Class Of Disturbances Research Articles

Robust parameter estimation for hybrid dynamical systems with linear parametric uncertainty

We consider the problem of estimating a vector of unknown constant parameters for a class of hybrid dynamical systems – that is, systems whose state variables exhibit both continuous (flow) and discrete (jump) evolution – with dynamics that depend linearly on the unknown parameters. Using a hybrid systems framework, we propose a hybrid estimation algorithm that can operate during both flows and jumps that, under a notion of hybrid persistence of excitation, guarantees convergence of the parameter estimate to the true value. Furthermore, we show that the parameter estimate is input-to-state stable with respect to a class of hybrid disturbances. Simulation results including a spacecraft application show the merits of our proposed approach.

A Suboptimal Economic Model Predictive Control Algorithm for Large and Infrequent Disturbances

We present a suboptimal economic model predictive control (MPC) algorithm that combines the strengths of two common suboptimal MPC approaches, one based on a warm start and one based on an optimality gap. This algorithm is specifically designed to address a class of large and infrequent disturbances that are relevant when considering discrete actuators and production scheduling in control problems. We establish that this algorithm provides the same nominal performance guarantee as optimal economic MPC and is inherently robust, in an economic context, to large and infrequent disturbances. This inherent robustness guarantee is not attained by either individual algorithm. We conclude with a small production scheduling example to demonstrate the benefits of the proposed algorithm for a practical application.

Generalized homogeneous control with integral action

AbstractA generalized homogeneous control with integral action for a multiple‐input plant operating under uncertainty conditions is designed. The stability analysis is essentially based on a special version of the nonsmooth Lyapunov function theorem for differential equations with discontinuous right‐hand sides. A Lyapunov function for analysis of the closed‐loop system is presented. For negative homogeneity degree, this Lyapunov function becomes a strict Lyapunov function allowing an advanced analysis to be provided. In particular, the maximum control magnitude and the settling‐time of the closed‐loop system are estimated and a class of disturbances to be rejected by the control law is characterized. The control parameters are tuned by solving a system of Linear Matrix Inequalities (LMIs), whose feasibility is proved at least for small (close to zero) homogeneity degrees. The theoretical results are illustrated by numerical simulations.

Adaptive Control on SE(3) for Spacecraft Pose Tracking With Harmonic Disturbance and Input Saturation

This article investigates the coupled attitude and orbit tracking maneuver control problem of a spacecraft system in close space missions with model uncertainty, unknown disturbance, and input saturation. An adaptive compact control scheme with featuring of disturbance rejection and antiwindup is reported. First, the exponential coordinates on Lie group SE(3) are employed to describe the relative pose, which includes the relative position and attitude, and the tracking error system is established by introducing an instrumental error variable, which contains exponential coordinates and velocity tracking error. Then, a dynamic disturbance compensator is constructed based on the idea of internal model design to finely compensate for a class of unknown harmonic disturbances. Furthermore, a nonsingular auxiliary system is proposed to overcome input saturation, in which a time-varying parameter is introduced to improve the performance of the antiwindup auxiliary system. This parameter makes the closed-loop system possess two properties: the timeliness of saturation compensation and the asymptotic convergence of tracking errors. With the developed control law, the stability of the obtained feedback system is strictly proved by means of Lyapunov stability theory. Finally, the numerical simulation is carried out for an on-orbit servicing mission, which validates the effectiveness of the proposed integrated controller in solving the pose tracking control problem.

Inherent Stochastic Robustness of Model Predictive Control to Large and Infrequent Disturbances

We introduce a new class of large, infrequent disturbances to complement the small, persistent disturbances typically considered in robustness analysis. This new class of disturbances includes discrete disturbances that become pertinent when considering discrete actuators and production scheduling in control problems. To properly account for the infrequent nature of these disturbances, we define a stochastic form of robustness. Under suitable assumptions, we prove that certain closed-loop systems subject to large, infrequent disturbances admit an SISS-Lyapunov function and are robust in this stochastic context. We apply these results to economic model predictive control (MPC) with a strictly dissipative nominal system and stage cost, which includes tracking MPC as a special case, and prove that economic MPC is robust to large, infrequent disturbances. Without dissipativity assumptions, we define and establish robust asymptotic performance for economic MPC. We present a simple tracking problem to illustrate the results of this work, and a production scheduling (economic MPC) problem, to demonstrate the relevance of this analysis to practical applications.

