Output Feedback Compensator Research Articles

Power based adaptive compensator of output oscillations

Power-based output feedback compensator for oscillatory systems is proposed. The average input-output power of an oscillatory signal serves as an equivalent control effort, while the unknown amplitude and frequency of oscillations are detected at each half-period. This makes the compensator adaptive and discrete, while the measured oscillatory output is the single available signal in use. The resulting discrete control scheme enables a drastic reduction of communication efforts in the control loop. The compensator is designed for 2nd order systems, while an extension to higher-order dynamics, like e.g. in case of two-inertia systems, is also provided. Illustrative experimental case study of the 5th order oscillatory system is provided.

Global state regulation of time-delay minimum-phase systems by delay-free dynamic compensation

This paper studies the global control problem, in the sense of “almost stabilization” or state regulation, for a class of time-delay minimum-phase nonlinear systems via delay-free dynamic compensation. Both dynamic state and output feedback control schemes are developed. By taking advantage of dynamic rather than static feedback, we design delay-independent dynamic state and output feedback compensators, respectively, to achieve asymptotic state regulation with global stability. In the case of dynamic state feedback, a structural condition is imposed on the inverse dynamics that are nonlinear yet imply linear zero dynamics. In the case of dynamic output feedback, more strict conditions on the nonlinearity are characterized to guarantee the existence of a dynamic output controller. In both cases, it is proved by the Lyapunov–Krasovskii functional method, combined with the Barbalat’s lemma, that all the states of the time-delay minimum-phase systems are regulated to zero and boundedness of the closed-loop system is ensured. Two examples are given to validate the proposed delay-free dynamic compensators.

Adaptive compensation control of nonlinear systems with unknown actuator failures

AbstractIn this paper, by using bound estimation method, Nussbaum function, K‐filters and higher‐order Lyapunov function, an adaptive output feedback compensation control scheme is proposed for uncertain nonlinear systems with infinite number of actuator failures and unknown control direction. A parametric model with unknown system uncertainties and infinite actuator failures is established, which is different from the existing results. This scheme ensures that closed‐loop signals are globally uniformly bounded. By properly selecting the design parameters, the tracking errors converges to a small neighborhood of the origin. Finally, two simulation examples are given to demonstrate its efficiency of the proposed design scheme.

Adaptive Output Feedback Compensation for a Class of Nonlinear Systems With Actuator and Sensor Failures

In this article, an adaptive output feedback compensation scheme is proposed for a class of uncertain nonlinear systems with a set of redundant actuators and a sensor. The sensor output is the only information available for output feedback. Both the actuators and the sensor may suffer from failures during operation and, therefore, all the system states are not available. To estimate the unmeasured states, a modified high-gain observer is designed which can not only ensure the closed-loop system stability but also improve the tracking performance. In the adaptive controller design, to overcome the complexity due to the unknown actuator and sensor failures coupled with the nonlinear functions and unknown parameters, an upper bound estimation method is adopted, which greatly simplifies the design procedure. It is proved that with the proposed scheme, the actuator and sensor failures can be compensated simultaneously, the reconfiguration can be adaptively updated without fault detection and isolation, and the real-tracking error can converge to a residual set, that is, mainly proportional to the sensor gain variation and measurement error.

Output feedback compensation to state and measurement delays for a first-order hyperbolic PIDE with recycle

This paper develops a novel observer-based output-feedback control law for a class of interconnected first-order hyperbolic partial integral differential equations (PIDEs) with in-domain, non-local coupling terms and measurement delay compensation. A transport PDE is introduced to account for in-domain recycle delay which results in an extended spatial domain with the PIDE and transport PDE being cascaded. Since standard backstepping approach cannot be applied, an affine Volterra integral transform is introduced which allows for the construction of a boundary controller for the PIDE and delay compensation. An observer backstepping transformation containing four kernels is realized, reconstructing the states throughout the delayed measurement. By the use of the backstepping method, a set of coupled kernel equations where one of the kernels has two boundary conditions is established. The existence and invertibility for the control and observer transformations are proved and the finite-time stability for the output system is established while results are illustrated by numerical simulations.

