Constant Input Disturbance Research Articles

Design Principles for Perfect Adaptation in Biological Networks with Nonlinear Dynamics.

Establishing a mapping between the emergent biological properties and the repository of network structures has been of great relevance in systems and synthetic biology. Adaptation is one such biological property of paramount importance that promotes regulation in the presence of environmental disturbances. This paper presents a nonlinear systems theory-driven framework to identify the design principles for perfect adaptation with respect to external disturbances of arbitrary magnitude. Based on the prior information about the network, we frame precise mathematical conditions for adaptation using nonlinear systems theory. We first deduce the mathematical conditions for perfect adaptation for constant input disturbances. Subsequently, we translate these conditions to specific necessary structural requirements for adaptation in networks of small size and then extend to argue that there exist only two classes of architectures for a network of any size that can provide local adaptation in the entire state space, namely, incoherent feed-forward (IFF) structure and negative feedback loop with buffer node (NFB). The additional positiveness constraints further narrow the admissible set of network structures. This also aids in establishing the global asymptotic stability for the steady state given a constant input disturbance. The proposed method does not assume any explicit knowledge of the underlying rate kinetics, barring some minimal assumptions. Finally, we also discuss the infeasibility of certain IFF networks in providing adaptation in the presence of downstream connections. Moreover, we propose a generic and novel algorithm based on non-linear systems theory to unravel the design principles for global adaptation. Detailed and extensive simulation studies corroborate the theoretical findings.

Uncovering Disturbance Observer and Ultra-Local Plant Models in Series PI Controllers

The paper settles two major liabilities and asymmetries of the theory of automatic control to the design of simple system controllers. It shows the most frequently used series proportional integral (PI) controllers as disturbance reconstruction and compensation-based structures and solves their designs using two types of linear system models. Beginning with the example of a simple integrator controlled by a P controller, it shows that constant input disturbances can be reconstructed by evaluating steady state values of the controller output. Thereby, the nearly steady state controller output can be simply achieved by using a low-pass filter with a time constant significantly longer than the time constant of stabilized processes. This disturbance observer (DOB) functionality can be demonstrated as being kept by series PI controllers designed by the pole assignment method. The DOB design can also be extended to first-order systems with internal feedback. However, there, the reconstructed disturbances depend both on the controller and the plant output steady state values. Because this feature is missing in industrial PI controllers, it indicates their connections with simpler, ultra-local (integral) linear system models. The interpretation of PI controllers as DOB-based structures allows a systematic consistent classification of all existing disturbance compensation structures and simplifies their comparisons with other modern and postmodern DOB-based alternatives. Given the breadth of use, improved understanding of PI control functionality also represents an important step to their optimal implementation and to research of innovative modifications, as illustrated by facilitating the flexible use of the new functional capabilities offered by embedded controls. By enhancing “the birth” of new solutions, it is then possible to better satisfy the permanently growing requirements of practice.

Multivariable control based on incomplete models via feedback linearization and continuous‐time derivative estimation

AbstractModels of nonlinear dynamical systems are typically composed of unknown and known parts due to the existence of mismatch between the true nonlinear system dynamics and their models. This article presents a multivariable control strategy for nonlinear systems that deals explicitly with the existence of incomplete models in a data‐driven framework. The proposed strategy uses feedback linearization and continuous‐time estimation of the unknown derivatives to achieve satisfactory closed‐loop performance for fast sampling applications with simple tuning of design parameters in the absence of a fully known system model. It is shown that this strategy possesses useful steady‐state properties, such as elimination of steady‐state error and rejection of constant input disturbances without any integral term, and ensures exponential convergence to the setpoints. Another contribution of this article is the development of methods for quantitative analysis of the stability and performance of the control strategy in the continuous‐time case. The approach is illustrated via a simulated example of reactor control. The proposed control strategy is broadly applicable and simplifies control design significantly for a large variety of systems.

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.