Output regulation for 1-D reaction-diffusion equation with a class of time-varying disturbances from exosystem

In this paper, we consider boundary output regulation for one-dimensional reaction–diffusion equation that has disturbances entering the system from in-domain and both boundaries. The reference signal and disturbances are generated from an exosystem with time varying coefficients. First, a feedforward control is designed on the basis of an infinite-dimensional regulator equation and a backstepping transformation. Second, with the measurement output, we design an observer to estimate both states of the plant and the external system. The output feedback boundary control is then designed by replacing the states with their estimates. As a result, we show that the output converges to the reference signal exponentially as time goes on.

Extended LQG/LTR design of disturbance cancelation controllers for a class of output disturbances

AbstractThis study develops an optimal design of the disturbance cancelation controllers for the output disturbances consisting of step, ramp and/or sinusoidal signals. A disturbance model with a particular structure is utilized to handle the three types of disturbance signals in a unified manner. A new quadratic performance index is introduced for the deviation from steady‐state behavior of the plant with disturbance. An optimal full‐state feedback control to minimize the new performance index is obtained by the parametric LQ approach with the aid of the explicit solution of related eigenstructure assignment problem. Additionally, an optimal output feedback controller of linear quadratic Gaussian (LQG) type is constructed using Kalman filter to estimate the plant and disturbance state variables. The classical LQG/LTR procedure is extended to achieve a systematic two‐step design of optimal disturbance cancelation controllers. A numerical design example is presented to illustrate the flexibility of the proposed design procedure.

Energy shaping dynamic tube-MPC for underactuated mechanical systems

This work investigates the tracking control problem for underactuated mechanical systems. To this end, we develop an extension of the dynamic tube Model Predictive Control (MPC) approach by combining an MPC design, an ancillary energy shaping controller constructed with the Interconnection and Damping Assignment Passivity-Based Control methodology, and an analytical expression of the dynamic tube. In addition, we extend the proposed approach by including the adaptive compensation of a class of unknown disturbances. The stability analysis is presented by employing a Lyapunov approach. The effectiveness of the proposed controller is demonstrated with simulations on two underactuated systems: a two-mass-spring-damper system with uncertain damping and either linear or nonlinear spring; an inertia-wheel-pendulum with unmodeled disturbances.

Robust Control for an Active Suspension System via Continuous Sliding-Mode Controllers

In this paper, a simple control methodology is proposed to stabilize the position of the sprung mass of the quarter car system. The simplicity of the structure of the proposal facilitates the application in real systems. Such methodology allows five different continuous sliding-mode controllers to be selected by means of two similar designs to mitigate the chattering effect. These robust controllers ensure the exponential stability of the sprung mass of a quarter car system in the presence of some class of non-vanishing disturbances. The closed-loop stability is guaranteed by means of a Lyapunov function approach and Input-to-State Stability properties. Some simulations and comparisons show the effectiveness of the proposed control schemes compared to a classic linear approach. Additionally, some experimental results show the effectiveness of the proposed controllers in the Quanser Active Suspension System.

Fuzzy Adaptive Observer-Based Fault and Disturbance Reconstructions for T-S Fuzzy Systems

This brief focuses on the observer-based state, fault and disturbance reconstructions for Takagi-Sugeno (T-S) fuzzy-approximation-based nonlinear dynamics subject to an enlarged class of disturbances and abrupt actuator fault. By developing a brand-new fuzzy adaptive observer (FAO), unknown system state, fault and disturbance can be reconstructed simultaneously, where some classic assumptions imposed on the disturbance such as the first-order derivative being equal to zero or generation from an exogenous system are removed successfully in our work. Significantly, to reduce the conservatism, the stability criterion of error dynamic is inferred in terms of using fuzzy Lyapunov functions, and expressed in a linear matrix inequality (LMI) framework. At last, simulation study on a real plant is provided to illustrate the practicability of the given procedure.