Output Feedback Constrained Regulation of Linear Systems via Controlled-Invariant Sets

Design of output feedback controllers applied to the regulation problem for constrained linear discrete-time systems via set-invariance techniques is studied. Output feedback controlled-invariant (OFCI) polyhedra are used to ensure that state and input constraints are satisfied even in the presence of additive disturbances and measurement noise. Necessary and sufficient conditions for a polyhedral set to be OFCI are presented. A dynamic output feedback compensator is proposed through the construction of an OFCI set for an augmented system. Based on the measured output and on the compensator state, which constitutes an estimate of the system state, a suitable control sequence is computed via linear programming to enforce the constraints. The uncertainty on the state is progressively reduced using the contraction of an invariant set associated to the estimator. With our approach, as illustrated through numerical examples, by embedding the estimator in the compensator structure and using the OFCI concept, it is possible to obtain solutions with larger sets of admissible initial states and admissible initial estimation errors, compared to approaches available in the literature.

Adaptive event-triggered output-feedback controller for uncertain nonlinear systems

This paper addresses the event-triggered output-feedback stabilization for a class of uncertain nonlinear systems. Essentially different from the related literature, the systems under investigation allow large uncertainties (whose size is unknown) coupling to unmeasurable states, which requires to integrate a comprehensive output-feedback compensation mechanism into the event-triggered philosophy and would bring substantial challenges to the event-triggered control. To solve the problem, a novel scheme of adaptive event-triggered output-feedback control is established for the systems. Specifically, an adaptive dynamic gain is introduced not only to counteract the large uncertainties but also to cope with the execution/sampling error. Then, an adaptive event-triggered output-feedback controller based on dynamic-gain observer is constructed to guarantee global convergence for the resulting closed-loop system while reducing execution/sampling. Particularly, the event-triggering mechanism involved is delicately designed by fully exploiting the dynamic gain, to enable the negative influence of the gain through the execution error to be counteracted (no matter how large the gain becomes) while precluding infinitely fast execution which violates the implementation of event-triggered controller in practice. Correspondingly, a distinctive analysis pattern is implemented for the closed-loop performance, due to the coupling of the dynamic-gain compensation mechanism and the event-triggering mechanism. Moreover, for more efficient resource saving, we further show the feasibility of adaptive dynamic event-triggering mechanism for the desired stabilization.

Adaptive Neural Output Feedback Compensation Control for Intermittent Actuator Faults Using Command-Filtered Backstepping.

Effectively compensating unknown intermittent actuator faults in uncertain decentralized nonlinear systems is a very difficult problem, and very few results have been obtained. In this article, to address this issue, an adaptive neural output feedback compensation control scheme based on command-filtered backstepping is developed. First, we design a bank of observers to estimate the system states and utilize neural networks with random hidden nodes to approximate the unknown functions of these observers. Second, a smooth projection algorithm is used to online update estimated parameters in the controllers such that the possible ceaseless increase in the estimated parameters caused by intermittent actuator faults can be eliminated. Due to the presence of intermittent jumps of unknown parameters, a modified Lyapunov function is developed to analyze the system stability. It is proved that the boundedness of all closed-loop system signals is ensured and the ultimate bound of the tracking error depends on design parameters, adjustable jumping amplitude of Lyapunov function, and minimum fault time interval. Third, by analyzing the system transient performance, the peaking phenomenon at the starting instant of the system operation can be removed, and a root mean square type of bound is established to illustrate that the transient tracking error performance is tunable by design parameters. Finally, simulations studies are done to illustrate the effectiveness of the theoretical results.

Quadrotor Flight Controller Design Using Classical Tools

A principal aspect of quadrocopter in-flight operation is to maintain the required attitude of the craft’s frame, which is done either automatically in the so-called supervised flight mode or manually during man-operated flight mode. This paper deals with the problem of flight controller (logical) structure and algorithm design dedicated for the man-operated flight mode. The role of the controller is to stabilise the rotational speeds of the Tait-Bryan angles. This work aims to extend the sustainable performance operating range of a proportional-integral-derivative output feedback compensator (PID) based flight controller by exploiting the concepts of feedforward inverse actuator model and the re-definition of input space in order to handle the non-linearity of the system under control. The proposed solution is verified numerically and implemented in the form of a discrete-time domain algorithm, obtained by emulation, using a physical quadrocopter model.

