Minimality of dynamic input-output decoupling for nonlinear systems

In this note we study the strong dynamic input-output decoupling problem for nonlinear systems. Using an algebraic theory for nonlinear control systems, we obtain for a dynamic input-output decouplable nonlinear system a compensator of minimal dimension that solves the decoupling problem.     

Nonlinear decoupling control of four-wheel-steering vehicles with an observer

This paper studies the input-output decoupling control for the nonlinear vehicle model consisting of three degrees of freedom. The technique of quasi-linearization is used to simplify the vehicle model, which preserves inherent coupling effects between longitudinal acceleration/braking force, steering angles and the vehicle states. By choosing the combined control inputs, the input-output map of the vehicle dynamical system is reconstructed. Based on the model, the input-output decoupling controller is proposed. Furthermore, an asymptotically stable observer is presented. A modified form of mean value theorem is used to design the observer for the nonlinear vehicle system with bounded Jacobian. The observer gain can be obtained by solving linear matrix inequalities (LMIs). Several simulations are carried out to show the improvements in vehicle handling and stability due to the inputoutput decoupling control.     

Input-output pseudolinearization on controlled invariant submanifolds

The original notion of input-output pseudolinearization on equilibrium submanifolds is extended to general controlled invariant submanifolds for nonlinear systems. Input-output pseudolinearizing feedback laws render the input-output behavior of linearizations about nominal trajectories in the submanifold trajectory-independent and equal to that of a fixed linear time-invariant system, thereby facilitating the subsequent construction of control laws for stabilization and tracking. Sufficient existence conditions are derived that are weaker than the familiar relative degree conditions for nonlinear input-output decoupling that have come to be associated with exact input-output linearization.     

具有时变时滞的不确定时滞系统的输入-输出能量解耦

提出一种针对具有时变时滞的范数有界不确定线性时滞系统的能量解耦方法,即从输入-输出的能量关系上实现解耦,使得任何一个输入的能量主要控制对应的一个输出的能量,对其它输出能量的影响尽可能小.所有结论均由线性矩阵不等式描述,求解非常方便.     

Input-output decoupling of Hamiltonian systems: The linear case

In this note we give necessary and sufficient conditions for a linear Hamiltonian system to be input-output decouplable by Hamiltonian feedback, i.e. feedback that preserves the Hamiltonian structure. In a second paper we treat the same problem for nonlinear Hamiltonian systems.     

Local input-output decoupling of discrete-time non-linear systems

A local treatment of the block input-output decoupling problem is given for discrete-time non-linear control systems. The major tools employed are the invariant and locally-controlled invariant distributions that have recently been extended to the discrete-time domain. A sufficient condition for the solvability of the problem with local stability about an equilibrium point is also given.     

Tuning of PI controllers with one-way decoupling in 2×2 MIMO systems based on finite frequency response data

A method of tuning for PI controllers with one-way lead/lag decoupling tuning is demonstrated for 2×2 input-output systems, based on finite frequency response data. The frequency response estimates are obtained from closed loop tests using an identification technique based on bandpass filters. The open-loop frequency response is calculated and used to tune PI controllers and to fit lead-lag compensators for decoupling by weighted least-squares. Separate optimization of the PI controllers and the lead-lag compensator is preferred. The tuning takes into account violations of desired multivariable robustness criteria. The method is illustrated by application to a paper machine headbox simulation and by experiments in distillation column temperature control.     

Input-output block decoupling of linear time-varying singularsystems

The input-output block decoupling problem by state feedback is studied for linear time-varying singular systems. First, an algorithm, the regularization algorithm, is developed such that the system can be made by state feedback to have a unique impulse-free solution. Second, another algorithm, the block decoupling algorithm, is proposed, which provides sufficient conditions for the solvability of the input-output block decoupling problem. Then, a decoupling feedback law is constructed such that the corresponding closed-loop system is regular, impulse-free, and noninteractive. Finally, an example is given to illustrate the applicability of the algorithms     

Canonical transformations used to derive robot control laws from a port-controlled Hamiltonian system perspective

This paper addresses the problem of deriving control laws for robot manipulators in the framework of port-controlled Hamiltonian systems via canonical transformations and passivity-based control. The control design is focused on the presentation of a new energy-shaping methodology for tracking control based on the introduction of virtual non-homogeneous fields where a desired energy is defined to compensate for the actual energy of the robot manipulator while a virtual field forces the system to track a general reference trajectory. This requires use of the Legendre-Fenchel transformation and allows for the derivation standard control laws in the robotics field such as PD control with gravity compensation or PD with precompensation. Finally, the passivity of the input-output mapping of the non-autonomous Hamiltonian system is analyzed in detail, resulting in new Lyapunov candidate functions having their roots in physics.     

Input-output decoupling of non-linear systems via a general class of dynamic compensation

An algorithm is presented for input-output decoupling of non-linear control systems with the use of a dynamic precompensator. The precompensator used is of non-linear form. Moreover, this algorithm solves the above problem in a local fashion, i.e. we find a neighbourhood of the initial state of the overall system (the original system together with the dynamic compensator) where we can achieve input-output decoupling using the appropriate feedback law.     

