Observer-based Output Feedback Research Articles

Extended state observer–based output feedback control for spacecraft pose tracking with control input saturation

This article proposed an extended state observer (ESO)–based output feedback control scheme for rigid spacecraft pose tracking without velocity feedback, which accounts for inertial uncertainties, external disturbances, and control input constraints. In this research, the 6-DOF tracking error dynamics is described by the exponential coordinates on SE(3). A novel continuous finite-time ESO is proposed to estimate the velocity information and the compound disturbance, and the estimations are utilized in the control law design. The ESO ensures a finite-time uniform ultimately bounded stability of the observation states, which is proved utilizing the homogeneity method. A non-singular finite-time terminal sliding mode controller based on super-twisting technology is proposed, which would drive spacecraft tracking the desired states. The other two observer-based controllers are also proposed for comparison. The superiorities of the proposed control scheme are demonstrated by theory analyses and numerical simulations.

Global exponential stabilisation of nonlinear systems by reduced-order observer-based output feedback control via matrix inequality approach

In this paper, we consider the global exponential stabilisation problem by output feedback for a class of nonlinear systems with the extended structure of nonlinearity over the existing control scheme. The new feature is that we present a newly designed reduced-order observer-based output feedback controller with a gain-scaling factor. In our proposed method, we provide more flexibility in the selection of control parameters by utilising a matrix inequality approach under the extended structure of nonlinearity. Using examples, we illustrate the improved results of the proposed control scheme over the existing control scheme.

Containment control of multi-agent systems with input saturation and unknown leader inputs

This paper investigates the containment control problem for multi-agent systems (MASs) with multiple leaders which have non-zero control inputs. Agents’ tracking errors are described by a linear system with an external disturbance. The containment control problem is then solved by applying a distributed observer-based output feedback controller. Anti-windup (AW) compensation is designed by convex conditions, to improve the performance in the presence of actuator saturation. Finally, simulations are presented to illustrate the effectiveness of the proposed method.

Hybrid adaptive observer-based output feedback predictive control for the alternating activated sludge process

In this paper, an adaptive observer-based predictive controller is designed for the alternating activated sludge process which represents a nonlinear hybrid system. Precisely, our objective is to control the dissolved oxygen concentration during the aerobic phase. First, a hybrid adaptive observer is designed to estimate conjointly the unmeasured state (the ammonia concentration) and the unknown parameter (the coefficient of performance of heterotrophic biomass). Then the estimated signals are used in the output feedback predictive control law. The convergence of the state estimation, parameter reconstruction and tracking control errors are established through a Lyapunov stability analysis. Numerical simulations are dedicated to highlight the good performances of the developed output feedback control approach.

Boundary Stabilization of Heat Equation with Multi-Point Heat Source

In this paper, we consider boundary stabilization problem of heat equation with multi-point heat source. Firstly, a state feedback controller is designed mainly by backstepping approach. Under the designed state controller, the exponential stability of closed-loop system is guaranteed. Then, an observer-based output feedback controller is proposed. We prove the exponential stability of resulting closed-loop system using operator semigroup theory. Finally, the designed state and output feedback controllers are effective via some numerical simulations.

Zonotopic Kalman filtering for stability augmentation and flight envelope estimation

This article introduces a novel methodology based on zonotopic Kalman filtering for stabilizing attitude dynamics and estimating flight envelopes of an unmanned helicopter via an observer-based (output) feedback control law and a reachability analysis, respectively. The helicopter dynamics is represented by a linear state-space model, based on which the feedback control law is designed. Since not all state variables are measurable, state information is acquired by applying a zonotopic Kalman filter to yield sets of state-variable estimates of the helicopter in terms of zonotopes. Not only are the resulting zonotopes used for the observer-based feedback control, but also for estimating the flight envelopes of the helicopter based on the reachability analysis. This approach is useful for enhancing pilot’s awareness about dynamic responses of the helicopter, which may undergo unsafe flight conditions due to actuator faults triggered by undesirable perturbations. The efficacy of the proposed methodology is demonstrated via an example, where we also expose the benefits of applying the zonotopic Kalman filter as compared with an ordinary stochastic Kalman filter.

