Linear Feedback Systems Research Articles

Indirect adaptive fuzzy prescribed performance control of feedback linearisable MIMO non‐linear systems with unknown control direction

An indirect adaptive fuzzy prescribed performance control scheme is developed for a class of uncertain multi-input and multi-output feedback linearisable non-linear systems with unknown control direction and external disturbances. The properties of symmetric matrix and hyperbolic tangent function are exploited and the predefined tracking performance boundary is used to design the adaptive fuzzy prescribed performance controller, which can avoid the possible singularity problem and calculating the inverse of matrix. A robust controller equipped with a Nussbaum-type function is constructed to compensate for the lumped errors and solve the unknown control direction problem. The proposed scheme guarantees that all the signals in the resulting closed-loop system are bounded and that the tracking errors converge to a small residual set with the prescribed performance bounds. Simulation results are used to demonstrate the effectiveness of the proposed approach.

Contraction-based stabilisation of nonlinear singularly perturbed systems and application to high gain feedback

ABSTRACTRecent development of contraction theory-based analysis has opened the door for inspecting differential behaviour of singularly perturbed systems. In this paper, a contraction theory-based framework is proposed for stabilisation of singularly perturbed systems. The primary objective is to design a feedback controller to achieve bounded tracking error for both standard and non-standard singularly perturbed systems. This framework provides relaxation over traditional quadratic Lyapunov-based method as there is no need to satisfy interconnection conditions during controller design algorithm. Moreover, the stability bound does not depend on smallness of singularly perturbed parameter and robust to additive bounded uncertainties. Combined with high gain scaling, the proposed technique is shown to assure contraction of approximate feedback linearisable systems. These findings extend the class of nonlinear systems which can be made contracting.

Prescribed-performance fault-tolerant control for feedback linearisable systems with an aircraft application

ABSTRACTThis paper investigates fault-tolerant control (FTC) for feedback linearisable systems (FLSs) and its application to an aircraft. To ensure desired transient and steady-state behaviours of the tracking error under actuator faults, the dynamic effect caused by the actuator failures on the error dynamics of a transformed model is analysed, and three control strategies are designed. The first FTC strategy is proposed as a robust controller, which relies on the explicit information about several parameters of the actuator faults. To eliminate the need for these parameters and the input chattering phenomenon, the robust control law is later combined with the adaptive technique to generate the adaptive FTC law. Next, the adaptive control law is further improved to achieve the prescribed performance under more severe input disturbance. Finally, the proposed control laws are applied to an air-breathing hypersonic vehicle (AHV) subject to actuator failures, which confirms the effectiveness of the proposed strategies.

RETRACTED: Characteristics of recursive backstepping algorithm and active damping of oscillations in feedback linearization for electromechanical system with extended stability analysis and perturbation rejection

In this paper, a technique for estimation of state variables and control of a class of electromechanical system is proposed. Initially, an attempt is made on rudimentary pole placement technique for the control of rotor position and angular velocity profiles of Permanent Magnet Stepper Motor. Later, an alternative approach is analyzed using feedback linearization method to reduce the error in tracking performances. A damping control scheme was additionally incorporated into the feedback linearization system in order to nullify the persistent oscillations present in the system. Furthermore, a robust backstepping controller with high efficacy is put forth to enhance the overall performance and to carry out disturbance rejection. The predominant advantage of this control technique is that it does not require the DQ Transformation of the motor dynamics. A Lyapunov candidate was employed to ensure global asymptotical stability criterion. Also, a nonlinear observer is presented to estimate the unknown states namely load torque and rotor angular velocity, even under load uncertainty conditions. Finally, the performances of all the aforementioned control schemes and estimation techniques are compared and analyzed extensively through simulation.

