Unknown Constant Disturbances Research Articles

A Parametric Predictor for Disturbance Attenuation of Discrete-Time Linear Systems With Input Delays.

In this article, a parametric predictor is constructed to predict the future state of a discrete-time linear system with a known constant input delay and external disturbances by introducing a tuning parameter. Then, a predictor-based feedback controller is given to attenuate the unknown disturbance signal. The ultimate bound of the state of the resulted closed-loop system is obtained when the state feedback control law based on this novel predictor is utilized. Based on the expression of the ultimate bounds, the capacity to attenuate the unknown disturbance is analyzed for the parametric predictor within a certain range of parameters. An easily calculated interval is provided for the range of the tuning parameter such that the proposed predictor achieves a better disturbance attenuation capacity. Moreover, for the unknown constant disturbance, the estimation error between the proposed predictor with an arbitrary parameter and the future state can be eliminated. Finally, two numerical examples are utilized to illustrate the effectiveness of the proposed parametric predictor for bounded time-varying disturbances.

Global consensus-based formation control of perturbed nonholonomic mobile robots with time varying delays

This paper proposes a smooth time-variant PID-like control scheme for networks composed of nonholonomic vehicles modeled as differential drive robots affected by unknown input constant disturbances and transmission variable time-delays in the communication channel. Using Barbalat’s Lemma and under the fact that the interconnecting graph is undirected and connected, it is proved that all robots positions asymptotically converge to a position in a given desired formation and they all agree on the center of this formation, while the orientations asymptotically reach a consensus value. Besides, it is proved that given the structure of the proposed new integral action, the external constant disturbances are rejected (exactly estimated) and that velocities converge to zero. Simulation results, with a robot network composed of eight nonholonomic vehicles and considering disturbances subjected to step changes, are presented to illustrate the robustness of the proposed control scheme.

Event-based adaptive fuzzy tracking control for nonlinear systems with guaranteed performance

This article is concerned with the problem of event-based adaptive prescribed time tracking control for a class of uncertain strict-feedback nonlinear systems. To ensure that the considered system possesses the user-specified tracking performance, an improved error transformation is constructed and incorporated with a novel fixed-time performance function with an infinite initial value, completely removing the restriction that the tracking error is less than the pre-assigned performance boundary in the initial interval. Then, the utilization of command filtered technique and two single parameter estimators severally related to the upper bounds of fuzzy logic systems-based unknown constant parameters and external disturbances not only obviates the “explosion of complexity” issue but also simplifies the control design procedure. On this basis, by skillfully synthesizing adaptive technology and event-triggered mechanism within the framework of command filtered backstepping technique, a novel adaptive fuzzy event-triggered control solution is presented to save the limited network resources. Under the developed controller, the tracking error is steered to converge to an adjustable asymmetric region within a pre-specified time, and the boundedness of all closed-loop signals is ensured. Finally, simulation studies are performed to demonstrate the effectiveness and practicability of the developed control solution.

Robust Boundary Controller Design with Proportional Integral Observer for a Linear 1D Heat Equation*

The problem of state estimation with boundary disturbance reconstruction and output regulation for linear 1D parabolic systems with a boundary measurement and unknown constant disturbance input on the opposite boundary is addressed. As the disturbance is unmatched it cannot be directly compensated by the measurement. The problem is addressed with an approach that consists of a backstepping observer for the nominal part with an asymptotic compensation term for the disturbance reconstruction and control offset compensation. The main difference to similar studies relies in the fact that the state space does not need to be extended, leading to a reduced-order observer setup. The effectiveness of the approach is illustrated using numerical simulations.

Global Asymptotic Position and Heading Tracking for Multirotors Using Tuning Function-Based Adaptive Hybrid Feedback

This letter considers the problem of global asymptotic position and heading tracking for multirotors. We propose a hybrid adaptive feedback control law that globally asymptotically tracks a position and heading reference in the presence of unknown constant disturbances in both the translational and rotational dynamics. By employing a tuning function-based backstepping approach, the number of parameter estimates are minimized. Moreover, we propose a novel control law for the translational subsystem, which leads to a simpler virtual control law when backstepping. Global asymptotic heading tracking is achieved through a novel construction of the desired rotation matrix. The theory is verified through experiments on a quadrotor.

