Minimum Phase Systems Research Articles

Inverse dynamics of serial and parallel underactuated multibody systems using a DAE optimal control approach

The inverse dynamics analysis of underactuated multibody systems aims at determining the control inputs in order to track a prescribed trajectory. This paper studies the inverse dynamics of non-minimum phase underactuated multibody systems with serial and parallel planar topology, e.g. for end-effector control of flexible manipulators or manipulators with passive joints. Unlike for minimum phase systems, the inverse dynamics of non-minimum phase systems cannot be solved by adding trajectory constraints (servo-constraints) to the equations of motion and applying a forward time integration. Indeed, the inverse dynamics of a non-minimum phase system is known to be non-causal, which means that the control forces and torques should start before the beginning of the trajectory (pre-actuation phase) and continue after the end-point is reached (post-actuation phase). The existing stable inversion method proposed for general nonlinear non-minimum phase systems requires to derive explicitly the equations of the internal dynamics and to solve a boundary value problem. This paper proposes an alternative solution strategy which is based on an optimal control approach using a direct transcription method. The method is illustrated for the inverse dynamics of an underactuated serial manipulator with rigid links and four degrees-of-freedom and an underactuated parallel machine. An important advantage of the proposed approach is that it can be applied directly to the standard equations of motion of multibody systems either in ODE or in DAE form. Therefore, it is easier to implement this method in a general purpose simulation software.

Filtered-dynamic-inversion control for unknown minimum-phase systems with unknown-and-unmeasured disturbances

This article presents a filtered-dynamic-inversion controller for multi-input multi-output linear minimum-phase systems. The controller requires limited model information, specifically, knowledge of the relative degree and the first nonzero Markov parameter. Furthermore, the controller is effective for stabilisation, command following and rejection of unknown-and-unmeasured disturbances. This article analyses the stability and closed-loop performance (i.e. command following error) of filtered dynamic inversion, which is a single-parameter high-parameter-stabilising controller. We show that for sufficiently large parameter the closed-loop is asymptotically stable, and the average power of the performance signal is arbitrarily small.

Robust Passivity and Feedback Design for Nonlinear Stochastic Systems with Structural Uncertainty

This paper discusses the robust passivity and global stabilization problems for a class of uncertain nonlinear stochastic systems with structural uncertainties. A robust version of stochastic Kalman-Yakubovitch-Popov (KYP) lemma is established, which sustains the robust passivity of the system. Moreover, a robust strongly minimum phase system is defined, based on which the uncertain nonlinear stochastic system can be feedback equivalent to a robust passive system. Following with the robust passivity theory, a global stabilizing control is designed, which guarantees that the closed-loop system is globally asymptotically stable in probability (GASP). A numerical example is presented to illustrate the effectiveness of our results.

Comparative analysis of traditional and modern controller for piezoelectric actuated nanopositioner

Nanopositioning, Precise control and manipulation of devices and materials at nanoscale is the most important constraint of nanotechnology. Nanopositioning stage consisting of piezoelectric actuator has widespread use in applications requiring positioning with precision at nanoscale. In this paper, open loop characteristics of the non minimum phase nanopositioning system are investigated. To guarantee high precision positioning and improvement in the system characteristics demands different types of feedback controllers. The main aim of the controller is to design a closed loop system with good dynamic characteristics and to maintain the desired stability margins. PID controller is a generic closed loop controller widely used for industrial control applications. This paper presents design of PID controller using Ziegler Nichols tuning method. This paper analyzes time and frequency response of traditional PID controller. Non minimum phase system can be stabilized more effectively by modern controller such as pole placement controller, Linear Quadratic Regulator (LQR) and H infinity controllers. This paper develops a methodology for the design of full state feedback controller using pole placement and LQR control techniques. Step response and frequency responses under variety of conditions are plotted and analyzed to verify the effectiveness of the proposed controllers. Closed loop system is analyzed in both time and frequency domain for different dynamic characteristics such as rise time, settling time, maximum overshot and stability margins. A comparative assessment based upon the system’s response characteristics of traditional PID controller, pole placement controller and LQR controller is presented. Simulation results for the performance analysis are carried out on MATLAB and demonstrate effectiveness and adaptability of controller for precise control of piezoelectric actuated nanopositioning system.