Development of flank wear model of cutting tool by using adaptive feedback linear control system on machining AISI D2 steel and AISI 4340 steel

The purpose of this paper is to build an adaptive feedback linear control system to check the variation of cutting force signal to improve the tool life. The paper discusses the use of transfer function approach in improving the mathematical modelling and adaptively controlling the process dynamics of the turning operation. The experimental results shows to be in agreement with the simulation model and error obtained is less than 3%. The state space approach model used in this paper successfully check the adequacy of the control system through controllability and observability test matrix and can be transferred from one state to another by appropriate input control in a finite time. The proposed system can be implemented to other machining process under varying range of cutting conditions to improve the efficiency and observability of the system.

Dynamic Surface Control for a Class of Nonlinear Feedback Linearizable Systems With Actuator Failures.

In this brief, we propose a dynamic surface control with actuator failure compensation for a class of feedback linearizable systems with locally Lipschitz nonlinearities. First, a dynamic surface state feedback control scheme is designed, which incorporates radial basis function networks in a novel approach, to compensate system uncertainties and dynamic changes induced by actuator failures. Then, an output feedback controller is obtained by means of high-gain observers. It is proved that our control schemes guarantee the uniform ultimate boundedness of the system, and that the output tracking error converges to an arbitrarily small residual set. Finally, a simulation is carried out to illustrate the performance of the designed control schemes.

Spectrum of Monodromy Operator for a Time-Delay System With Application to Stability Analysis

This note studies the spectral properties of monodromy operators, which play an important role in stability analysis of linear time-invariant time-delay feedback systems. The note is motivated by the fact that this operator can actually be defined naturally on four spaces, where the difference stems from different choices for the function space on which the infinite-dimensional state of such a time-delay system is assumed to take its value. It is first shown that the spectrum of the monodromy operator is independent of the spaces on which it is defined. This implies that stability of time-delay systems is independent of the underlying function spaces. It is further shown that the operator spectrum is continuous at monodromy operators, which justifies the spectrum computation of the monodromy operator through its approximation by any sort of tractable operators. A numerical study relevant to the theoretical development is provided and a practical implication of our theoretical study is suggested.

Adaptive Control Augmentation for the Longitudinal Dynamics of a Hypersonic Glider

The descent longitudinal trajectory control methodology of a hypersonic glider to carry out a pullup maneuver is presented. A dynamic pole placement controller is implemented as the baseline controller. The baseline controller is augmented with an adaptive controller to cancel out the matched and unmatched uncertainties. The differences between the pole placement and the augmented pole placement controller are presented in terms of performance with the help of Monte Carlo simulations. The dynamic pole placement controller is shown to have robustness in the presence of time-invariant and time-varying errors in the aerodynamic coefficients, control surface, and gravimetric uncertainties. The augmented controller improves the performance of the baseline controller in the presence of these uncertainties. This is concluded with a reduction in the tracking error norm and the control surface norm, which is the energy of the deviation between the reference and real control signal; . The use of the adaptive controller, however, reduces the time delay margin of the system. The contribution of this paper lies in the application and determination of the performance of a piecewise constant adaptive augmentation setup to a nonminimum phase linear time-varying state feedback system.

A New Measure To Improve the Reliability of Stiction Detection Techniques

A variety of methods have been developed to identify the presence of stiction in linear closed-loop systems. One of the commonly used approaches is based on identification of a Hammerstein model (linear dynamic model preceded by static nonlinear element) between the controller output and process output. These techniques utilize the fact that control valve stiction introduces nonlinearities in the otherwise linear feedback system. However, the present work shows that these techniques could provide ambiguous results depending on the frequency response of the controller and the process of interest. Therefore, in this work, a reliability measure to validate the results from Hammerstein model-based stiction detection approaches is proposed. This measure of reliability is important from an industrial perspective because (i) it helps in reducing false alarms and (ii) it improves the computational speed by guiding the selection of search space in the linear model identification step. The applicability of this rel...

