Input-output pseudolinearization for nonlinear systems

An input-output pseudolinearized system has the property that its family of linearizations about constant operating points has input-output behavior that is independent of the operating point. We develop a necessary and sufficient condition for existence of a state feedback and state coordinate change that transforms a given system into a pseudo-normal form that is input-output pseudolinearized. These ideas are applied to obtain new approaches to approximate tracking and approximate inversion of nonlinear systems     

On the equivalence between stable inversion for nonminimum phase systems and reciprocal transfer functions defined by the two-sided Laplace transform

In this paper, the two-sided Laplace transform, a classical but not very common mathematical tool, is revived to express the stable inversion for linear nonminimum phase systems that was recently proposed from the viewpoint of state-space representations. It is demonstrated that those two different expressions for the stable inversion are mathematically equivalent. Simple examples are presented to illustrate the two-sided Laplace transform as a direct and intuitive approach to stable inversion. The two-sided Laplace transform approach is also applied to the development of an iterative learning control for nonminimum phase systems that needs neither a precise inversion model nor Fourier-Transform computations, but instead requires only measuring the system response with time reversals.     

Inversion of sampled-data system approximates the continuous-time counterpart in a noncausal framework

Although correspondence between the poles of a continuous-time and sampled-data system with a piecewise constant input is simple and desirable from the stability viewpoint, the relationship between zeros is intricate. Inversion of a sampled-data system is mostly unstable irrespective of the stability of the continuous-time counterpart. This makes it difficult to apply inversion-based control techniques such as perfect tracking, transient response shaping or iterative learning control to sampled-data systems. Although recently developed noncausal inversion techniques help us to circumvent unboundedness of the inversion caused by unstable zeros, whether the inversion of sampled-data systems approximates the continuous-time counterpart or not as the sample period is shortened is still to be determined. This article gives a positive conclusion to this problem.     

Evaluating Viewpoint Entropy for Ribbon Representation of Protein Structure

While many measures of viewpoint goodness have been proposed in computer graphics, none have been evaluated for ribbon representations of protein secondary structure. To fill this gap, we conducted a user study on Amazon's Mechanical Turk platform, collecting human viewpoint preferences from 65 participants for 4 representative superfamilies of protein domains. In particular, we evaluated viewpoint entropy, which was previously shown to be a good predictor for human viewpoint preference of other, mostly non‐abstract objects. In a second study, we asked 7 experts in molecular biology to find the best viewpoint of the same protein domains and compared their choices with viewpoint entropy. Our results indicate that viewpoint entropy overall is a significant predictor of human viewpoint preference for ribbon representations of protein secondary structure. However, the accuracy depends on the type and composition of the structure: while most participants agree on good viewpoints for structures with mainly beta sheets, viewpoint preference varies considerably for complex arrangements of alpha helices. Finally, experts tend to choose viewpoints of both low and high viewpoint entropy to emphasize different aspects of the respective structure.     

Linearization of nonlinear systems about constant operating points

For bilinear-realizable nonlinear systems described by a Volterra series, an input-output definition of the linearized system about a constant operating point is given. This definition is then compared to the usual notion of linearization in terms of a bilinear realization of the nonlinear system. Properties of the linearized system with respect to the original nonlinear system are developed, and implications for analysis and design of nonlinear systems are discussed.     

Dimensioning problems in system design using bicausal bond graphs

System inversion techniques and bond graph representations are used here to present a methodology for the dimensioning of actuating components for the proper operation of the overall system based on dynamic and energy criteria associated to some prescribed specifications. The proposed methodology to deal with the so-called sizing problem is then illustrated by the validation of the actuators of a two-link manipulator for a specified end-effector trajectory. The study shows that the components imposing limitations to the system performance and the causes of their inappropriateness can conveniently be identified and analysed.     

LPV decoupling for control of multivariable systems

This article investigates methods for decoupling multivariable linear parameter varying (LPV) systems and proposes a new interaction measure for decoupled proportional-integral (PI) feedback control design in LPV systems. The proposed approach seeks to benefit the multivariable control of multi-input multi-output (MIMO) systems with variable operating conditions, variable parameters or nonlinear behaviour. This method can improve the tracking performance and reduce the operating conditions variability of such systems with significant coupling in the system dynamics. We design MIMO decoupling feedback LPV controllers to address loop interaction effects. The proposed method uses a parameter-dependent static inversion or SVD decomposition of the system to minimise the effects of the off-diagonal terms in the MIMO system transfer function matrix. A new parameter-dependent interaction measure is introduced based on the SVD decomposition and static inversion which is subsequently utilised for tuning multi-loop PI controller gains. Numerical examples are presented to illustrate the validity of the proposed LPV decoupling methods, as well as the use of the proposed interaction measures for a decoupled multi-loop PI control design.     