An Improved Sliding-Mode Current Control of Induction Machine in Presence of Voltage Constraints

This article proposes a novel approach to design sliding-mode control (SMC) for an induction motor (IM) in the presence of operational constraints. Different from the traditional techniques in SMC, the proposed method assumes the existence of a constant input disturbance and incorporates it in the switching current control law. Effectively, this leads to integral action through disturbance estimation together with an antiwindup mechanism naturally occurring when the control signal reaches its operational limits. The finite-time convergence of the SMC law is established through a Lyapunov analysis. Experimental evaluations are performed on an industrial-sized IM, where the current dynamics of the motor are controlled using SMC, and a velocity proportional–integral (PI) controller is used for the outer-loop control system. Experimental results reveal that the proposed sliding-mode current control systems provide much improved closed-loop control performance over the traditional SMC system. Further comparative experimental studies with well-designed PI current controllers provide insight into the characteristics of the proposed current control systems.

Adaptive feedback linearization control for twin rotor multiple-input multiple-output system

This paper deals with the tracking problem of a twin rotor multiple-input multiple-output system (TRMS) described by an Euler-Lagrange forced model with constant uncertain parameters and input disturbances. The control of TRMS system is the benchmark problem for control of helicopter which has been a challenging problem due to flexible dynamics, nonlinearities and cross coupling. The control objective is to make this systems track to the given trajectories accurately in spite of the influences of uncertainties and input disturbances. We propose the adaptive feedback linearization controller by using 03 adaptive parameters that stand for the unknown mass parameters of parts in the TRMS. By choosing appropriately controller parameters, the effects of the input disturbances that are friction, cable, gyro moments and the effects caused by the main propeller speed and the tail propeller speed on the vertical and horizontal movements to the yaw and pitch angles will be attenuated. Two functions, including unknown mass parameter adaption and the disturbances attenuation to guarantee the errors of the pitch and yaw angles, are implemented simultaneously by the adaptive feedback linearization controller. The simulation and experimental results show that the good robustness of the TRMS controlled by the proposed controller can be obtained arbitrarily.

Disturbance rejection in formation keeping control of nonholonomic wheeled robots

This paper presents the results of formation keeping control of a group of nonholonomic wheeled robots within the port-Hamiltonian framework and in the presence of matched input disturbances. Two scenarios on the internal damping of the dynamics of the robots are considered: strictly output passive and loss less robots. For strictly output passive robots, the distributed formation keeping controllers drive the robots towards a desired formation, while internal-model-based controllers locally compensate the harmonic input disturbance for each of the robots. Moreover, the effect of constant input disturbances is studied considering internal-model-based controllers. For lossless robots, results on formation keeping control are presented. Simulation results illustrate the effectiveness of the approach. Copyright (c) 2016 John Wiley & Sons, Ltd.

Stabilization of Discrete-Time Linear Systems With Quantization and Noise Input

In this paper, our main concern is the problem of stabilization of discrete-time linear systems with both quantization and noise input. Stabilizability by means of quantizers that perform adaptations called “zooming” is analyzed. The noise input can be separated into an additive white noise part and a deterministic constant input disturbance. The analysis of mean-square stability of the system with noise input is essentially the asymptotic stability of the system disturbed by a constant input. It is shown that the system with the constant input disturbance is asymptotically stabilized by the quantized feedback control policy if the system without noise input can be stabilized by a linear state feedback law. Both the state quantization and the input quantization are studied.

Robust integral control of port-Hamiltonian systems: The case of non-passive outputs with unmatched disturbances

Regulation of passive outputs of nonlinear systems can be easily achieved with an integral control (IC). In many applications, however, the signal of interest is not a passive output and ensuring its regulation remains an open problem. Also, IC of passive systems rejects constant input disturbances, but no similar property can be ensured if the disturbance is not matched. In this paper we address the aforementioned problems and propose a procedure to design robust ICs for port-Hamiltonian models, that characterize the behavior of a large class of physical systems. Necessary and sufficient conditions for the solvability of the problem, in terms of some rank and controllability properties of the linearized system, are provided. For a class of fully actuated mechanical systems, a globally asymptotically stabilizing solution is given. Simulations of the classical pendulum system illustrate the good performance of the scheme.