Robust Output Feedback Control Design for Inertia Emulation by Wind Turbine Generators

Wind generation has gained widespread use as a renewable energy source. Most wind turbines and other renewables connected to the grid through converters result in a reduction in the natural inertial response to grid frequency changes. The doubly-fed induction generator (DFIG) can be controlled to compensate for this reduction and, in fact, provide faster response than traditional synchronous machines. This paper proposes to design observer based output feedback linear quadratic regulator (LQR) and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> control laws to realize the inertia emulation function and deliver fast frequency support. The aim is to track the reference speed by a diesel synchronous generator (DSG) in order to reach the desired inertia. The control signal is computed based on a reduced order model using the balanced truncation technique. A comparison with selective modal analysis (SMA) and balanced truncation model reduction techniques is presented. Comprehensive results show the effective emulation of synthetic inertia by implementing the control laws on a nonlinear three-phase diesel-wind system. The proposed technique is analyzed for different short circuit ratio (SCR) scenarios.

Control Design for Uncertain Switched Nonlinear Systems: Adaptive Neural Approach

This paper addresses adaptive neural output feedback control for uncertain nonlinear switched systems. The main difficulty for control design comes from the loss of the precise information on those virtual coefficients of each subsystem. To overcome this difficulty, we give a robust observer design scheme by using convex combination approach. Furthermore, develop an observer-based output feedback control strategy. During the procedure of control design, adaptive neural control approach is used to deal with the unknown nonlinear functions and backstepping technique is employed to construct the ideal control laws. It is shown that the presented control law achieves the control issue of getting small tracking error, meanwhile, ensuring boundedness of all the closed-loop signals. Finally, a simulation example is used to test our results.

Prescribed-Time Stabilization of a Class of Nonlinear Systems by Linear Time-Varying Feedback

This article studies the problem of prescribed-time global stabilization of a class of nonlinear systems, where the nonlinear functions are unknown but satisfy a linear growth condition. By using solutions to a class of parametric Lyapunov equations containing a time-varying parameter that goes to infinity as the time approaches the prescribed settling time, linear time-varying feedback is designed explicitly to solve the considered problem, with the help of a Lyapunov-like function. It is shown moreover that the control signal is uniformly bounded by a constant depending on the initial condition. Both linear state feedback and linear observer-based output feedback are considered. The effectiveness of the proposed approach is illustrated by a numerical example borrowed from the literature.

Integrated energy saving and position tracking controller for the hydraulic lifting servo system

High energy efficiency and tracking accuracy are both vital for hydraulic lifting servo systems. However, the appropriate hardware configuration and its corresponding nonlinear controller is always a problem to be solved. To address this multi-objective task, an integrated energy-saving and position tracking controller is developed. Specifically, to reduce the substantial energy dissipation, a system configuration referring to the structure of the three-position-six-way valve is proposed. To ensure accurate tracking performance, a hybrid observer-based output feedback controller is developed. By doing so, the function of flow regeneration and the property of flow matching are achieved, and the tracking accuracy is guaranteed by using only position signal. To validate the effectiveness of the proposed method, a common Lyapunov function is used to prove the stability of the multi-model system, and case studies are conducted to demonstrate the system performance.

Boundary Output Feedback Stabilization of the Linearized Schrödinger Equation with Nonlocal Term

In this paper, we are concerned with the boundary output feedback stabilization problem of a Schrodinger equation with a nonlocal term. Firstly, we design an explicit boundary state feedback controller by backstepping approach. Under this controller, the closed-loop system is proved to be exponentially stable from the equivalence between the original system and the target system. Then, we propose an observer-based output feedback controller by replacing the state in state feedback controller with its estimation. The resulting closed-loop system admits a unique solution which is exponentially stable. Finally, some numerical examples are presented to illustrate the effectiveness of the proposed feedback controller.

