Continuous-time Transfer Function Models Research Articles

Process Monitoring of Antisolvent Based Crystallization in Low Conductivity Solutions Using Electrical Impedance Spectroscopy and 2-D Electrical Resistance Tomography

Industrial process monitoring is an important field of research where different chemical processes are monitored and controlled. In this work, electrical impedance spectroscopy (EIS) was used to analyze antisolvent based crystallization of sucrose solutions. The impedance and phase spectra were recorded for four known sucrose concentrations in water, and for each case, four predetermined amounts of ethanol were added. As a result, sixteen different solutions involving sucrose solutions of different concentrations and ethanol to water ratios were analyzed. Significant differences were observed in the magnitude and phase spectra of the solutions in the frequency range of 50 kHz to 300 kHz. The experimentally obtained data from the EIS were converted into frequency response models. Three continuous-time transfer function models of the first-order, second-order, and a second-order with a zero were estimated and compared. In addition, a 2-D electrical resistance tomography (ERT) system with a low conductivity sensor unit was designed and tested with demineralized water, tap water and industrial food grade saturated sucrose solution. Non-conducting phantom and sugar crystals were observed within the saturated sucrose solution using the Bayesian reconstruction algorithm. These demonstrations have the potential to be developed into a multi-frequency ERT systems for monitoring the distribution of the crystals in the reactor. The EIS modality can be a complementary process analytical technology (PAT) tool indicating supersaturation status and provide quality assurance.

New developments in the CAPTAIN Toolbox for Matlab with case study examples

The CAPTAIN Toolbox is a collection of Matlab algorithmic routines for time series analysis, forecasting and control. It is intended for system identification, signal extraction, interpolation, forecasting and control of a wide range of linear and non-linear stochastic systems across science, engineering and the social sciences. This article briefly reviews the main features of the Toolbox, outlines some recent developments and presents a number of examples that demonstrate the performance of these new routines. The examples range from consideration of global climate data, through to electro-mechanical systems and broiler chicken growth rates. The new version of the Toolbox consists of the following three modules that can be installed independently or together: off-line, time-varying parameter estimation routines for Unobserved Component (UC) modelling and forecasting; Refined Instrumental Variable (RIV) algorithms for the identification and estimation of both discrete and ‘hybrid’ continuous-time transfer function models; and various routines for Non-Minimal State Space (NMSS) feedback control system design. This new segmented approach is designed to provide new users with a gentler introduction to Toolbox functionality; one that focuses on their preferred application area. It will also facilitate more straightforward incorporation of novel algorithms in the future.

Closed-loop identification of systems using hybrid Box–Jenkins structure and its application to PID tuning

The paper describes a closed-loop system identification procedure for hybrid continuous-time Box–Jenkins models and demonstrates how it can be used for IMC based PID controller tuning. An instrumental variable algorithm is used to identify hybrid continuous-time transfer function models of the Box–Jenkins form from discrete-time prefiltered data, where the process model is a continuous-time transfer function, while the noise is represented as a discrete-time ARMA process. A novel penalized maximum-likelihood approach is used for estimating the discrete-time ARMA process and a circulatory noise elimination identification method is employed to estimate process model. The input–output data of a process are affected by additive circulatory noise in a closed-loop. The noise-free input–output data of the process are obtained using the proposed method by removing these circulatory noise components. The process model can be achieved by using instrumental variable estimation method with prefiltered noise-free input–output data. The performance of the proposed hybrid parameter estimation scheme is evaluated by the Monte Carlo simulation analysis. Simulation results illustrate the efficacy of the proposed procedure. The methodology has been successfully applied in tuning of IMC based flow controller and a practical application demonstrates the applicability of the algorithm.

Identification of MIMO Continuous-Time Models Using Simultaneous Step Inputs

A new approach for identification of multi-input multi-output (MIMO) continuous-time transfer function models using simultaneous step input signals is proposed. MIMO processes exhibit directionality which implies that the output gains depend on the input magnitudes as well as the ratios of the inputs. Due to this directionality issue, MIMO models estimated by sequentially changing one input at a time often do not result in satisfactory tracking performance when used for model based control. In the proposed methodology all of the inputs are changed simultaneously to resemble controlled conditions. While the identification tests remain multi-input in its true sense, the parameter estimation steps involve estimation of the parameters of a single transfer function at a time. Moreover, the time delays are estimated in the same way as the coefficients in the model. Simulation results are presented to demonstrate the robustness of the methodology and its applicability to processes with high input–output dimensio...

Comparison of Prediction Models for a Dual-Hormone Artificial Pancreas

In this paper we compare the performance of five different continuous time transfer function models used in closed-loop model predictive control (MPC). These models describe the glucose-insulin and glucose-glucagon dynamics. They are discretized into a state-space description and used as prediction models in the MPC algorithm. We simulate a scenario including meals and daily variations in the model parameters. The numerical results do not show significant changes in the glucose traces for any of the models, excepted for the first order model. From the present study, we can conclude that the second order model without delay should provide the best trade-off between sensitivity to uncertainties and practical usability for in vivo clinical studies.

