Numerical Study on Identification of Transfer Functions in a Feedback System and Model Reduction

A unified theory of identification in a feedback system is presented from the viewpoint of inverse problem on reactor noise. A power reactor described by a 4 block feedback model is expressed in terms of equivalent correlation functions as a 5 block feedback model with an additional loop, if one of subsystems of the reactor becomes unstable, however, the total system is stable by negative feedback effects, and if noise sources are not independent. The addition of a loop in the feedback system leads errors in estimation of open loop transfer functions. In the case, modified open loop transfer functions are identified instead of original ones. From the viewpoint of reactor diagnosis, notes on system identification are discussed on an open loop transfer function in a low power reactor and on effects of diagonalization in covariance space of noise sources.

Identification of Transfer Function in a Feedback System and Autoregressive Analysis

Although the dynamic characteristics of the baroreflex system have been described by baroreflex transfer functions obtained from open-loop analysis, the predictability of time-series output dynamics from input signals, which should confirm the accuracy of system identification, remains to be elucidated. Moreover, despite theoretical concerns over closed-loop system identification, the accuracy and the predictability of the closed-loop spontaneous baroreflex transfer function have not been evaluated compared with the open-loop transfer function. Using urethane and α-chloralose anaesthetized, vagotomized and aortic-denervated rabbits (n = 10), we identified open-loop baroreflex transfer functions by recording renal sympathetic nerve activity (SNA) while varying the vascularly isolated intracarotid sinus pressure (CSP) according to a binary random (white-noise) sequence (operating pressure ± 20 mmHg), and using a simplified equation to calculate closed-loop-spontaneous baroreflex transfer function while matching CSP with systemic arterial pressure (AP). Our results showed that the open-loop baroreflex transfer functions for the neural and peripheral arcs predicted the time-series SNA and AP outputs from measured CSP and SNA inputs, with r2 of 0.8 ± 0.1 and 0.8 ± 0.1, respectively. In contrast, the closed-loop-spontaneous baroreflex transfer function for the neural arc was markedly different from the open-loop transfer function (enhanced gain increase and a phase lead), and did not predict the time-series SNA dynamics (r2; 0.1 ± 0.1). However, the closed-loop-spontaneous baroreflex transfer function of the peripheral arc partially matched the open-loop transfer function in gain and phase functions, and had limited but reasonable predictability of the time-series AP dynamics (r2, 0.7 ± 0.1). A numerical simulation suggested that a noise predominantly in the neural arc under resting conditions might be a possible mechanism responsible for our findings. Furthermore, the predictabilities of the neural arc transfer functions obtained in open-loop and closed-loop conditions were validated by closed-loop pharmacological (phenylephrine and nitroprusside infusions) pressure interventions. Time-series SNA responses to drug-induced AP changes predicted by the open-loop transfer function matched closely the measured responses (r2, 0.9 ± 0.1), whereas SNA responses predicted by closed-loop-spontaneous transfer function deviated greatly and were the inverse of measured responses (r, −0.8 ± 0.2). These results indicate that although the spontaneous baroreflex transfer function obtained by closed-loop analysis has been believed to represent the neural arc function, it is inappropriate for system identification of the neural arc but is essentially appropriate for the peripheral arc under resting conditions, when compared with open-loop analysis.

Self–excited combustion oscillations arise from a coupling between unsteady combustion and acoustic waves, and can cause structural damage to many combustion systems. Active control provides a way of extending the system's stable operating range by interrupting the damaging thermoacoustic interaction. The active controller considered injects some fuel unsteadily into the burning region, thereby altering the heat–release rate, in response to an input signal detecting the oscillation. Although the feasibility of such a control configuration was demonstrated on laboratory–scale experiments over 15 years ago, the triple requirement for full–scale applications is to adapt the controller response to varying operating conditions and to guarantee that the controller will cause no harm, while relying as little as possible on a particular combustion model. As a first step towards meeting these requirements, a self–tuning regulator (STR) is proposed in this paper for a class of combustion systems that satisfy some fairly non–restrictive assumptions. An open–loop transfer function from the controller output voltage driving the actuator to the pressure signal detecting the oscillation is derived, and is shown to be the product of a time delay τ tot and a transfer function that satisfies certain structural properties. Using the open–loop transfer function, it is shown that the stabilizing STR structure is that of a simple phase–lead compensator if τ tot=0, and the same compensator combined with a Smith controller if τ tot=0. The adaptive rule for the adjustment of the STR parameters is derived from a Lyapunov stability analysis. Promising results are obtained on a simulation based on a nonlinear premixed flame model and on an experimental set–up which consists of a laminar flame burning in a Rijke tube.

A new tuning method for Fractional Order Controllers (FOC) based on Bode’s ideal transfer function as a reference model is proposed in this paper. The proposed fractional order controller parameters are obtained by a simple tuning technique in two steps. In the first step, the open loop reference fractional integrator is designed according to the desired performances, and then approximated by a rational transfer function using Charef’s or Oustaloup’s approximation method. In the second step, a standard pole placement technique is used to align each pole of the plant transfer function with the nearest one of the Rational Function Approximation (RFA). The FOC transfer function is then obtained by gathering the remained poles and zeros of the RFA. The most innovative character of the proposed method is its simplicity and its remarkable performances in terms of robustness towards the variation of the static gain. Simulation of some illustrative examples confirms and validates the proposed method.