Semi-global bipartite consensus tracking of singular multi-agent systems with input saturation

This paper investigates the problem of bipartite consensus tracking for a class of linear singular multi-agent systems under a signed graph topology, where the control input of each agent is subject to saturation. By exploiting a parametric algebraic Riccati equation (ARE)-based low-gain feedback approach, a static state feedback control protocol and a dynamic observer-based output feedback control protocol are developed utilizing local information. It is shown that under the presented protocols, semi-global bipartite consensus tracking can be achieved if the underlying signed communication graph is structurally balanced and contains a spanning tree rooted at the leader. A numerical example is finally given to illustrate the effectiveness of the theoretical results.

Adaptive Observer-Based Sliding Mode Control for a Two-Wheeled Self-Balancing Robot under Terrain Inclination and Disturbances

This paper investigates an output feedback sliding mode control scheme for a two-wheeled self-balancing robot under terrain inclination and disturbances. First of all, an adaptive high-gain observer is designed for the robot to estimate, simultaneously, the unmeasured states and the unknown terrain inclination angle which appears nonlinearly in the dynamics of the wheeled robot, using the only measured linear and angular positions. Then, the estimated states and the reconstructed unknown inclination angle are used by an appropriate continuously implemented sliding mode controller whose the design is based on the boundary layer approximation approach to reduce the chattering phenomenon. The objective of the proposed robust controller is to ensure the tracking control of the two-wheeled robot despite the unknown terrain inclination and the presence of friction disturbances. The stability of the adaptive observer-based output feedback system is established through a Lyapunov analysis, and it is inspired from sliding modes theory. Numerical simulations results highlight the effectiveness of the proposed tracking control scheme applied on two-wheeled self-balancing robot subject to terrain inclination even in the presence of unavailable disturbances.

Stability Analysis for Input Saturated Discrete-Time Switched Systems With Average Dwell-Time

This paper studies the stability analysis of the input saturated discrete-time switched systems with average dwell-time based on the parametric discrete-time Riccati equation. The state feedback controller and the observer-based output feedback controller are designed to guarantee the exponential stability of the closed-loop system. The proposed method is simple and easy to operate in practice. The designed controllers can be computed easily by solving the parametric discrete-time Lyapunov equation. The main advantages of this paper are that the stability analysis is based on the properties of the saturation function and limited structure information of the actuator saturation and that the designed controllers have good robustness to the structure uncertainty of the input saturation. The simulation results illustrate the effectiveness of the proposed methods.

Observer‐based output feedback H∞ control of two‐dimensional systems with periodic scheduling protocol and redundant channels

In this study, the observer-based output feedback H ∞ control problem is investigated for the two-dimensional (2D) networked control system (NCS) in form of Fornasini–Marchesini second model. The communication from the controller to the actuator is carried out through a shared network medium, where only one signal gets the network access at each transmission instant. To avoid data collisions, the periodic scheduling protocol is employed to assign the network access priority to the actuator in chronological order. To improve the reliability of data transmission, redundant channels are applied to deliver the measurement observed by the sensor to the controller. The aim of the addressed problem is to design an observer-based output feedback controller so that the considered 2D NCS satisfy a predefined H ∞ performance index. Sufficient condition is given to ensure the H ∞ performance of the closed-loop system via the Lyapunov theory and stochastic analysis. Moreover, the observer-based output feedback controller is designed to achieve the desired H ∞ performance index, under which the controller parameters are determined by solving certain optimisation problems. Finally, a numerical example is given to demonstrate the feasibility of the proposed approach.