Control of AGC in Interconnected Power System with Diverse Sources of Power Generation

In this paper, automatic generation control (AGC) of two area interconnected power system having diverse sources of power generation is studied. A two area power system comprises power generations from hydro, thermal and gas sources in area-1 and power generations from hydro and thermal sources in area-2. All the power generation units from different sources are equipped with speed governors. A continuous time transfer function model of the system for studying dynamic response for small load disturbances is presented. A proportional-integral-derivative (PID) automatic generation control scheme is applied only to power generations from thermal and gas sources and power generation from hydro source is allowed to operate at its scheduled level with only speed governor control. The two area power system is simulated for different nominal loading conditions. Particle Swarm Optimization (PSO) is used to obtain the optimal PID gains for various cases using integral squared error plus integral time absolute error (ISE+ITAE) performance index for fitness evaluation. Some of the transient responses are shown for different nominal loading conditions due to step load disturbances in the system.

Continuous-Time Identification Using Sinusoidal Inputs: An Integral Equation Approach

An integral equation approach for identification of continuous-time transfer function models from sinusoidal test data is proposed. Using a single-frequency sinusoidal input signal, the algorithm simultaneously estimates the model parameters and the time delay from the process response and the analytical expression of the input. Estimation equations for first-, second-, and a general nth-order models are derived. Simulation results for identification of first- and second-order processes are presented to demonstrate the efficacy of the proposed methodology. The robustness of the algorithm is demonstrated using identification results for different noise levels in the output. Use of sinusoids with widely varying frequency and phase shows the flexibility in input design. Identification results of a simulated continuous stirred tank reactor are also presented.

Reversing hydrology: Estimation of sub-hourly rainfall time-series from streamflow

A novel solution to the estimation of catchment rainfall at a sub-hourly resolution from measured streamflow is introduced and evaluated for two basins with markedly different flow pathways and rainfall regimes. It combines a continuous-time transfer function model with regularised derivative estimates obtained using a recursive method with capacity for handling missing data. The method has general implications for off-line estimation of unknown inputs as well as robust estimation of derivatives. It is compared with an existing approach using a range of model metrics, including residuals analysis and visuals; and is shown to recover the salient features of the observed, sub-hourly rainfall, sufficient to produce a precise estimate of streamflow, indistinguishable from the output of the catchment model in response to the observed rainfall data. Results indicate potential for use of this method in environment-related applications for periods lacking sub-hourly rainfall observations.

Comment on ‘Projection-based identification algorithm for grey-box continuous-time models’ by Ichiro Maruta and Toshiharu Sugie

Although the paper by Maruta and Sugie (2013) makes an interesting contribution to the literature on the estimation of parameters in grey-box, continuous-time transfer function models, some of the simulation results are flawed and give a misleading impression of how the algorithm suggested by the authors compares with the well known and closely related SRIVC algorithm.

A Simple Transfer-Function-Based Approach for Estimating Material Parameters From Terahertz Time-Domain Data

A novel parametrically efficient approach to estimating the spectra of short transient signals is proposed and evaluated, with an application to estimating material properties, including complex refractive index and absorption coefficient, in the terahertz frequency range. This technique includes uncertainty analysis of the obtained spectral estimates, allowing rigorous statistical comparison between samples. In the proposed approach, a simple few-parameter continuous-time transfer function model explains over 99.9% of the measured signal. The problem, normally solved using poorly numerically defined Fourier transform deconvolution methods, is reformulated and cast as a time-domain dynamic-system estimation problem, thus providing a true time-domain spectroscopy tool.

Identification of Continuous-time Transfer Function Models from Non-uniformly Sampled Data in Presence of Colored Noise

This paper considers the problem of continuous-time model identification from non-uniformly sampled input-output data, having the measured output corrupted by colored noise. We concentrate on the continuous-time transfer function model identification. A Box-Jenkins model structure is used to describe the system, thus providing independent parameterizations for the plant and the noise. Monte Carlo simulation analysis is also used to illustrate the properties of the proposed estimation method.

The advantages of directly identifying continuous-time transfer function models in practical applications

The direct identification and estimation of continuous-time models from sampled data is now mature. This paper does not present any new methodology, nor does it compare the performance of existing methods. Its main aim is to discuss the advantages of direct, continuous-time model identification with the help of illustrative examples that are all based on real data from practical applications. Although the specific method of statistical parameter estimation is relatively unimportant in this regard, the latest and most sophisticated time domain identification algorithm that is freely available to the reader is used in these examples in order to ensure that the results reflect the best performance that can be achieved at this time by time-domain identification.

Identification of integrating processes with time delay

A set of methods for identification of continuous-time transfer function models for integrating processes with time delay is proposed. The step, piecewise constant and piecewise linear inputs are considered which indeed cover most of the input signals commonly used in industries. For all of the three types of input signals, estimation equations to simultaneously obtain model parameters and the time delay are derived. The final parameter estimation equations are in a form suitable for the least-squares solution. Mathematical formulation of the methods is presented using the example of an integrating process with a first order lag dynamics and a zero which can be extended for other structures. An instrumental variable method to deal with the bias issue in least-squares solutions is used. Simulation results are presented to demonstrate the efficacy of the algorithms and their relative performance.