A general approach to input-output pseudolinearization fornonlinear systems

A nonlinear system is said to be input-output pseudolinearized if its family of linearizations about constant operating points has input-output behavior that is independent of the particular operating point. The problem of constructing static state feedback laws that achieve input-output pseudolinearization for a general class of nonlinear systems is considered. A generalization of the well-known structure algorithm to the case of parameterized families of linear systems plays an important role     

Robust nonlinear control associating robust feedback linearization and H/sub /spl infin// control

In this note, a robust nonlinear controller for a nonlinear system subject to model uncertainties is proposed. Such a controller associates a "robust feedback linearization" with a robust linear H/sub /spl infin// controller. The robust feedback linearization exactly transforms the nonlinear system into a linear system equal to the linear approximation of the original nonlinear system around a nominal operating point. The robustness of the resulting overall nonlinear controller is proved by theoretical arguments and illustrated through an application example, the control of a magnetic bearing system.     

Fuzzy linear pulse-transfer function-based sliding-mode control fornonlinear discrete-time systems

In this paper, a nonlinear discrete-time system in the presence of input disturbance and measurement noise is approximated by N subsystems described by the linear pulse-transfer functions. Although the input disturbance and the measurement noise are unknown, they are modeled as known pulse-transfer functions. The approximation error between the nonlinear discrete-time system and the fuzzy linear pulse-transfer function system is represented by the linear time-invariant dynamic system in every subsystem, whose degree can be larger than that of the corresponding subsystem. Besides the input disturbance and the measurement noise, uncertainties are caused by the approximation error of the fuzzy-model and the interconnected dynamics resulting from the other subsystems. Owing to the presence of input disturbance, measurement noise, or uncertainties, a disadvantageous response occurs. Based on Lyapunov redesign, the switching control in every subsystem is designed to reinforce the system performance. Due to the time-invariant feature for a constant reference input, the operating point can approach the sliding surface in the manner of finite-time steps. The stability of the overall system is verified by Lyapunov stability theory     

Feedback linearization families for nonlinear systems

Characterizations are developed for parameterized, linear, dynamic feedback control laws that can arise when linearizing a nonlinear, dynamic feedback control law for a specified nonlinear system about a family of constant operating points. Such characterizations are important in applying the recently-developed extended linearization design approach to various types of control problems. To illustrate, the input-output decoupling problem is considered.     

Filtering adaptive neural network controller for multivariable nonlinear systems with mismatched uncertainties

This paper synthesizes a filtering adaptive neural network controller for multivariable nonlinear systems with mismatched uncertainties. The multivariable nonlinear systems under consideration have both matched and mismatched uncertainties, which satisfy the semiglobal Lipschitz condition. The nonlinear uncertainties are approximated by a Gaussian radial basis function (GRBF)‐based neural network incorporated with a piecewise constant adaptive law, where the adaptive law will generate adaptive parameters by solving the error dynamics between the real system and the state predictor with the neglection of unknowns. The combination of GRBF‐based neural network and piecewise constant adaptive law relaxes hardware limitations (CPU). A filtering control law is designed to handle the nonlinear uncertainties and deliver a good tracking performance with guaranteed robustness. The matched uncertainties are cancelled directly by adopting their opposite in the control signal, whereas a dynamic inversion of the system is required to eliminate the effect of the mismatched uncertainties on the output. Since the virtual reference system defines the best performance that can be achieved by the closed‐loop system, the uniform performance bounds are derived for the states and control signals via comparison. To validate the theoretical findings, comparisons between the model reference adaptive control method and the proposed filtering adaptive neural network control architecture with the implementation of different sampling time are carried out.     

Optimal PMU-based monitoring architecture design for power systems

This paper is dedicated to a new methodology for designing an optimal monitoring architecture by using a limited number of PMUs (Phasor Measurement Units) and PDCs (Phase Data Concentrators). The optimal design problem consists in defining the optimal location of both PMUs and PDCs by maximizing the expected value of the trace of the observability gramian of the power system over a large number of set point scenarios, while minimizing some communication infrastructure costs. Furthermore, a nonlinear dynamical state-observer, based on the Extended Kalman Filter, is proposed. This state-observer allows to take transient phenomena into account for wide-area power systems described by algebraic-differential equations, without needing nonlinear inversion techniques. The overall approach is illustrated with the IEEE 10 generator 39 bus New England power system.     

