Class Of Non-minimum Phase Systems Research Articles

Applicability analysis of extended state observer-based control for systems subject to parametric disturbances

This paper discusses the applicability of Extended State Observer (ESO)-based control when systems are subjected to different types of parametric disturbances. The applicability is analyzed by establishing the characteristic polynomial of the closed-loop system. It is found that High-Bandwidth ESO-based control is beneficial to the elimination of state-parameter disturbances, but it has a negative impact on the elimination of input-parameter disturbances. In spite of this, the ESO-based control with suitable bandwidth can still be applied to systems which are subject to input-parameter disturbances. A Full-Order ESO-based control scheme is proposed so that disturbance rejection-based control is realized for a class of non-minimum phase systems. Numerical simulations are carried out to verify the correctness of the conclusions and the effectiveness of the proposed controller.

Static output feedback passivation revisited and global asymptotic stabilizing properties of a controller

SummaryThe class of systems that can be globally asymptotically stabilized by the well‐known control law , is extended, in respect to literature. This control law is suitable for application to systems of unknown structure, and it is shown that it is more advantageous than the linear control law. The stability proof is based on solutions of a newly introduced problem, which is a specialization of the passivation by static output feedback control of a system with nonzero feedforward matrix. Necessary and sufficient conditions for existence of a solution of the problem are given, which include the minimum phase property of the given system. It is explained why the new concept cannot be applied to nonminimum phase systems. It is proved that a class of nonminimum phase systems can be stabilized by the same control law, where is a matrix function, rather than a constant matrix. Illustrative example are given.

Sampled-data repetitive control for a class of non-minimum phase nonlinear systems subject to period variation

ABSTRACTThe robust sampled-data repetitive control (RC, or repetitive controller, also designated RC) problem for non-minimum phase nonlinear systems is both challenging and practical. This paper proposes a sampled-data output-feedback RC design for a class of non-minimum phase systems with measurable nonlinearities to improve the robustness against the period variation. The design relies on additive-state decomposition, by which the output-feedback RC problem is decomposed into an output-feedback RC problem for a linear time-invariant component and a state-feedback stabilisation problem for a nonlinear component. Thanks to the decomposition, existing controller design methods in both the frequency domain and the time domain are employed to make the robustness and discretisation for a continuous-time nonlinear system tractable. In order to demonstrate the effectiveness, an illustrative example is given.

Optimal iterative learning control for a class of non-minimum phase systems

In this paper, an optimal iterative learning control (ILC) approach is proposed for a class of repetitive non-minimum phase (NMP) systems. The control law synthesis is based on the resolution of a quadratic criterion which minimises the errors between the setpoint references and the system outputs at each iteration for each trial. The resolution of the control problem uses a new gain which avoids matricial inversion problems appearing in classical ILC algorithms such as direct model inversion (I-ILC) and optimal ILC (Q-ILC). The new optimal ILC approach improves the learning convergence significantly compared to the previously mentioned algorithms. Furthermore, sufficient and necessary stability conditions are established with convergence properties. The effectiveness of the proposed method is proved by simulations with an NMP mass-spring damper system.

Optimal iterative learning control for a class of non-minimum phase systems

In this paper, an optimal iterative learning control (ILC) approach is proposed for a class of repetitive non-minimum phase (NMP) systems. The control law synthesis is based on the resolution of a quadratic criterion which minimises the errors between the setpoint references and the system outputs at each iteration for each trial. The resolution of the control problem uses a new gain which avoids matricial inversion problems appearing in classical ILC algorithms such as direct model inversion (I-ILC) and optimal ILC (Q-ILC). The new optimal ILC approach improves the learning convergence significantly compared to the previously mentioned algorithms. Furthermore, sufficient and necessary stability conditions are established with convergence properties. The effectiveness of the proposed method is proved by simulations with an NMP mass-spring damper system.

Additive‐state‐decomposition‐based tracking control framework for a class of nonminimum phase systems with measurable nonlinearities and unknown disturbances

SUMMARYThis paper aims to propose an additive‐state‐decomposition‐based tracking control framework, based on which the output feedback tracking problem is solved for a class of nonminimum phase systems with measurable nonlinearities and unknown disturbances. This framework is to ‘additively’ decompose the output feedback tracking problem into two more tractable problems, namely an output feedback tracking problem for a linear time invariant system and a state feedback stabilization problem for a nonlinear system. Then, one can design a controller for each problem respectively using existing methods, and these two designed controllers are combined together to achieve the original control goal. The main contribution of the paper lies on the introduction of an additive state decomposition scheme and its implementation to mitigate the design difficulty of the output feedback tracking control problem for nonminimum phase nonlinear systems. To demonstrate the effectiveness, an illustrative example is given. Copyright © 2013 John Wiley & Sons, Ltd.

Study on the Model Feedback Control System for a Class of Non-Minimum Phase Systems

In the present paper, we examine model feedback control systems (MFCSs). Because MFCSis simple, the MFCS has been applied in many applications such as the trajectory control of robotmanipulators, serially connected water tanks, etc. The control structure of the MFCS is limited, butYamada and Moki reported about whether or not MFCS can represent all of the stabilizing controllersof a minimum phase plant. However, no research has been reported whether or not MFCS can representall of the stabilizing controllers of a non-minimum phase plant. The purpose of the present paper isto give a solution to the question as to whether or not all of the stabilizing controllers for a plantare expressible in the MFCS structure. The relation between MFCS and the parameterization of allstabilizing controllers for a class of non-minimum phase plants is shown. A simple design method tospecify control characteristics is also presented.