Output Synchronization on Strongly Connected Graphs

In this technical note, we study output synchronization of networked multiagent systems. The agents, modeled as nonlinear systems with relative degree one, exchange information over a network described by an interagent communication graph. Inspired by the results of Igarashi , we extend our earlier results on output synchronization to include the case of strongly connected graphs. We first demonstrate output synchronization for input-output passive systems communicating over strongly connected graphs and include the practical case of constant time delays in communication. It is well known (Byrnes ) that weakly minimum phase systems with relative degree one are feedback equivalent to a passive system with a positive definite storage function. We exploit this feedback equivalence to develop control laws for output synchronization of such systems, exchanging outputs on strongly connected graphs, and in the presence of communication delays. A numerical example is also presented to illustrate the proposed results.

一类高超声速飞行器自适应容错控制器设计

The hypersonic aircraft control system design must deal with the extra prominent dynamics characteristics: highly coupled, strongly nonlinear, time variational and so on. Thus, during the course of control system study and design for the hypersonic aircraft, the following factors must be considered: plant elastic deformation, multi-inputs multi-outputs, uncertain aerodynamatic parameters, sensors and actuator failures, which is differ from the traditional aircrafts control system design. To solve the failure problem of the actuator in the course of the hypersonic aircraft flight, one kind of adaptive backstepping fault-tolerant control method based on the observer and controller designed synthetically is brought up. At first, we develop the research model based on a SISO output feedback nonlinear unobservered minimum phase system under the condition of single channel actuator failure of the hypersonic aircraft, then adopt K -filter to reconstruct state vectors. When only the output is measureable, the dissertation designs one new observer to estimate convergence state vector and design the adaptive control law to guarantee the system boundedness. In the course of adaptive backstepping design, the dissertation employes the dynamic surface control strategy to eliminate the explosion of terms by introducing a series of first order filters to obtain the differentiation of the virtual control inputs. Lyapunov stability theorem guarantees the error uniformly bound. Both theory analysis and simulation verification show the simplicity and effectiveness of this method. At last the pitch channel of hypersonic aircraft is studied as an example to validate the above theory.

Consensus of output-coupled linear multi-agent systems under fast switching network: Averaging approach

This study addresses the problem of consensus of multi-agent systems, consisting of a set of identical MIMO LTI systems, under a time-varying network that has a well-defined average (with uniform convergence to the average). The information delivered through the communication network is the output of each system. First, it is shown that consensus is reached asymptotically by using a group of compensators if the network switches sufficiently fast and the compensators are designed such that the multi-agent system asymptotically achieves consensus for the average of the network. Further, we find a relation between the two agreements, one obtained from considering the switching network and the other obtained from replacing the network with its average. Then, for a class of minimum phase systems, we remove the fast switching condition by redesigning the compensators. Finally, the formation stabilization of unicycle-type mobile robots is dealt with as an application of the problem, and it is demonstrated via a computer simulation.

An Improved Analytical PID Controller Design for Non-Monotonic Phase LTI Systems

An improved technique of analytical design of proportional-integral-derivative (PID) controllers in frequency-domain for non-monotonically decreasing phase systems by means of gain crossover frequency and phase margin specifications is presented in this brief. The proposed method guarantees a minimum phase margin inside the desired bandwidth, assuring better performance to step response for the closed-loop system. In order to achieve this feature, it is necessary to redefine the concept of phase margin when the uncontrolled process presents a non-monotonically decreasing phase inside the bandwidth. Hence, the phase margin can still be used as a good robustness indicator and allows the Bode stability criterion to be used for monotonic minimum-phase or non-monotonic minimum-phase systems.

