Single-input Single-output Transfer Function Research Articles

Simultaneous separation of ternary mixture using modified dual compression middle vessel batch distillation column: Control and dynamic optimization

BackgroundMultivessel batch distillation has been found to be an effective method for the separation of multi-component mixtures. In this article, an effort has been made to devise a fast middle vessel batch distillation column (MVBDC) for the ternary separation of an Ethanol/Propanol/Butanol mixture by the means of inducing vapor compression in the system. MethodsASPEN PLUS V12 has been used to generate the initial steady-state flowsheet of the process for equipment sizing. In contrast, ASPEN Dynamics was used to evaluate the performance of the batch distillation with various control structures and to perform a dynamic optimization on the proposed batch distillation column. MATLAB was used to identify single-input single-output transfer functions for more effective PID controller tuning. Significant FindingsThe proposed Middle vessel batch distillation was found to separate each component of the mixture to a purity of 99 mol% in 22 h (for the cascade control structures) and 21.73 h (for the temperature control structure). This was found to be significantly lesser than the batch time of a conventional batch distillation column (28.12 h), while the energy consumed by the proposed column was 3.4 MMkcal lesser than the energy consumed by the conventional column. Dynamic optimization further reduced the batch time by 14.4% while simultaneously reducing the energy consumed by 20.3%.

Robust model predictive control via multi-scenario reference trajectory optimization with closed-loop prediction

This paper presents a two-layer control structure to address parameter uncertainty within a plant. The lower layer is formulated as a nominal MPC that computes control actions to regulate the underlying plant, and the upper layer computes optimal set-point trajectories for the lower level to track. The upper layer is formulated as an optimization problem that takes into account the closed-loop behavior of uncertain plant scenarios under the action of nominal MPC. The upper layer facilitates the lower layer in avoiding constraint violations and producing less conservative control actions by assigning time-varying set-point trajectories to the nominal MPC. The benefits of this approach are illustrated through application to linear single-input–single-output transfer function case studies, and a nonlinear multi-input multi-output evaporator process.

Parameter Design Oriented Analysis of the Current Control Stability of the Weak-Grid-Tied VSC

This paper studies the dynamic behaviors of weak-grid-tied VSCs with simplified transfer functions, which provides an accurate stability analysis and useful indications for tuning system parameters. A reduced-order multi-input multi-output (MIMO) transfer function that contains four single-input single-output (SISO) transfer functions for the weak-grid-tied VSC is first presented. It is found that the four SISO transfer functions share the same equivalent open-loop transfer function, i.e., the same stability conclusion. The Bode plots of the equivalent open-loop transfer function show that the inner current loop behaves as a band-pass filter whose maximum gain is approximately at the frequency of the PLL's bandwidth. By stability criterion, the harmonic amplification and instability occur when its maximum gain exceeds 0 dB caused by high PLL's bandwidth, large grid impedance or high active power. It is also found that the target system is less stable when it works as an inverter than as a rectifier, due to the risk of the local positive feedback in the inverter mode. An effective criterion is further proposed to guide the selection of a proper PLL's bandwidth to ensure the stability of the VSC system. Simulation results validate the correctness of the analysis and the efficacy of the criterion.

Small-Signal Stability Enhancement Approach for VSC-HVDC System Under Weak AC Grid Conditions Based on Single-Input Single-Output Transfer Function Model

The voltage source converter (VSC) system has stability issue under weak AC grid conditions. In this paper, the multi-input multi-output (MIMO) transfer function model of VSC system in frequency-domain is derived. Then, the individual channel analysis and design (ICAD) approach is employed to develop the equivalent single-input single-output (SISO) feedback control model for stability analysis. On that basis, the stability of VSC system and the coupling interaction intensity among the multiple control loops, including the active power control (APC), reactive power control (RPC) and phase-locked-loop (PLL) are investigated. The results show that larger PLL bandwidth increases the coupling degree of active power control (APC) and reactive power control (RPC) closed loops, resulting in the instability of the system under weak AC grid conditions. Finally, a derivative feedback compensation (DFC) approach is proposed to enhance the stability margin for VSC system connected to weak AC grid. The results based on MATLAB-based theoretical analysis and electromagnetic transient (EMT) simulations show that the proposed DFC approach can effectively suppress the instability of VSC system due to the close coupling of APC and RPC closed loops caused by the large PLL bandwidth, thus effectively improve the stability margin of the system.

SISO Transfer Functions for Stability Analysis of Grid-Connected Voltage-Source Converters

Converter-grid interaction is of great interest in a weak-grid condition. This paper presents a single-input–single-output (SISO) open-loop transfer function for the stability analysis of grid-connected voltage-source converters. Differing from the conventional input impedance method and the eigenvalue analysis, an alternative multi-input–multi-output closed-loop system is developed in the paper and it eventually yields an SISO open-loop transfer function. This enables the application of a single Nyquist curve for analyzing the overall system stability. The model is validated against time-domain simulations as well as experimental results showing excellent accuracy for predicting the system stability.

