based Boundary Control for an Antistable Stochastic Heat Equation With Unknown Disturbance

In this paper, a novel control strategy namely disturbance observer-based control is first applied to stabilization and disturbance rejection for an anti-stable stochastic heat equation with Neumann boundary actuation and unknown boundary external disturbance generated by an exogenous system. A disturbance observer-based boundary control is designed based on the backstepping approach and estimation/cancellation strategy, where the unknown disturbance is estimated in real time by a disturbance observer and rejected in the closed-loop, while the in-domain multiplicative noise whose intensity is within a known finite interval is attenuated. It is shown that the resulting closed-loop system is exponentially stable in the sense of both mean square and almost surely. A numerical example is demonstrated to validate the effectiveness of the proposed control approach.

Active vibration control of horizontal-axis wind turbine blades using disturbance observer-based boundary control approach

This paper addresses the issue of controlling vibration in horizontal-axis wind turbine (HAWT) blades under unknown boundary and distributed disturbances using an observer-based boundary control approach. In this regard, an actuator configuration, involving four active tendons mounted on the tip of the blade, is proposed to generate the out-of-plane and in-plane boundary control forces. The out-of-plane and in-plane governing equations are given as a set of PDEs and ODEs under parametric and direct excitations using Rayleigh beam theory including rotary inertia. A new disturbance observer is introduced to estimate boundary disturbances and subsequently combined with a new boundary control law for alleviating the HAWT blade vibration in the presence of unknown but bounded distributed disturbances. The uniform boundedness of the closed-loop system under unknown bounded distributed disturbances is confirmed via employing the Lyapunov’s direct method together with LaSalle–Yoshizawa’s theorem. Moreover, it is proved that the closed-loop system is uniformly exponentially stable in the absence of distributed and boundary disturbances. The reference NREL 5 MW HAWT blade is selected as the case study and the blade element momentum theory (BEMT) is employed to compute the aerodynamic load. Then, the open-loop and closed-loop responses of the blade under wind shear inflow and a predefined boundary disturbance are compared to demonstrate the performance of the closed-loop system in operational conditions.

New observer-based boundary control approaches to vibration reduction and disturbance attenuation of a flexible arm

This paper addresses the vibration reduction and disturbance attenuation problems of a flexible arm, which is modelled as a fourth-order partial differential equation. The main control objectives lie in reducing the influence of the disturbance, steering the flexible arm to the desired angular position and suppressing the vibration, simultaneously. To achieve the objectives, firstly, two different disturbance observers are designed. Secondly, we construct boundary controllers based on the two designed disturbance observers and boundary measurable signals. Then, with the two disturbance observers, the boundary disturbance compensation is achieved, and with the designed boundary controllers, the uniform boundedness of the flexible arm is guaranteed. Moreover, the well-posedness of the closed-loop system under the designed boundary controllers is discussed by means of the operator semigroup theory. Finally, the effectiveness and advantages of the proposed controllers are demonstrated through simulations and physical experiments.

Observer-based boundary control for an asymmetric output-constrained flexible robotic manipulator

Observer-based boundary control for an asymmetric output-constrained flexible robotic manipulator

Observer-based boundary control of distributed port-Hamiltonian systems

An observer-based boundary controller for infinite-dimensional port-Hamiltonian systems defined on 1D spatial domains is proposed. The design is based on an early-lumping approach in which a finite-dimensional approximation of the infinite-dimensional system derived by spatial discretization is used to design the observer and the controller. As long as the finite-dimensional approximation approaches the infinite-dimensional model, the performances also do. The main contribution is a constructive method which guarantees that the interconnection between the controller and the infinite-dimensional system is asymptotically stable. A Timoshenko beam model has been used to illustrate the approach.

Observer-based boundary control of the sine–Gordon model energy

The problem of observer-based boundary control of the sine–Gordon model energy is first posed. A Luenberger-type observer for the sine–Gordon equation is analysed, and explicit bounds on the system parameters ensuring the exponential decay of the estimation error are obtained. With the use of this observer a speed-gradient output feedback for sine–Gordon model energy control is proposed. The achievement of the control goal is established under the assumption that system’s energy does not vanish in finite time. It is shown that the transient time in energy is close that the transient time in observation error, i.e. the closed-loop system has a reasonable performance. It is also shown that the conditions on the observer gain sufficient for the state estimation error convergence are “almost” necessary in the sense that violation of these conditions makes the state estimation error transients too long.

Observer-based boundary control of semi-linear parabolic PDEs with non-collocated distributed event-triggered observation

This paper deals with the problem of boundary control for a class of semi-linear parabolic partial differential equations (PDEs) with non-collocated distributed event-triggered observation. A semi-linear Luenberger PDE observer with an output error based event-triggering condition is constructed by using the event-triggered observation to exponentially track the PDE state. By the estimated state, a feedback controller is proposed. It has been shown by the Lyapunov technique, and a variant of Poincaré–Wirtinger inequality that the resulting closed-loop coupled PDEs is exponentially stable if a sufficient condition presented in terms of standard linear matrix inequality (LMI) is satisfied. Moreover, a rigorous proof is provided for existence of a minimal dwell-time between two triggering times. Finally, numerical simulation results are given to show the effectiveness of the proposed design method.

Disturbance observer-based boundary control for a suspension cable system moving in the horizontal plane

This paper addresses the suppressing problem of cable vibration and the positioning control design for a suspension cable system of a helicopter with disturbances. Hamilton’s principle is applied to obtain a distributed parameter system for the suspension cable system of a helicopter. Two observers are employed to restrain the effect of unknown external disturbances. Based on the proposed disturbance observers and Lyapunov’s direct method, two boundary control laws are designed, which are provided by the actuators at the top and bottom boundaries of the suspension cable, respectively. Under the proposed control laws, the oscillation amplitude and the error between the bottom boundary payload and the desired point are proven to be uniformly ultimately bounded. Moreover, they will converge to a small neighbourhood of zero by selecting proper design parameters. Meanwhile, some sufficient conditions are provided to guarantee the validity of the proposed control laws. Finally, simulation results show the rationality and effectiveness of the control scheme developed in this paper.

Observer-Based Boundary Control Design for the Suppression of Stick–Slip Oscillations in Drilling Systems With Only Surface Measurements

We develop an observer-based boundary controller for the rotary table to suppress stick–slip oscillations and to maintain the angular velocity of the drill string at a desired value during a drilling process despite unknown friction torque and by using only surface measurements. The control design is based on a distributed model of the drill string. The obtained infinite dimensional model is converted to an ordinary differential equation–partial differential equation (ODE–PDE) coupled system. The observer-based controller is designed by reformulating the problem as the stabilization of an linear time-invariant (LTI) system which is affected by a constant unknown disturbance and has simultaneous actuator and sensor delays. The main contribution of the controller is that it requires only surface measurements. We prove that the equilibrium of the closed-loop system is exponentially stable, and that the angular velocity regulation is achieved with the estimations of unknown friction torque and drill bit velocity. The effectiveness of the controller is demonstrated using numerical simulations.

Observer-based boundary control for 2D Burgers equation

The 2D Burgers equation has extensively been considered as a benchmark problem by flow control researchers. The flavour of the problem is its multidimensionality and non-linearity, which are the reasons for making the governing equation a good start for developing a well defined understanding of control of flows. This paper demonstrates that an infinite dimensional observer can be designed, and by the aid of the observer, a simple boundary feedback control can be achieved under severe noise and disturbance scenarios. The results are in good compliance with the theoretical claims.