Robust output tracking control of a class of non-minimum phase systems and application to VTOL aircraft

In this article, we study the output tracking control of a class of MIMO nonlinear non-minimum phase systems in the presence of input disturbances. In order to attenuate the effects of disturbances, the method of uncertainty and disturbance estimator (UDE) is extended to the controller design for non-minimum phase systems. Due to the fact that the accumulated disturbances is composed of internal states and external disturbances, a different stability analysis is given, and the overall closed-loop system is proved to be semi-globally stable. The proposed state-feedback controller not only forces system outputs to asymptotically track desired trajectories, but also drives the unstable internal dynamics to follow bounded and causal ideal internal dynamics (IID) solved via stable system centre (SSC) method. Simulation results demonstrate that the proposed controller achieves excellent tracking and disturbance rejection performance via the example of VTOL aircraft which has been the benchmark of nonlinear non-minimum phase systems.

Modified PI Control using Model Driven Control for Certain Class of Non-minimum Phase Systems

In this paper, we examine PI (Proportional-Integral) control using model driven control for certain class of non-minimum phase systems. PI control systems work as one of powerful methods for controlling several plants. However, PI control remains two difficulties. One is that there exist plants which cannot be stabilized by PI controller. The other is that when P-parameter and I-parameter in the PI controller is adjusted using previously proposed methods, the sets of P-parameter and I-parameter, which guarantee the stability of PI control system, are related to each other. Therefore if P-parameter is changed, the set of I-parameter which make the feedback control system stable is also changed. If the sets of P parameter and I-parameter are independent each other, then we can easily settle P-parameter and I-parameter in the PI controller to achieve desirable control specifications. However, no paper gives the sets of P-parameter and I-parameter which are independent each other. The purpose of this paper is to overcome these problems and propose a modified PI control systems such that the stability of control system is guaranteed and the sets of P-parameter and I parameter, which guarantee the stability of PI control system, are independent. The modified PI control systems is built based on fusion of the idea of the model driven control and the parametrization of all stabilizing controllers for certain class of non-minimum phase systems. A numerical example is illustrated to show the effectiveness of the proposed method.

71巻707号,C編(2005-7)正誤表

71巻707号,C編(2005-7)正誤表

Use of State Feedback to Achieve a Nonovershooting Step Response for a Class of Nonminimum Phase Systems

The problem of tracking a known reference without overshooting is of great practical importance in a number of applications. However, nonminimum phase systems have received little attention in connection with obtaining a nonovershooting response. Using state feedback, this paper develops an eigenvector placement technique to construct an invariant set which guarantees a nonovershooting step response for a class of nonminimum phase SISO systems.

The Parametrization of All Stabilizing Repetitive Controllers for Cetain Class of Non-Minimum Phase Systems

In the present paper, we give explicit parametrization of all causal stabilizing repetitive controllers for single-input/single-output continuous time certain class of non-minimum phase systems. The parametrization of all causal stabilizing repetitive controllers was first studied by Hara and Yamamoto. Katoh and Funahashi give the parametrization for the class of all stabilizing repetitive controllers for minimum phase biproper plants by solving the Bezout equation explicitly. However, Katoh and Funahashi assumed the plant is asymptotically stable. Using parallel compensation technique, Yamada and Okuyama gave explicit parametrization of all repetitive controllers for minimum phase systems that is not necessarily stable. We expand the result by Yamada and Okuyama and give the parametrization of all causal stabilizing controllers for certain class of non-minimum phase systems. Finally, a numerical example is used to illustrate the effectiveness of the proposed method.

804 モデル駆動制御を援用したあるクラスの非最小位相系に対する PI 制御

804 モデル駆動制御を援用したあるクラスの非最小位相系に対する PI 制御

Tracking in a class of nonminimum-phase systems with nonlinear internal dynamics via sliding mode control using method of system center

A method of asymptotic output tracking in a class of causal nonminimum-phase uncertain nonlinear systems is considered. Local asymptotic stability of output tracking-error dynamics are provided for the specified class of systems with the nonlinear hyperbolic at the origin internal dynamics forced by a reference output profile and external disturbances defined by a known linear exosystem. The nonlinear vector field of the internal dynamics is expanded in a power series, obtained at a selected operational point in the internal dynamics state space. The presented technique employs some linear algebraic methods and sliding mode control approach. The solution is a complete constructive algorithm.

A Direct Adaptive Controller for Non-minimum Phase Multivariable Systems with Arbitrary Time Delays

A direct adaptive multivariable control scheme based on the ideas of model reference adaptive controllers is presented, which is applicable to minimum and a certain class of non-minimum phase systems. The general time delay case is considered, where the individual transfer functions of the multivariable system may have different arbitrary time delays. In order to stabalize nonminimum-phase adaptive control and to weight the control cost, the plant output vector is augmented by filtered plant input signals. Adaptive feedforward control is included to compensate measurable load changes or other disturbances. A new estimation algorithm is introduced, which is related to "fixed gain" ana stochastic approximation techniques.