Global robust attitude tracking with torque disturbance rejection via dynamic hybrid feedback

In this paper an approach to the design of robust global attitude tracking controllers for fully actuated rigid bodies is proposed. The challenge of simultaneously dealing with topological obstructions to global attitude tracking and with disturbances affecting the attitude dynamics is tackled by means of a hybrid hierarchical design that exploits the cascade structure of the underlying mathematical model. The proposed hierarchical strategy is based on an inner–outer loop paradigm comprising a dynamic control law for angular velocity tracking (inner loop) and a hybrid control law for attitude tracking (outer loop). By leveraging recent tools for the stability analysis of hybrid systems, we prove a robust global tracking property by assuming mild properties on the dynamics of the velocity feedback. We also discuss a few relevant examples satisfying these properties, encompassing harmonic disturbance compensators and conditional integrators, capable of rejecting unknown constant disturbances with an intrinsic anti-windup action.

Sampled-Data Integral Control of Nonholonomic Systems With Unknown Constant Disturbances

This note studies the asymptotic regulation problem for a class of nonholonomic systems with unknown constant disturbances, where system nonlinearities admit a lower-triangular form. First, following a new state transformation, the considered systems with unknown constant disturbances are converted into a class of auxiliary systems without disturbances. Second, two sampled-data controllers are designed for the auxiliary systems by using the high-gain method. Third, it is shown that with the introduced state transformation, the desired sampled-data <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">integral</i> controllers are obtained to asymptotically regulate the considered systems. The proposed control strategy is applied to asymptotically regulate a unicycle type mobile robot model.

Linear-Convex Optimal Steady-State Control

We consider the problem of designing a feedback controller for a multivariable linear time-invariant system, which regulates a system output to the solution of an equality-constrained convex optimization problem despite unknown constant exogenous disturbances; we term this the linear-convex optimal steady-state (OSS) control problem. We introduce the notion of an optimality model, and show that the existence of an optimality model is sufficient to reduce the OSS control problem to a stabilization problem. This yields a design framework for OSS control that unifies and extends existing design methods in the literature. We illustrate the approach via an application to optimal frequency control of power networks, where our methodology recovers centralized and distributed controllers reported in the recent literature.

An adaptive speed observer for a class of nonlinear mechanical systems: Theory and experiments

We propose a solution to the problem of adaptive speed observer for a class of mechanical systems containing cross terms in the velocity (momenta). We focused our attention on mechanical systems with unknown constant input disturbances and Coulomb friction matrix, which generate products of unmeasurable velocities and unknown friction parameters. The adaptive speed observer proposed is based on the well-known Immersion and Invariance technique. We ensure global convergence of the speed observer, while the friction parameters estimation remain bounded. Our approach is validated through simulations and experimental results.

Tracking Controller Design for Satellite Attitude Under Unknown Constant Disturbance Using Stable Embedding

We propose a tracking control law for the fully actuated rigid body system in the presence of any unknown constant disturbance by employing quaternions with the stable embedding technique and Lyapunov stability theory. The stable embedding technique extends the attitude dynamics from the set of unit quaternions to the set of quaternions, which is a Euclidean space, such that the set of unit quaternions is an invariant set of the extended dynamics. Such a stable extension of the system dynamics to a Euclidean space allows us to employ well studied Lyapunov techniques in Euclidean spaces such as LaSalle–Yoshizawa’s theorem. A robust tracking control law is proposed for the attitude dynamics subject to unknown constant disturbance and the convergence properties of the tracking control law is rigorously proven. It is demonstrated with the help of numerical simulations that the proposed control law has a remarkable performance even in some challenging situations.