Observation and stabilisation of coupled time‐fractional reaction–advection–diffusion systems with spatially‐varying coefficients

This study solves the problem of observer-based output feedback stabilisation of a coupled time-fractional reaction–advection–diffusion system with space-dependent coefficients. In light of the backstepping approach, the Mittag–Leffler convergent observer is derived to enable stabilisation by output feedback. By the fractional Lyapunov method, the Mittag–Leffler stability of the estimation error system is then established. Using the separation principle yields a stabilising output feedback controller, with which the closed-loop stability is proved. Finally, the feasibility of the proposed approach is tested by fractional numerical examples when the kernel matrix equation has not the explicit solution.

Consensus of Discrete-Time Multiagent Systems With State, Input, and Communication Delays

In this paper, we study the consensus problem for high-order discrete-time multiagent systems with state, input, and communication delays, where the input and communication delays can be arbitrarily large yet exactly known. Moreover, the communication delays are different for different agents. Nested predictor-based state feedback protocols and full-order/reduced-order observer-based output feedback protocols are established to solve the problem. It is shown that both the input and communication delays can be compensated completely. Furthermore, linear matrix inequalities-based approaches are provided to design state feedback gains and observer gains. A numerical example is worked out to illustrate the effectiveness of the proposed approaches.

Distributed output feedback consensus control of networked homogeneous systems with large unknown actuator and sensor delays

This paper studies observer-based output feedback consensus control of networked homogeneous systems in the presence of unknown bounded actuator and sensor delays. A transport partial differential equation (PDE) is used to describe the dynamics of the delay state, and then a distributed observer on the basis of the estimate delay state and relative output information is designed to estimate the neighborhood consensus error. Predictor-based consensus protocols are proposed by utilizing the observer state and the estimate delay state. Lyapunov functions are explicitly constructed to analyze system stability, and the delay mismatch robustness of the consensus protocols is proved. Simulation results performed on low-Earth-orbit satellite formation flying are presented to illustrate the effectiveness of the proposed scheme.

Output feedback stabilization for 1-D wave equation with variable coefficients and non-collocated observation

In this paper, we consider exponential stabilization for a 1-D wave equation with variable coefficients and Neumann boundary actuation. A novel transformation is constructed to convert the wave equation into an equation of the same type with constant coefficient and low order term. By using the backstepping approach, we design a state observer via non-collocated boundary displacement and velocity measurement. An observer based output feedback is then designed using the backstepping gain to stabilize the system exponentially. The well-posedness and the exponential stability of the closed-loop system are proved. As an illustration, some numerical simulations are presented.

Laser Sintering Control for Metal Additive Manufacturing by PDE Backstepping

Metal additive manufacturing (AM) has been intensively advanced due to numerous industrial applications, such as automobiles, aerospace, consumer electronics, and medical devices. The dynamics of the melt pool via laser sintering for metal AM has been studied by means of the thermodynamic phase change model known as the “Stefan problem”. In this article, we develop a control design for the laser power to drive the depth of the melt pool to the desired set point. The governing equation is described by a partial differential equation (PDE) defined on a time-varying spatial domain, which is dependent on the PDE state, and the optical penetration of the laser energy affects the PDE dynamics in the domain as well as at the surface boundary. First, we design the full-state feedback control law utilizing the entire spatial profile of the temperature in the melt pool and the moving interface position. The closed-loop system is proven to satisfy some conditions to validate the physical model, and its origin is shown to be exponentially stable. Next, we propose an observer-based output feedback control law by reconstructing the temperature profile with the availability of only the measured interface position and prove the analogous properties of the closed-loop system. Numerical simulation for a controller designed on a single-phase Stefan model is conducted on a more complex and realistic two-phase Stefan model, which incorporates the cooling effect from the solid phase. In addition, a bias in the interface location measurement is considered. The numerical results illustrate the robustness of the proposed feedback. By lowering the initial temperature in the solid and by increasing the interface sensor bias to more extreme levels, which leads to the controller’s failure (where the failure is exhibited through the entire metal freezing and the melt pool disappearing), we explore the limits of how much uncertainty our control law can handle.