ADRC based input disturbance rejection for minimum-phase plants with unknown orders and/or uncertain relative degrees

The capability of ADRC is studied for linear time-invariant SISO minimum-phase systems with unknown orders, uncertain relative degrees, and unknown input disturbances. It is proved that ADRC can reject the unknown input disturbance and guarantee the close-loop stability for the plants with unknown but bounded relative degrees. Meanwhile, some close-loop performances can be achieved. The influence of the sensor noise is also discussed. And it is demonstrated by numerical examples that one ADRC with fixed parameters can be applied to a group of plants of different orders, relative degrees, and parameters.

Robust design of nonlinear internal models without adaptation

We propose a solution to the problem of semiglobal output regulation for nonlinear minimum-phase systems driven by uncertain exosystems that does not rely upon conventional adaptation schemes to estimate the frequency of the exogenous signals. Rather, the proposed approach relies upon regression-like arguments used to derive a nonlinear internal model able to offset the presence of an unknown number of harmonic exogenous inputs of uncertain amplitude, phase and frequency. The design methodology guarantees asymptotic regulation if the dimension of the regulator exceeds a lower bound determined by the actual number of harmonic components of the exogenous input. If this is not the case, a bounded steady-state regulation error is ensured whose amplitude, though, can be arbitrarily decreased by acting on a design parameter of the regulator.

Nonlinear output regulation with adaptive conditional servocompensator

An output feedback controller with adaptive conditional servocompensator is developed for robust output regulation of a class of nonlinear minimum-phase systems. It is shown that the controller achieves asymptotic regulation and can be tuned to recover the transient performance of a state feedback sliding-mode-controller.

Sensitivity Function Based Active Disturbance Rejection Control for the Plant with Unknown Order and Uncertain Relative Degree

The active disturbance rejection control (ADRC) design based on the sensitivity function is studied for the linear time-invariant SISO minimum-phase system with unknown order and uncertain relative degree. It is proved that ADRC can reject the disturbance and guarantee the close-loop stability provided that the relative degree of such plant is bounded.

The design of nonovershooting and nonundershooting multivariable state feedback tracking controllers

We consider the use of linear multivariable feedback control to achieve a nonovershooting and nonundershooting step response. Recently, Schmid and Ntogramatzidis (2010) [13] introduced a linear state feedback controller design method to avoid overshoot. In this paper, we describe conditions under which the design method may be modified to avoid undershoot. The method is applicable to square and nonsquare systems, minimum and nonminimum phase systems, and also strictly proper and bi-proper systems.

Amplitude‐phase constraints based blind and semi‐blind channel estimation for OFDM systems

ABSTRACTIn this paper, a new blind channel estimation method for orthogonal frequency division multiplexing systems is presented. The proposed approach based on the amplitude‐phase constraints of the channel frequency response first estimates the channel amplitude‐frequency response, and then calculates the channel‐frequency response of the equivalent minimum phase system by its amplitude‐frequency response. The zeros of the actual system and its equivalent minimum phase system are symmetric about the unit circle, and the symmetric relationships are easily determined according to the finite alphabet property of information symbols. A semi‐blind estimation method based on the blind estimation method is also proposed in this paper, and it greatly reduces the numerical complexity of the blind method. Unlike existing statistical blind channel estimators, the proposed method requires short data records especially for phase‐shift keying modulation. Compared with the existing finite alphabet based method, the proposed method has a lower numerical complexity. Comparison of the proposed method with training based estimation method, which is presented by computer simulations, show the effectiveness of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.