Seismic upgrade of structures using the H∞ control problem for a general system interconnection paradigm

This paper presents a novel approach for the modification and seismic upgrading of shear-frame structures by attaining and implementing optimal changes in stiffness, changes in mass, and added damping (referred to as the structural changes). A general system interconnection paradigm is proposed and presented. The paradigm is assigned with a passive controller that consists of the structural changes and has simulated feedback on the structural response and the seismic excitation. A newly formulated optimization problem is required to satisfy constraints on maximum total story accelerations and maximum interstory drifts. The objective is to minimize the H∞ norm of a singled out response of the general system interconnection closed-loop transfer function matrix, making it a single-input single-output transfer function case. The control problem is solved by utilizing the first-order steepest descent method, an H∞ synthesis algorithm, for calculating the free parameters of a passive controller which consists of the structural changes. Their method is further enhanced for seismic design needs, by imposing boundaries on the free parameters according to the dynamic response of the structure to given ground motion ensemble. Two numerical examples of a 9-story shear-frame structure and 10-story moment resisting frame are studied. Optimal changes in mass, stiffness, and damping are obtained, and results show significant improvement in the peak dynamic response. The results indicate the efficiency of the proposed procedure that possesses the capability of attaining optimal changes in all physical characteristics of the structure (mass, stiffness, and damping) while adhering to preassigned maximum response levels.

Transfer function representation of cyclic consensus systems

This paper presents explicit forms of transfer functions for a class of cyclic consensus systems with different kinds of network topologies; directed, undirected and different numbers of reference agents. Each agent of consensus systems is assumed to satisfy a scalar integrator dynamics which is driven by a common consensus protocol and an independent exogenous input. It is shown that every single-input single-output (SISO) transfer function between the exogenous input of one agent and the state of another generally different agent, is always minimum phase. In addition, the poles and zeros, system degrees and relative degrees of those SISO transfer functions are specified. These results are interpreted in relation to the controllability and closed loop performance of a networked system with one leader agent. Furthermore, our transfer function representations are applied to an investigation of stability margins for a closed loop cyclic consensus system.

STATE-SPACE MODEL IDENTIFICATION USING INPUT AND OUTPUT DATA WITH STEADY STATE VALUES

In this paper, we propose a new deterministic off-line identification method that obtains a state-space model by using input and output data with steady state values. This method is composed of the method, M. Kosaka, K. Koizumi and H. Shibata Transactions of the Society of Instrument and Control Engineers 36(4), 2000, 319-327. zeroing the 0 ∼ N-tuple integral values of output error of single-input single-output transfer function model and Ho-Kalman's method, H.P. Zeiger and A.J. Mc Ewen, IEEE Transactions on Automatic Control, AC 19-2, 1974, 153. The feature is that this method can identify by using step responses and, consequently, this is suitable for mechanical system identification in which noise and vibration are undesirable. Numerical simulations of multi-input multi-output system identification and experimental results are illustrated.

State-space Model Identification Using Input and Output Data With Steady State Values Zeroing Multiple Integrals of Output Error

This study proposes a new deterministic off-line identification method that obtains a state-space model using input and output data with steady state values. This method comprises of two methods: Zeroing the 0∼N-tuple integral values of the output error of single-input single-output transfer function model (Kosaka et al., 2004) and Ho-Kalman’s method (Zeiger and McEwen, 1974). Herein, we present a new method to derive a matrix similar to the Hankel matrix using multi-input and multi-output data with steady state values. State space matrices A, B, C, and D are derived from the matrix by the method shown in Zeiger and McEwen, 1974 and Longman and Juang, 1989. This method’s utility is that the derived state-space model is emphasized in the low frequency range under certain conditions. Its salient feature is that this method can identify use of step responses; consequently, it is suitable for linear mechanical system identification in which noise and vibration are unacceptable. Numerical simulations of multi-input multi-output system identification are illustrated.

定常値をもつ入出力信号を用いた状態空間モデルの同定

In this paper, we propose a new deterministic off-line identification method that delivers a state-space model by using input and output data with steady state values. This method combines the method zeroing the 0N-tuple integral values of output error of single-input single-output transfer function model and Ho-Kalman's method. The feature is that this method can identify by using step responses and, consequently, this is suitable for a mechanical system identification in which persistent fluctuations are unacceptable. Numerical simulations of multi-input multi-output system identification are illustrated and the practicability is verified by application to a pneumatic two link arm system.

Inherent Feedback Limitations for Distributed Systems *

The purpose of this paper is to show that the Bode integral constraint holds for two classes of linear time invariant single input, single output (SISO) systems. The paper examines the structural properties of SISO transfer functions of parabolic and hyperbolic systems, and relates these properties via the sensitivity integral constraint to feedback system design constraints.

A note on topological realizations of transfer functions in canonical forms

This note investigates the canonical realization of the single-input single-output transfer function. An algorithm for generating all canonical realizations of the transfer function is presented and the alternative formulas for the total number of realizations of the denominator are derived.

Parameter identification using prior information†

Abstract We consider the problem of identifying some unknown gain parameters in a single-input single-output transfer function, which is written as the ratio of proper, stable transfer functions. This technique is a generalization of currently available techniques of identification, which do not use prior information. It usually involves the identification of fewer parameters and is faster in convergence and less susceptible to errors caused by the presence of unmodeled dynamics. Extensions to the discrete-time systems and some multivariable systems are also covered.

On the exact model matching of 3-D discrete systems using feedback control

The exact model matching problem of single input-single output (SISO) systems using feedback control is considered. The closed loop transfer function of a given system is described by its 3-D transfer function, equal to a `desired' transfer function. Since the numerator of a SISO transfer function is not affected by static state feedback, series compensation is used in order to achieve the desired numerator. The problem of selecting the series compensators in the present 3-D case is generally quite involved. However, the model matching problem is very much simplified if the desired 3-D transfer function is factorizable and the state feedback is used to factorize the given transfer function. A step-by-step example is provided to illustrate the procedures.