Structure invariance for uncertain nonlinear systems

A unified study of three control problems associated to multi-input multi-output nonlinear systems with uncertainties is presented, namely, input-state linearization by static state feedback, input-output decoupling by static state feedback and input-output decoupling by dynamic compensation. For each of these problems, geometric conditions which describe intrinsic structural invariance properties are given     

On input-output parametric invariance in linear systems

The problem of the invariance of the input-output behavior of time-invariant linear systems under perturbations in the system matrices and initial conditions is examined. Previous results are unified and expanded upon, and new results for invariance in the presence of perturbations in the output matrix are given. Conditions for input-output invariance are related to the subspace of reachable states and its orthogonal complement, and to the subspace of unobservable states.     

DECOUPLING WITH STABILITY: APPLICATION TO THE REAL TIME CONTROL OF A WATER STORING PLANT

In this paper, results on decoupling with stability are applied to the real‐time control of a water storing plant. The conditions of decoupling with stability are verified on the approximate linear model of the system, and a decoupling state feedback providing pole assignment is designed. The state feedback controller achieves input‐output decoupling with stability, allowing controlling the levels of the water in the tanks independently. Simulation and experimental results are also presented showing a good performance of the designed controller.     

On the decoupling of linear time-varying control systems

Some recent results concerning the input-output decoupling problem of time-invariaut systems, for which the decoupling matrixB*is not invertible, are extended to time-varying systems. It is shown that the maximum number of input-output pairs which can be decoupled by linear state feedback is equal to rankB*(t) = r, whereris assumed to be constant over the entire time interval of interest. An illustrative example is provided.     

Feedback decoupling of structured systems

The feedback decoupling of structured linear systems is considered. Using results gathered on decoupling and the graph characterization of the structure at infinity, a necessary and sufficient decoupling condition for structured systems is developed. This condition has a graphical interpretation in terms of shortest input-output paths     

多变量鲁里叶系统鲁棒输入、输出稳定性的Gap度量界

本文讨论了多变量鲁里叶系统鲁棒输入，输出稳定性问题，文中利用Ｇａｐ度量作为系统中非结构型摄动的测量手段，给出了当系统线性部分的摄动量和Ｇａｐ度量满足某种估计式，同时非线性部分的扇形斜率也受到某种类型摄动时，闭环系统仍能保持稳定的若干充分条件。     

Sensitive decoupling control of linear disturbed-parameter systems

The input-output decoupling control problem for a generalized multivariable linear model, covering most practical situations, is treated for the case where the model involves disturbances in the parameters. A sensitive decoupling controller is derived which maintains the decoupling conditions to first order in the parameter variations, about their nominal values.     

Modeling and input-output decoupling of hypersonic vehicles

This paper studies the problems of modeling and input-output decoupling of generic hypersonic vehicles. Dynamical equations of hypersonic vehicles are derived using Lagrangian approach, which capture the dominating characteristics and primary interactions. Then, based on the simplified model, the original decoupling problem is reformulated as an asymptotical stability problem of the corresponding error system. The popular dynamic inversion is employed to design the decoupling controller, which can achieve steady-state decoupling. However, external disturbance will greatly destroy the effect of decoupling before the system reaches steady state. To this end, based on the error system, robust H _∞ theorem can be easily used to address this issue by reducing the impact of disturbance on error system outputs, which ultimately results in approximate decoupling. Moreover, the degree of approximate decoupling can be enhanced by choosing a small performance index γ. Simulations verify the effectiveness of proposed controllers.     

Non-Markovian Quantum Error Deterrence by Dynamical Decoupling in a General Environment

A dynamical decoupling(DD) scheme for the prevention of errors in the non-Markovian (usually corresponding to low temperature, short time, and strong coupling) regimes suitable for qubits constructed out of a multilevel structure is studied. We use the effective spin-boson model (ESBM) introduced recently [K. Shiokawa and B. L. Hu, Phys. Rev. A70, 062106 (2004)] as a low temperature limit of the quantum Brownian oscillator model, where one can obtain exact solutions for a general environment with colored noises. In our decoupling scheme, a train of pairs of strong pulses are used to evolve the interaction Hamiltonian instantaneously. Using this scheme we show that the dynamical decoupling method can suppress 1/f noise with slower and hence more accessible pulses than previously studied, but it still fails to decouple super-Ohmic types of environments.      

Robust input-output energy decoupling for uncertain singular systems

1 Introduction During recent years, singular systems have at- tracted the interest of a number of researchers due to the fact that they appear more naturally in the study of naturally occurring systems than regular systems (state-space systems), e.g. in economic, circuit, and boundary control systems, and chemical processes[1～3]. Many contributions have been made to the study of these systems, and a great number of results on the theory of regular systems have been generalized to the area of …