Set membership inversion and robust control from data of nonlinear systems

A set membership method for right inversion of nonlinear systems from data is proposed in the paper. Both the cases where the system to invert is known or unknown and therefore identified from data are addressed. The method does not require the invertibility of the regression function describing the system and ensures tight bounds on the inversion error. In the case of unknown system, the method allows the derivation of a robust right‐inverse, guaranteeing the inversion error bound for all the systems belonging to the uncertainty set which can be defined from the available prior and experimental information. Based on such a set membership inversion, two methods for robust control of nonlinear systems from data are introduced: nonlinear feed‐forward control (NFFC) and nonlinear internal model control (NIMC). Both the design methods ensure robust stability and bounded tracking errors for all the systems belonging to the involved uncertainty set. Two applicative examples of robust control from data are presented: NFFC control of semi‐active suspension systems and NIMC control of vehicle lateral dynamics.Copyright © 2013 John Wiley & Sons, Ltd.     

Local stability analysis and domain of attraction estimation for a class of uncertain nonlinear discrete‐time systems

This paper proposes a linear matrix inequality based method for the estimation of domain of attraction for a class of discrete‐time nonlinear systems subject to uncertain constant parameters. Recursive algebraic representations of the system dynamics and of the Lyapunov stability conditions are applied to obtain convex conditions which guarantee the system robust local stability while providing an estimate of the domain of attraction. A large class of discrete‐time nonlinear systems and of Lyapunov functions can be embedded in the proposed methodology including the whole class of regular rational functions of the system state variable and uncertain parameters. Numerical examples illustrate the application of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

基于逆阵更新方法的局部非线性结构频响分析

针对含有非线性连接的大型局部非线性结构,采用描述函数表示其所连接的非线性内力,将非线性结构频响表示为拟线性动柔度矩阵(Quasilinear Receptance Matrix),提出一种逆阵更新(Inverse Matrix Updating Method,IMU)方法,将求解系统动柔度(频响特性)的高阶矩阵求逆转化为低阶矩阵的求逆,从而获得大型局部非线性结构主频响应的快速计算方法.仿真结果表明,本文的分析方法具有较好的稳定性,并能大幅提高大型局部非线性结构主频响应的计算效率.     

Adaptive passivity-based control for maximum power extraction of stand-alone windmill systems

This paper addresses the high performance regulation of stand-alone windmill systems consisting of a wind turbine coupled to a generator and a battery charging system, which is a challenging problem for at least two reasons. First, the dynamics of the overall system are described by a highly coupled set of nonlinear differential equations. Since the range of operating points of the system is very wide, classical linear controllers yield below par performances. Second, in many applications it is desirable to extract from windmill systems their maximum power. This operating point is a nonlinear function of the wind speed, which is hard to measure. In this paper, a nonlinear passivity-based controller that ensures asymptotic convergence to the maximum power extraction point, which is rendered adaptive combining it with a wind speed estimator previously proposed by the authors, is proposed. Detailed computer simulations are presented to validate the approach.     

Real time adaptive nonlinear model inversion control of a twin rotor MIMO system using neural networks

This paper investigates the development and experimental implementation of an adaptive dynamic nonlinear model inversion control law for a Twin Rotor MIMO System (TRMS) using artificial neural networks. The TRMS is a highly nonlinear aerodynamic test rig with complex cross-coupled dynamics and therefore represents the control challenges of modern air vehicles. A highly nonlinear 1DOF mathematical model of the TRMS is considered in this study and a nonlinear inverse model is developed for the pitch channel of the system. An adaptive neural network element is integrated thereafter with the feedback control system to compensate for model inversion errors. The proposed on-line learning algorithm updates the weights and biases of the neural network using the error between the set-point and the real output. The real-time response of the method shows a satisfactory tracking performance in the presence of inversion errors caused by model uncertainty. The approach is therefore deemed to be suitable to apply real-time to other nonlinear systems with necessary modifications.     

地震波阻抗参数混沌控制反演

分析了地震非线性反演的混沌现象, 并且从测井资料出发, 以非线性动力学不动点理论及混沌控制理论为基础, 提出了混沌控制反演方法, 数值实验和应用实例表明, 该方法能有效地控制非线性反演系统在反演选代过程中出现的混沌现象, 得到较真实可靠的反演结果.