Robustness of Model Predictive Control to (Large) Discrete Disturbances

Abstract In recent years, theoretical results for model predictive control (MPC) have been expanded to address discrete actuators (decisions) and high-level planning and scheduling problems. The application of MPC-style methods to scheduling problems has been driven, in part, by the robustness afforded by feedback. The ability of MPC, and feedback methods in general, to reject small persistent disturbances is well-recognized. In many planning and scheduling applications, however, we must also consider an additional class of discrete and infrequent disturbances, such as breakdowns and unplanned maintenance. In this paper, we establish that nominal MPC is robust, in a stochastic context, to this class of discrete and infrequent disturbances. We illustrate these results with a nonlinear blending example.

Theories for design and analysis of robust [formula omitted] fault detectors

This paper deals with model-based fault detection and isolation problems, for linear time invariant systems subject to a large class of uncertainties and disturbances. A new approach based on non-smooth optimization techniques, is proposed to synthesize a state–space realization of the fault detection filter, within the H∞/H− setting. A set of new criteria for robust fault detection performance analysis is too proposed, using the generalized structured singular value theory. The proposed theories are illustrated on a satellite example, under a large class of nonlinear dependent uncertainties. Through a deep analysis of the example, it is shown how the H∞/H− design – μg analysis tools can serve as a general theory, to solve fault detection problems.

Sliding Mode Control of a Distributed-Parameter Wafer Spin Clean Process

In this study, a temperature controller for chemical fluids, which are impinged on a rotating silicon wafer, is presented. The chemical fluid is heated by a heating plate that is mounted below the rotating wafer. The thermal behavior of the system is modeled as a distributed-parameter system. In order to deal with this problem setting, a second-order sliding mode controller is proposed. The controller is inspired by the finite-dimensional generalized super-twisting algorithm. Finite-time convergence despite the presence of a certain class of disturbances is proven by means of a Lyapunov function. The algorithm is implemented and tested on the real system.

Attitude Coordination Control for Spacecraft With Disturbances and Event-Triggered Communication

In this article, a novel distributed attitude coordination control scheme is proposed for a group of rigid spacecraft with unknown disturbances. The communication topology is described by a general directed graph, and the leader's attitude is available to only a small fraction of followers. Different from existing attitude coordination control schemes, here an event-triggered communication strategy without Zeno phenomenon is designed, which avoids continuous communication between neighboring spacecraft and considerably reduces the communication burden. Moreover, a nonlinear observer is constructed for each follower, which enables us to estimate and compensate for a large class of disturbances exactly. The proposed scheme is able to ensure the boundedness of all closed-loop signals and steer the attitude tracking errors into an arbitrarily small residual set, regardless of the intermittent communication. Simulation results illustrate the effectiveness of the proposed scheme.

Nonlinear disturbance observer based geometric control of quadrotors

AbstractThis paper proposes a nonlinear disturbance observer based controller (NDOBC) for quadrotors utilizing the rotation matrices for attitude dynamics. The proposed observer does not make the assumption that the disturbance is constant or its upper bound is known. The only assumptions are that the disturbance and its derivatives are bounded and hence can handle constant disturbance as a special case. The proposed disturbance observer can handle large class of disturbances and the NDOBC is shown to be locally input to state stable with respect to the derivatives of the disturbances present in attitude dynamics as well as translational dynamics. The proposed controller as well as the nonlinear disturbance observer has been formulated on the nonlinear manifold SE(3) where the rotational dynamics evolve on SO(3) while the translational dynamics evolve on . Simulation results as well as implementation on a hardware setup establish the effectiveness of the proposed NDOBC.

Robust output feedback stabilization for two heterodirectional linear coupled hyperbolic PDEs

We solve in this article the problem of robust output feedback regulation for a system composed of two hyperbolic equations with collocated input and output in presence of a general class of disturbances and noise. Importantly, the robustness of the controller is considered with respect to delays in the actuation and in the measurements but also with respect to uncertainties on parameters, most importantly transport velocities. The proposed control law introduces three degrees of freedom (by means of tuning parameters) on which we give general conditions to guarantee the existence of robustness margins. We show that to tune these degrees of freedom and allow potential robustness trade-offs, it is necessary to consider all the different types of uncertainties simultaneously as it is the only way to ensure the existence of non-zero robustness margins. Provided that these conditions are satisfied, these tuning parameters enable a trade-off between performance and robustness, between disturbance rejection and sensitivity to noise. The existence of robustness margins and the Input To State Stability of the system are proved combining backstepping transformations and classical complex analysis techniques.