Conditions on input disturbance suppression for multivariable nonlinear systems on the basis of feedforward passivity

In this paper, we consider the problem of input disturbance suppression for nonlinear systems based on feedforward passivity. First, we show that integral control can sufficiently suppress a class of slowly variant (including constant) input disturbance and track constant references provided certain closed-loop stability is achieved. Then, sufficient conditions of integral controllability for nonlinear processes are presented. These conditions are further relaxed by using an input and output transformation.

NOISE TOLERANT IDENTIFICATION OF CONTINUOUS-TIME SYSTEMS WITH UNKNOWN CONSTANT INPUT DISTURBANCE USING ILC METHOD

This paper considers the problem of noise tolerant identification of a class of continuous-time systems with unknown constant-input disturbance. To this aim, we first propose an extended formulation of identification method using iterative learning control (ILC) scheme based on sampled I/O data in the presence of measurement noise. The proposed ILC method has distinctive features as follows. Its learning law works in the prescribed finite dimensional parameter space and employs I/O data of all past trials efficiently. Also the time-derivative of tracking error is not required. Then, it is presented how the parameter estimation can be achieved by the proposed ILC method and how robust it is against measurement noise through numerical examples.

Adaptive exponential stabilization of mobile robots with unknown constant‐input disturbance

AbstractThis paper concentrates on the discussions on stabilization of mobile robots with unknown constant‐input disturbance. Continuous time‐varying adaptive controllers are designed for mobile robots in a chain‐form by using Lyapunov approach. With the property of homogeneous systems, uncertain mobile robots governed by the proposed control algorithms become homogeneous of order 0 to achieve exponential stability. Simulation results validate the theoretical analysis. © 2001 John Wiley & Sons, Inc.

Remarks on "Robustness analysis of nonlinear feedback systems: an input-output approach"

In our previous paper (1999) Sec. VII contains two examples of adaptive controllers (Examples 8 and 9) for which the nonlinear gap robustness margin is zero and which are destabilized by arbitrarily small perturbations in the gap metric. The proof that the robustness margin is zero makes use of the fact that the parameter estimate /spl Theta/(t) tends to infinity as t/spl rarr//spl infin/ when there is a constant input disturbance of size /spl epsi/>0. The purpose of this present note is: a) to complete the argument given in the above paper to prove the unboundedness of /spl Theta/(t) and b) to give an alternative proof that the convergence of the state x(t)/spl rarr/0 is a consequence of the unboundedness of /spl Theta/(t) in Example 9.

Nonlinear adaptive controller with integral action

This note reveals a new significant property of the adaptive controller design technique proposed by Krstic, Kanellakopoulos and Kokotovic (1994). Namely, it is shown that with the use of special plant model parametrization the standard backstepping design results in an adaptive controller with integral action. The latter means that the controller completely rejects constant input disturbances. It is shown that the revealed property can be extended to nonlinear and nonadaptive cases.

Nonlinear tracking and input disturbance rejection with application to pH control

This paper presents a nonlinear observer-based controller configuration for a class of nonlinear single-input single-output systems with certain observability and stability properties. Particular attention is paid to the effect of input disturbances typically present in chemical processes. It is pointed out that conventional feedback linearizing internal model controllers reject output disturbances linearly, but that they can experience significant performance degradation in the presence of input disturbances. This problem is shown to originate in the lack of the linear superposition property. It is proven that the proposed control architecture rejects constant input disturbances from the control signal and then recovers linear reference tracking. The convenient tuning and improved performance are illustrated for pH neutralization.

Errors in state variable reconstruction when an observer is subject to constant input disturbances and measurement noise

The effect of constant input disturbances and measurement noise when an observer is used to reconstruct the state variable is investigated and an expression is derived for the steady-state error in the reconstructed state variable. A simple illustrative example is included.