One Step Anti-Windup Design for Nonlinear Systems: An Indirect LMI-Based Approach

This paper proposes an indirect linear matrix inequality (LMI) approach to design one step anti-windup dynamic output feedback compensator for a class of nonlinear systems subject to actuator saturation. When the system state satisfies certain conditions, the nonlinear system can be reconstructed accurately by T-S fuzzy model, based on Lyapunov stability analysis and a result about matrix inequality, we show that the feasibility of an LMI guarantees the solvability of the corresponding one step anti-windup compensator. Once the solvability issue is determined, then we give an algorithm of one step anti-windup nonlinear dynamic output feedback compensator. The effectiveness of the proposed method is illustrated with numerical example.

A Dynamic Feedback Framework for Control of Time-Delay Nonlinear Systems With Unstable Zero Dynamics

This paper presents a dynamic feedback framework for the control of time-delay cascade systems with unstable zero dynamics. Both dynamic state and output feedback control strategies are studied. Recognizing the difficulty of controlling time-delay systems via static feedback, we develop a systematic method, by taking advantage of dynamic feedback, for the design of delay-free, dynamic state and output feedback compensators that achieve global state regulation with stability. The controlled plants under consideration not only cover time-delay nonlinear systems in the normal form, but also include a class of time-delay cascade systems beyond the normal form. In the case of state feedback, the zero dynamics are not required to be “minimum phase” but satisfy certain regularity conditions. In the output feedback case, appropriate conditions are characterized for the zero dynamics so that the existence of a dynamic output controller is ensured. A key feature of the proposed control strategies is the utilization of dynamic gains to counteract the effect of time-delay nonlinearities and unstable zero dynamics.

Semiglobal Asymptotic Stabilization of Lower Triangular Systems by Digital Output Feedback

Digital control of nonlinear systems is studied by output feedback. It is proved that for nonlinear systems with a lower triangular structure, semiglobal asymptotic stabilization is still possible via discretized output feedback as long as a sampling time is small. The establishment of semiglobal asymptotic stabilizability needs no restrictive condition on the nonlinearities and/or unmeasurable states of the system, such as a linear growth condition or an output-dependent growth condition as commonly required in the case of global output feedback stabilization. It involves, however, tedious but subtle stability analysis due to the hybrid nature of the closed-loop system. A design method through “sample and hold” is developed to construct a semiglobally asymptotically stabilizing, digital output feedback compensator that consists of a high-gain nonlinear observer and controller, both with saturated states.

On the Existence of Stable Real nth-Order Transfer Functions With Desired Phase at n Frequencies

We consider the following question: Given n distinct non-negative frequencies {ω 1 , ω 2 , ... ω n }, does there always exist a stable real nth-order transfer function (TF) with a desired phase at these frequencies? For n even, we prove that the answer is yes and propose a numerical algorithm for obtaining such TFs. For n > 1 odd, we conjecture that the answer is no. These results are useful for designing lower-order output feedback compensators that solve the multi-agent consensus problem for high-order linear agent dynamics.

Observer‐based output feedback compensator design for linear parabolic PDEs with local piecewise control and pointwise observation in space

This study presents an observer-based output feedback compensator design for a linear parabolic partial differential equation (PDE), where a finite number of actuators and sensors are active over partial areas and at specified points in the spatial domain, respectively. In the proposed design method, a Luenberger-type PDE observer is first constructed by using the non-collocated pointwise observation to exponentially track the PDE state. Based on the estimated state, a collocated local piecewise state feedback controller is then proposed. By employing a Lyapunov direct method, integration by parts, Wirtinger's inequality and first mean value theorem for definite integrals, sufficient conditions on the exponential stability of the resulting closed-loop coupled PDEs are presented in terms of standard linear matrix inequalities. Furthermore, both open-loop and closed-loop well-posedness analysis results are also established by the C 0 -semigroup method. Numerical simulation results are presented to show the effectiveness of the proposed design method.

Output feedback adaptive sensor failure compensation for a class of parametric strict feedback systems

Abstract In this paper, an adaptive output feedback compensation control scheme is proposed for a class of nonlinear systems with unknown sensor failures. For estimating the unmeasured states, a novel switching-type adaptive observer is constructed, in which the observer gains are tuned in a switching manner. To compensate for the failure effects on transient performance, a new error signal which contains an adaptive compensation coefficient is introduced into backstepping procedure. It is shown that the proposed controller can guarantee the closed-loop system is globally uniformly ultimately bounded, and system output converges to an adjustable neighborhood of the origin. Simulation results are presented to illustrate the effectiveness of the proposed scheme.