On closed-loop system identification using polyspectral analysis given noisy input–output time-domain data

In this paper, a fractional-order derivative controller has been designed to control a double integrator plant towards satisfying the specific design criterions of frequency domain. The design approach employs a reference model. The open loop transfer function of the reference model is given by the Bode's ideal transfer function. The design is accomplished in two stages. At first, the reference model is obtained from the given design specifications and the transfer function of the continuous-time fractional-order derivative controller is derived subsequently. In the next stage, the fractional-order controller (FOC) has been realised in delta-domain involving continued fraction expansion method. The efficacy of the presented design methodology has been established through a comparative study with one of the conventional approaches pertaining to discrete-time implementation of FOC. The robustness of the closed loop controlled system is also tested against the uncertain plant gain. The essential simulation results have been presented using MATLAB.

Identification of transfer functions and statistical inverse problems

The aim of the paper is to present the simple method of determining a fractional order controller to control the pump in Festo MPS® PA Compact Workstation. Transfer function of the controller follows directly from using of Bode's ideal transfer function as a reference one for the open loop system. Such systems generally are unsensitive to gain changes in the open loop. In Festo MPS® PA Compact Workstation by using a corresponding controllers a level and a flow rate can be set up as a cascade control system. The design process allows to use conventional continuous P, I, PI, PID controllers and discontinuous controllers (two-point controllers). In the presented study the fractional order controller is tested to obtain parameters controller of this system.

Improved Decentralized PID Controller design for MIMO Processes

The synthesis of fixed order controllers for nonlinear systems with sector bounded nonlinearities is considered. The authors constructed an inner and outer approximation of the set of absolutely stabilising linear controllers by casting the closed loop system as a Lure–Postnikov system. The inner approximation is based on the well-known sufficient conditions that require strict positive realness (SPR) of open loop transfer function (possibly with some multipliers) and a characterisation of SPR transfer functions that require a family of complex polynomials to be Hurwitz. The outer approximation is based on the condition that the open loop transfer function must have infinite gain margin, which translates to a family of real polynomials being Hurwitz. The authors illustrate the proposed methodology through the construction of an inner and outer approximation of absolutely stabilising controllers for a mechanical system.

The proposed cascade control design for both minimum and non-minimum phase delayed time processes is based on the keeping the open loop transfer function same. The controller parameters are interms of the tuning paramter and process parameters for both primary and secondary time delayed processes. The proposed controller parameters having tuning paramters and are tuned based on the desired robust stability factor Ms. Numurous different order minimum and non minimum processes are tested by the proposed method and four examples are presented to show the effectiveness of the proposed method. The proposed method have evaluated based on the integral error creteria such as ITSE, ISE, ITAE and IAE values with desired robustness. The proposed method have compared with the recent literature methods and gives improved performance both unperturbed and purturbed processes. The proposed technique was validated on the cascade experimental setup and outcomes demonstrated significant improvements in performance.

In this paper, we investigate the structure of the transfer function set which includes all the transfer functions deduced from the plant available information. It is shown that when an upper bound of the plant transfer function's H/sup /spl infin//-norm has been supplied, and the noise contaminating the time domain identification experiment data is not too significant, such a transfer function set can be parameterized by a linear fractional transformation of two transfer function matrices. One of them is a fixed transfer function matrix which is completely determined by the plant available information and the noise magnitude. The other is a norm bounded, structure fixed, free transfer function matrix. Moreover, it is shown that the problem of analytically obtaining the fixed complexity nominal model that best approximates this transfer function set is as difficult as the /spl mu/-synthesis problem. >

From the viewpoint of stochastic inverse problem, identification of transfer functions in feedback systems has been examined by the previous papers[1][2]. In this paper it is applied for a new approach to electroencephalography (EEG). Some transfer functions between measurement regions of EEG are identified by our method of inverse problem in a stochastic feedback system. In our method for stochastic inverse problem an innovation model must be self-consistent: Since an innovation model equivalent to correlation functions has minimum phase and suitable properties from the theoretical considerations[3], innovation models with their properties are selected for dynamic analysis of EEG. Hence, a stochastic feedback model in the stationary process can be determined from EEG time series data of measurement regions, and we can obtain transfer functions between measurement regions.

In this chapter, the authors explore how to apply the Youla parameterization method to MIMO systems. Similar to the SISO feedback loop, they discuss the role of neoclassical control for MIMO feedback control design. The authors present equivalent MIMO feedback loops which Youla parameterization technique could be utilized either directly (Internal Model Control) or utilized to compute a MIMO feedback controller. In neoclassical control, the performance and robustness criteria are achieved by direct frequency loop-shaping of three different closed-loop transfer function matrices, Youla, sensitivity, and complementary sensitivity. The authors then investigate the performance and robustness criteria for MIMO feedback controller design. They also extend their MIMO control design approach to unstable plants.