Minimization of the least upper bound of the real parts of quasipolynomial roots and the limit stability degree of linear dynamic feedback system

For the class of quasipolynomials that are characteristic for the mathematical models of the industrial control systems, the upper estimate of the degree of stability was established and shown to correspond to the multiple real root of the characteristic system equation; the reachability conditions for this upper estimate were established.

K-dimensional invariant cones of random dynamical systems in [formula omitted] with applications

We investigated a linear random dynamical system which strongly preserves a cone C of dimension-k (abbr. k-cone) in Rn. Under some general assumptions, it is shown that such system admits a measurable family of k-dimensional subspaces and a measurable family of (n−k)-dimensional subspaces which are complementary to each other and form into a tempered invariant splitting of Rn. We further apply the measurable bundles so obtained to study the linear random monotone cyclic feedback systems, as well as the linear competitive–cooperative tridiagonal systems. This generalizes the Floquet theory for these deterministic non-autonomous (or time-periodic) systems to the random systems.

Peaking-Free Output-Feedback Adaptive Neural Control Under a Nonseparation Principle.

High-gain observers have been extensively applied to construct output-feedback adaptive neural control (ANC) for a class of feedback linearizable uncertain nonlinear systems under a nonlinear separation principle. Yet due to static-gain and linear properties, high-gain observers are usually subject to peaking responses and noise sensitivity. Existing adaptive neural network (NN) observers cannot effectively relax the limitations of high-gain observers. This paper presents an output-feedback indirect ANC strategy under a nonseparation principle, where a hybrid estimation scheme that integrates an adaptive NN observer with state variable filters is proposed to estimate plant states. By applying a single Lyapunov function candidate to the entire system, it is proved that the closed-loop system achieves practical asymptotic stability under a relatively low observer gain dominated by controller parameters. Our approach can completely avoid peaking responses without control saturation while keeping favourable noise rejection ability. Simulation results have shown effectiveness and superiority of this approach.

A simplified adaptive neural network prescribed performance controller for uncertain MIMO feedback linearizable systems.

In this paper, the problem of deriving a continuous, state-feedback controller for a class of multiinput multioutput feedback linearizable systems is considered with special emphasis on controller simplification and reduction of the overall design complexity with respect to the current state of the art. The proposed scheme achieves prescribed bounds on the transient and steady-state performance of the output tracking errors despite the uncertainty in system nonlinearities. Contrary to the current state of the art, however, only a single neural network is utilized to approximate a scalar function that partly incorporates the system nonlinearities. Furthermore, the loss of model controllability problem, typically introduced owing to approximation model singularities, is avoided without attaching additional complexity to the control or adaptive law. Simulations are performed to verify and clarify the theoretical findings.

An adaptive learning controller for MIMO uncertain feedback linearizable nonlinear systems

Most of available results in adaptive learning controllers (ALCs) with input learning technique have considered the single-input single-output nonlinear systems. This paper presents an ALC for MIMO uncertain feedback linearizable systems whose uncertainty is in their linear parameters. Since only an output signal is available for measurement, a high gain observer is used to estimate the unmeasurable state. The estimated state is then utilized to implement the ALC. The proposed ALC learns the input gain parameters of the state equation as well as the internal parameters. In addition, the desired input is also learned using an input learning rule to track the whole command history. In the proposed ALC, the tracking errors are bounded and the mean-square tracking error is \(O(\epsilon )\) as the task is repeated. Single-link and two-link manipulators are presented as simulation examples to confirm the feasibility and the performance of the proposed ALC.

Adaptive actuator failure compensation for multivariable feedback linearizable systems

SummaryA feedback linearization‐based adaptive control scheme is developed for multivariable nonlinear systems with redundant actuators subject to uncertain failures. Such an adaptive controller contains a direct adaptive actuator failure compensator to compensate the uncertain actuator failure, a nonlinear feedback to linearize the nonlinear dynamics, and a linear feedback to stabilize the linearized system. The key new design feature is the estimation of both the failure patterns and the failure values, for direct adaptive actuator failure compensation, newly developed for multivariable feedback linearizable nonlinear systems. With direct control signal adaptation, the adaptive failure compensation design ensures closed‐loop stability and asymptotic output tracking in the presence of actuator failure uncertainties. Simulation results from an application to attitude control of a near‐space vehicle dynamic model are presented to verify the desired system performance with adaptive actuator failure compensation. Copyright © 2015 John Wiley & Sons, Ltd.