Impact of inductive current transformers on synchrophasor measurement in presence of modulations

Instrument Transformers (ITs) are essential devices for all the measurement tasks, f.i. metering, protection and diagnostics, in electricity grids, since they scale voltage and current down to levels compatible with measuring instruments. At the input of Power Quality (PQ) instruments and Phasor Measurement Units (PMUs), inductive voltage and current transformers (VTs and CTs) are still the most used ITs, even if, their performance in presence of disturbances is not fully assessed. This paper analyses the impact of the inductive CTs on the measurement of fundamental synchrophasors, by a PMU, in presence of a particular class of disturbances, the undesired modulations on current signals. Experimental tests, on two different CTs, show that there are critical situations, where, even compensating CT systematic ratio and phase errors, 1) CT exceeds its accuracy class limit and 2) considering the sole contribution of CT, PMU performance stays very close to the error limits of the standards.

Walking With Hand Motion/Force Control and CoM/VRP and Trunk Compliance for Disturbance Accommodation

Walking control along preplanned footholds is ensured with the well-known DCM/VRP stabilization approach. To accommodate an external disturbance, the proposed walking controller uses CoM/VRP compliance, i.e. modification of the original DCM trajectories in accordance with the measured/estimated disturbance. The disturbance can also be accommodated with the compliance in the trunk. The class of disturbances considered does not require the re-planning of the footholds. While walking, the hand(s) are allowed to contact the environment for postural robustness and/or to perform a desired hand motion/force control task, such as surface polishing or cleaning. The resulting hand reaction wrenches are also accommodated with the CoM/VRP compliance. Angular momentum damping with arm swinging can be employed to increase the robustness at the feet contacts. The proposed controller is quite efficient from the computational point of view since it does not involve a general iterative solver. It is shown via simulations that the robot is able to walk dynamically in a stable way, undisturbed by the external perturbations and the hand reaction wrenches.

Stubborn State Estimation for Delayed Neural Networks Using Saturating Output Errors.

This paper is concerned with the stubborn state estimation of delayed neural networks that subject to a general class of disturbances in measurements, including outliers and impulsive disturbances as its special cases. This class of disturbances may be unbounded, irregular, and assorted; therefore, they can hardly be suppressed by existing identification-based estimation approaches. In this paper, a stubborn state estimator is constructed by intentionally devising a saturation scheme on the injection of output estimation error. The embedded saturation can effectively resist the influences from these measurement disturbances by saturating them. Moreover, the saturation threshold in the designed scheme is not constant but governed by a dynamic equation with parameters to be designed. Benefiting from this adaptiveness, the estimator obtains more freedom in dealing with various disturbances. By combining a novel Lyapunov functional, the generalized sector condition and two latest integral inequalities, a delay-dependent criterion is derived in a less conservative way to check whether the estimation error system with this dynamic saturation is globally stable. A sufficient condition with two tuning scalars is further provided to codesign the gain of the state estimator and the evolution law of the saturation threshold. Finally, two numerical examples are used to illustrate the stubbornness of this state estimator in the presence of measurement outliers or impulsive disturbances.

Prediction‐based sliding mode control of non‐linear systems with input delay using disturbance observer

In this study, stabilisation of input-delay non-linear systems in the presence of disturbance based on prediction variable is studied. For both disturbance estimation and delay compensation, an extended prediction variable as well as adaptive sliding mode controller are proposed in which the open-loop system is not required to be stable. In the proposed prediction variable one needs to estimate disturbance in the future. In order to solve this problem a new non-linear disturbance observer (NDOB) is proposed. Considering the NDOB in the closed-loop system, the stability analysis of error dynamic is performed. And the asymptotic stability of non-linear system with input delay is guaranteed for some class of disturbance. Simulation results finally validate the good performance and robustness of the proposed controller based on disturbance observer.