Local Proportional-Integral Boundary Feedback Stabilization for Quasilinear Hyperbolic Systems of Balance Laws

The proportional-integral (PI) boundary stabilization of nonlinear hyperbolic systems of balance laws is investigated for the $H^2$-norm, in which the control and output measurements are all located at the boundaries. The boundary conditions of the system are subject to unknown constant disturbances. The induced closed-loop system is proven to be locally exponentially stable with respect to the steady states. To this end, a set of matrix inequalities is given by constructing a new Lyapunov function as a weighted $H^2$-norm of the classical Cauchy solution and the integral of boundary output. Furthermore, the traffic flow dynamics of a freeway section are modeled with the Aw--Rascle--Zhang model. To stabilize the oscillations of traffic demand, a local PI boundary feedback controller is designed with integration of on-ramp metering and variable speed limit control. The exponential convergence of the nonlinear traffic flow dynamics in an $H^2$ sense is achieved and validated with simulations.

A Distributed Formation Control Scheme with Obstacle Avoidance for Multiagent Systems

This study considers the problem of formation control for second-order multiagent systems. We propose a distributed nonlinear formation controller where the control input of each follower can be expressed as a product of a nonlinear term that relies on the distance errors under the leader–follower structure. In the leader–follower structure, a small number of agents are assumed to be the leaders, and they are responsible for steering a group of agents to the specific destination, while the rest of the agents are called followers. The stability of the proposed control laws is demonstrated by utilizing the Lyapunov function candidate. To solve the obstacle avoidance problem, the artificial potential approach is employed, and the agents can avoid each possible obstacle successfully without getting stuck in any local minimum point. The control problem of multiagent systems in the presence of unknown constant disturbances is also considered. To attenuate such disturbances, the integral term is introduced, and the static error is eliminated through the proposed PI controller, which makes the system stable; the adaptive controller is designed to reduce the effect of time-varying disturbances. Finally, numerical simulation results are presented to support the obtained theoretical results.

Optimal regulation of flow networks with transient constraints

This paper investigates the control of flow networks, where the control objective is to regulate the measured output (e.g. storage levels) towards a desired value. We present a distributed controller that dynamically adjusts the inputs and flows, to achieve output regulation in the presence of unknown constant disturbances, while satisfying given input and flow constraints. Optimal coordination among the controllers minimizing a suitable cost function of the inputs at the nodes, is achieved by exchanging information over a communication network. Exploiting an incremental passivity property, the desired steady state is proven to be globally asymptotically attractive under the closed loop dynamics. Two case studies (a district heating system and a super-conducting DC network) show the effectiveness of the proposed solution.

Nonlinear Adaptive Control of Hydraulic System With Observing and Compensating Mismatching Uncertainties

Hydraulic servomechanism is the typical mechanical/hydraulic double-dynamics coupling system with heavy nonlinearity, parametric uncertainties, and mismatching uncertainties input problems. How to estimate and compensate mismatching uncertainties by observer is a very important issue. This paper proposes an extended-state-observer (ESO)-based nonlinear adaptive control scheme for the motion tracking control of the hydraulic valve-controlled single-rod actuator system. This paper provides a solution to estimate and compensate the mismatching disturbances, i.e., the mechanical dynamics uncertainties. With the developed method, both the hydraulic dynamics uncertainties and the mechanical dynamics uncertainties can be estimated and compensated effectively. Moreover, the parameters adaptive mechanism is also supplemented with ESO to further improve the tracking performance. The parametric uncertainties, modeling, and unknown external disturbances are comprehensively addressed. In theory, the asymptotic tracking can be achieved even in the presence of unknown external constant disturbances and parametric uncertainties. Besides giving the theoretical results and proof, the effectiveness of the proposed method is verified through extensive comparative experiments.

A Constructive Globally Convergent Adaptive Speed Observer For Port‐Hamiltonian Mechanical Systems with Non‐Holonomic Constraints

AbstractThis paper presents an adaptive speed observer for general port‐Hamiltonian mechanical systems with non‐holonomic constraints in the presence of unknown friction forces and constant disturbances. Unlike the observers recently reported in the literature, which have been designed either under the assumptions of no friction and the absence of disturbances or for a specific class of mechanical systems with the requirement of an explicit solution of certain Partial Differential Equations (PDEs) that cannot be derived a priori, this observer proposes a design that obviates the solution of PDEs and ensures global convergence for general mechanical systems with k‐non‐holonomic constraints. The observer is totally constructive and given by explicit expressions. The simulation results testify to the effectiveness and the robust features of the developed observer.