A Study on Fire Power Performances of Combat Vehicles with Suspension Systems

When the combat vehicle runs on an off-road, the vertical displacement occurs. This vertical displacement variation affects fire power performance for a weapon system mounted on the combat vehicle. We focus on the hit probability which is one of the fire power performances. The combat vehicle is simulated with a quarter car system. We measure the vertical displacement using the quarter simulation model. The passive suspension system and the active suspension system with the use of the linear state feedback system are considered. The active suspension system with the feedback control has better performances for the hit probability than the passive suspension system has.

Remarks on a Triangular Form for 1-Flat Pfaffian Systems with Two Inputs

We consider 1-flat nonlinear control systems with two inputs and a given 1-flat output. The control systems are represented as Pfaffian systems. It is well-known that flat systems can be transformed to Brunovsky normal form after applying an endogenous dynamic feedback, and only for static feedback linearizable systems this transformation is possible without dynamic feedback. However, there exists a normal form, denoted as implicit triangular form, which is a generalization of the Brunovsky normal form, and even systems which are not static feedback linearizable might possibly be transformed to this normal form without applying a dynamic feedback. Given a two-input nonlinear control system and a fixed 1-flat output, we provide necessary and suficient conditions to check whether such a transformation exists. Furthermore, we provide an algorithm to find this transformation.

A Predictor Observer for Seeker Delay in the Missile Homing Loop

In this work, we employ a classical predictor observer for linear feedback systems to stabilize a well-known missile guidance law degraded by an optical seeker measurement delay in the near-collision course of a missile-target intercept engagement. In the framework of a canonical, planar intercept missile guidance problem, coupled with a delay in the measurement of the missile-to-target line-of-sight angle, we tailor the general formula for the predictor observer to the guidance law. We then use numerical simulations to evaluate the performance of the delaycompensated guidance law. The results indicate that for the scenario considered, the predictor observer is able to stabilize the guidance kinematics for realistic values of the measurement delay, thus encouraging further feasibility studies for using this approach in practice.

A Novel Dissipativity-Based Control for Inexact Nonlinearity Cancellation Problems

When dealing with linear systems feedback interconnected with memoryless nonlinearities, a natural control strategy is making the overall dynamics linear at first and then designing a linear controller for the remaining linear dynamics. By canceling the original nonlinearity via a first feedback loop, global linearization can be achieved. However, when the controller is not capable of exactly canceling the nonlinearity, such control strategy may provide unsatisfactory performance or even induce instability. Here, the interplay between accuracy of nonlinearity approximation, quality of state estimation, and robustness of linear controller is investigated and explicit conditions for stability are derived. An alternative controller design based on such conditions is proposed and its effectiveness is compared with standard methods on a benchmark system.

Inducing sustained oscillations in feedback-linearizable single-input nonlinear systems

The present paper concerns the induction of stable sustained oscillation in feedback-linearizable single-input affine nonlinear dynamical systems via continuous-time state feedback control. The proposed application-oriented control approach is based on the conception of a state feedback controller that ensures the tracking of a limit cycle characterized in terms of the feedback-linearized system. Boundedness and convergence of the closed-loop trajectories are established following the Lyapunov theoretical framework and applying LaSalle׳s stability principle. The proposed approach is demonstrated with computer-simulated control experiments, showing that it ensures the convergence of the state trajectories of the controlled system to a designed limit cycle and that the methodology can, in principle, be applied to any single input feedback linearizable system.