Adaptive fuzzy output feedback and command filtering error compensation control for permanent magnet synchronous motors in electric vehicle drive systems

In this paper, under the circumstance of parametric uncertainties and external load disturbance, an adaptive fuzzy output feedback and command filtering error compensation control is proposed for permanent magnet synchronous motors (PMSMs) in electric vehicle systems. First, fuzzy logic systems (FLSs) are used to approximate unknown nonlinear functions, and a fuzzy reduced-order observer is set up to estimate the angle speed of the PMSMs. Then, the command filtering error compensation control is utilized to handle the “explosion of complexity” problem arose from the derivation of virtual control functions and reduce the error caused by the command filter, which improves the control accuracy. In addition, the adaptive backstepping technique is exploited to construct the adaptive fuzzy controllers to guarantee the tracking error converge to a small neighborhood of the origin. Finally, simulation results verify the effectiveness and advantages of the proposed theoretic result.

Hybrid Adaptive Multi-Sinusoidal Disturbance Cancellation

A stable, single-input, single-output linear system is considered whose input is affected by biased multi-sinusoidal disturbances with uncertain frequencies belonging to a given range, unknown phases and amplitudes. The problem of exponential disturbance rejection by output feedback from any initial condition is addressed and solved. The knowledge of the sign of the real part (or the imaginary part) of the transfer functions, evaluated at the frequencies belonging to the given range, is sufficient to design a novel hybrid output feedback compensator. The critical parameters of the linear controller, which are related to the unknown frequencies, are updated every predetermined time interval and are generated by an exponentially converging adaptive observer, starting from any initial condition compatible with the given range. The output is exponentially driven to zero while the unknown disturbance is reconstructed.

Transition between grid-connected mode and islanded mode in VSI-fed microgrids

This paper investigates the behaviour of a microgrid system during transition between grid-connected mode and islanded mode of operation. During the grid-connected mode the microgrid sources will be controlled to provide constant real and reactive power injection. During the islanded mode the sources will be controlled to provide constant voltage and frequency operation. Special control schemes are needed to ensure proper transition from constant P–Q mode to constant f–V mode and vice versa. Transition from one mode to other will introduce severe transients in the system. Two kinds of transition schemes based on the status of the off-line controller are discussed and a comparative study is presented for various step changes in the load. An additional-pole-placement-based output feedback controller augmentation during transition between the modes is proposed to reduce the transients. A static output feedback compensator design is proposed for the grid connected to island mode transition and a dynamic output feedback compensator design is proposed for resynchronisation. The performance of the output feedback controllers is tested under various operating conditions and found to be satisfactory for the tested conditions.

Structural Properties of a Class of Linear Hybrid Systems and Output Feedback Stabilization

In this paper, we deal with the problem of output feedback stabilization for a class of linear hybrid systems. This problem is addressed by characterizing the structural properties of such a class of systems. Namely, reachability, controllability, stabilizability, observability, constructibility, and detectability are framed in terms of algebraic and geometric conditions on the data of the system. Two canonical forms, recalling the classical Kalman decompositions with respect to reachability and observability, are given. By taking advantage of this characterization, duality between control and observation structural properties is established and necessary and sufficient conditions for the existence of a linear time-invariant output feedback compensator are stated. Compared with previous results, no assumption is needed on the plant about minimum phaseness, relative degree, or squareness.

Sensorless H∞ speed-tracking synthesis for surface-mount permanent magnet synchronous motor

In this paper, a sensorless speed tracking control is proposed for a surface-mount permanent magnet synchronous motor by using a nonlinear H∞-controller via stator currents measurements for feedback. An output feedback nonlinear H∞-controller was designed such that the undisturbed system is uniformly asymptotically stable around the desired speed reference, while also the effects of external vanishing and non-vanishing disturbances, noise, and input backlash were attenuated locally. The rotor position was calculated from the causal dynamic output feedback compensator and from the desired speed reference. The existence of the proper solutions of the perturbed differential Riccati equations ensures stabilizability and detectability of the control system. The efficiency of the proposed sensorless controller was supported by numerical simulations.