Adaptive high gain observer extension and its application to bioprocess monitoring

The adaptive version of the high gain observer for the strictly triangular systems subjected to constant unknown disturbances is proposed here. The adaptive feature is necessary due to the fact that the unknown disturbance enters in a way that cannot be suppressed by the high gain technique. The developed observers are then applied to a culture of microorganism in a bioreactor, namely, to the model of the continuous culture of Spirulina maxima. It is a common practice that just the biomass (or substrate) concentration is directly measured as the output of the process for monitoring and control purposes. This paper thereby shows both by theoretical analysis and numerical simulation that the adaptive high-gain observers offer a realistic option of online software sensors for substrate estimation.

Almost-Global Formation Tracking Control for Multiple Vehicles With Disturbance Rejection

This paper studies the anti-disturbance control scheme for multiple vehicles formation tracking a specified trajectory. By communicating connections, these vehicles form a vehicle network. The communication topology of the network is a directed acyclic graph. Each node vehicle is modeled as a fully actuated rigid body on SE(3)(a Special Euclidean group) with an unknown constant disturbance, except the root node, which is used to specify the trajectory to be tracked. By means of Euclidean group operation and the convex combination theory on Euclidean group, the problem is first converted to the leader-follower tracking control for two vehicles. Then, without using local coordinates, an almost-globally exponential anti-disturbance tracking control law with the knowledge of the leader’s acceleration is designed by using Lyapunov stability theory which achieves formation tracking a given trajectory. To overcome the difficulties in practical obtaining acceleration information of the vehicle being tracked, a dynamic acceleration estimator is designed by using singular perturbation method, thereafter the formation tracking control law based on the acceleration estimator is constructed. For demonstration of the result, some numerical examples have been included.

Design of Integral Controllers for Nonlinear Systems Governed by Scalar Hyperbolic Partial Differential Equations

The paper deals with the control and regulation by integral controllers forthe nonlinear systems governed by scalar quasi-linear hyperbolic partial differentialequations. Both the control input and the measured output are located on the boundary.The closed-loop stabilization of the linearized model with the designed integral controlleris proved first by using the method of spectral analysis and then by the Lyapunov directmethod. Based on the elaborated Lyapunov function we prove local exponential stabilityof the nonlinear closed-loop system with the same controller. The output regulationto the set-point with zero static error by the integral controller is shown uponthe nonlinear system. Numerical simulations by the Preissmann scheme are carriedout to validate the robustness performance of the designed controllerto face to unknown constant disturbances.

IMPLEMENTATION OF ROBUST COMPOSITE NONLINEAR FEEDBACK FOR ACTIVE FRONT STEERING BASED VEHICLE YAW STABILITY

In this paper, Robust Composite Nonlinear Feedback (CNF) was implemented on Active Front Steering (AFS) vehicle system for yaw stability control. In this control system, the main objective is to get excellent transient response of vehicle yaw rate and at the same time resist to side wind disturbance. To cater unknown constant disturbance, non-integral function for Robust CNF version is used. Meanwhile for vehicle model, 7 degree of freedom vehicle body with Pacejka Tire formula model for typical passenger car is used to simulate controlled vehicle. The computer simulation by Matlab software is performed to evaluate the system performance in J-Turn and Single sine steer with magnitude from 1 to 3.1 degree with additional 400 Nm external side wind disturbance. By using typical Proportional Integration and Derivative (PID) control auto-tuned by Matlab as comparison, the new designed controller demonstrates higher capability to track reference signal faster and having minimal tracking error during disturbance occur where having less than 0.01 degree compared 0.22 degree by PID. The Robust CNF based designed control system is able to compensate disturbance effect efficiently and also has super-fast tracking as classical CNF.

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.