A robust disturbance reduction scheme for linear small delay systems with disturbances of unknown frequencies

A robust disturbance reduction scheme for linear small delay systems with disturbances of unknown frequencies is presented in this paper. Unlike other methods, the proposed scheme does not require disturbance frequencies to be known. The linear systems modeled in this study are nominally stable and minimum phase systems with relative degree. The control structure is an integration of Astrom’s modified Smith predictor and the proposed scheme. The proposed scheme consists of an input disturbance reduction controller (IDRC) and a residual disturbance reduction controller (RDRC). The IDRC using an artificial neural network (ANN) is proposed to reduce unknown load disturbances and modeling uncertainties in stable systems and unstable systems. The ANN can appropriately approximate the product of an inverse time delay and a nonnegative gain in the IDRC. The residual signals including residual disturbances and residual uncertainties are suppressed by the RDRC based on a disturbance observer. Simulation examples are illustrated to show the effectiveness of the proposed robust disturbance reduction scheme for linear delay uncertain systems with periodic or non-periodic unknown load disturbances.

Synthesis of continuous-time dynamic quantizers for quantized feedback systems

This paper focuses on analysis and synthesis methods of continuous-time dynamic quantizers for quantized feedback systems. Our aim is to find a quantizer such that a given linear system is optimally approximated by the given linear system with the quantizer in terms of invariant set analysis. In the case of minimum phase systems, this paper clarifies that an optimal dynamic quantizer and its performance are parameterized by a design parameter. Otherwise, this paper derives the stable quantizer synthesis condition that can be recast as parameter dependent linear matrix inequalities.

730 並列モデルを用いた非最小位相系の未知外乱推定

Many methods have been proposed for the unknown disturbance estimation. However, these methods are mainly for minimum phase systems but a few methods can be applied to non-minimum phase systems. Moreover, it is difficult to improve unknown disturbance estimation performances because of the phase lags of non-minimum phase systems. In the present paper, a new design procedure of an unknown disturbance observer by using a parallel feedforward mode is proposed and the effectiveness of the proposed method is verified by numerical simulations.

Asymptotic Stability of the Golden‐Section Control Law for Multi‐Input and Multi‐Output Linear Systems

This paper is concerned with the problem of the asymptotic stability of the characteristic model‐based golden‐section control law for multi‐input and multi‐output linear systems. First, by choosing a set of polynomial matrices of the objective function of the generalized least‐square control, we prove that the control law of the generalized least square can become the characteristic model‐based golden‐section control law. Then, based on both the stability result of the generalized least‐square control system and the stability theory of matrix polynomial, the asymptotic stability of the closed loop system for the characteristic model under the control of the golden‐section control law is proved for minimum phase system.

Positive stable realizations of fractional continuous-time linear systems

Positive stable realizations of fractional continuous-time linear systemsConditions for the existence of positive stable realizations with system Metzler matrices for fractional continuous-time linear systems are established. A procedure based on the Gilbert method for computation of positive stable realizations of proper transfer matrices is proposed. It is shown that linear minimum-phase systems with real negative poles and zeros always have positive stable realizations.

The Frequency Modulation Response of Vertical-Cavity Surface-Emitting Lasers: Experiment and Theory

The FM response of vertical-cavity surface-emitting lasers (VCSELs), i.e., the dynamic wavelength tuning behavior, is scrutinized. The FM amplitude and phase shift are measured up to 80 MHz for GaAs-, InP-, and GaSb-based VCSELs from 763 to 2300 nm. From measurements, it is found that the FM response consists of three components: intrinsic thermal tuning (dominating to several megahertz) with characteristic 1/√(if) behavior, the plasma effect (dominating from several megahertz), and a small effect (10-100 Hz) caused by the interaction of laser chip and submount. All effects are modeled and the measurement data are fitted to obtain effective thermal diffusivities, strength of the plasma effect, and time constant of the laser chip submount interaction. Comparing thermal models with different asymptotic behaviors, an approximation of the heat source in the laser with a nonzero thickness turned out to be necessary. Due to the plasma effect, with influence starting at 100 kHz, VCSELs cannot be considered a minimum phase system, which makes separate amplitude and phase measurements essential for device characterization. The “ N time constants model” is the proper choice for empirical description of the intrinsic thermal tuning component. The best fit coefficients to a rational frequency response are given for use in time-domain simulation programs.