An optimal control of a wastewater treatment reactor by catalytic ozonation

This paper deals with the control of a wastewater treatment pilot by catalytic ozonation. In general, catalytic ozonation processes operate with a deliberate ozone overproduction to obtain a treated water which respects discharge standards. But, in this case, the oxygen consumption is not optimal and the operating costs are important. The objective of this study focuses on the optimization of the catalytic ozonation reactor. A continuous-time transfer function model is identified to represent the pilot behavior, and an optimal control is proposed to obtain a significant abatement of the pollutant. In this application, the pollutant abatement is represented by the absorbance.

Identification of a MIMO continuous-time transfer function model with different denominators

This paper is about the identification of a MIMO continuous-time (CT) transfer function model with different denominators. A new algorithm is proposed with two main steps. The first step consists of the estimation of an overparameterized MIMO CT reinitialized partial moment model and the second one performs a moment-based transfer function model reduction. For the unknown structure case, a system structure estimation procedure is given.

Performance assessment and redesign of PI controllers with pulse excitations

In this paper a methodology is presented to assess the performance of PI controllers from closed-loop response data for pulse setpoint signal. Here a previously published technique is extended to evaluate and redesign single-input single-output (SISO) control loops for single and double pulses. The paper describes a system identification procedure for continuous-time transfer function models and demonstrates how it can be used for control performance assessment and controller redesign.

On embedded FIR filter models for identifying continuous-time and discrete-time transfer functions: the RPM approach

For identifying a continuous-time (CT) transfer function model, data filtering is a solution which provides the necessary unmeasurable input--output derivative approximations. In discrete-time (DT) system identification, the well-known ARX model can be used successfully if the estimate is performed with suitable prefiltered data. This article describes the reinitialised partial moment (RPM) model which embeds implicitly a finite impulse response filter in both CT and DT domains. With knowledge of the important role of data prefiltering in standard methods, this RPM model embedded filter gives particular properties to this original tool. Although both the CT RPM model and the DT RPM model present an embedded filter, the formulation and the implementation in the CT and the DT domains are different. Therefore, the aim of this article is to present a tutorial on the RPM models and to give an overview of all the applications.

StepID - A Matlab-based toolbox for identification fromstep response

Abstract For advanced control, transfer function models are widely used and identification from step response is a common choice in process industries to obtain such models. Over the last decade, significant developments have taken place in the field of identification from step response using the so-called integral equation approach. However, these developments have not been included in the identification tools available commercially. This work focuses on development of a MATLAB toolbox in the form of a graphical user interface (GUI) that will be a specialized tool for identification from step response. Due to the recent advancement in data storage capacity, industries have become repositories of enormous amounts of data. However, proper tools are needed to extract valuable information from raw data. The development of the toolbox started as an Undergraduate Research Experience Program (UREP) project from the 5th cycle and it was further modified and extended in the 7th cycle. The functionality of the toolbox includes data import from an excel file or a MAT file, preprocessing of data and the use of different methods to estimate continuous time transfer function model parameters of different orders under different conditions of the process. The toolbox includes methodologies to estimate model parameters and time delay simultaneously under steady or unsteady initial conditions using least squares and instrumental variable method. Methodologies to handle higher order models and non-minimum phase processes are also included. Finally, the toolbox has the capability to choose the best model from a list of models obtained using different methods.

Automatic generation control of interconnected power system with diverse sources of power generation

In this paper, automatic generation control (AGC) of two area interconnected power system having diverse sources of power generation is studied. A two area power system comprises power generations from hydro, thermal and gas sources in area-1 and power generations from hydro and thermal sources in area-2. All the power generation units from different sources are equipped with speed governors. A continuous time transfer function model of the system for studying dynamic response for small load disturbances is presented. A proportional-integral-derivative (PID) automatic generation control scheme is applied only to power generations from thermal and gas sources and power generation from hydro source is allowed to operate at its scheduled level with only speed governor control. The two area power system is simulated for different nominal loading conditions. Genetic algorithm (GA) is used to obtain the optimal PID gains for various cases using integral squared error plus integral time absolute error (ISE+ITAE) performance index for fitness evaluation. Some of the transient responses are shown for different nominal loading conditions due to step load disturbances in the system. Keywords: Two area power system, Diverse sources of power generation, Automatic generation Control , Genetic algorithm, PID controller

Data-Based Mechanistic Modeling of Flow-Concentration Dynamics of Non-Point Source Pollution: A Case of Upper Vaal Water Management Area

This study aimed at applying the Data Based Mechanistic (DBM) modelling approach to develop a simple, parsimonious and discernable Flow-Concentration (F-C) model that can be partitioned into the various identifiable pathways associated with the pollutant at the catchment scale. An attempt was made to model the occurrence of acid mine drainage (AMD) in the Vaal River by using an indicator water quality parameter (sulphate concentration). The optimal Instrumental Variable (IV) methods of identifying and estimating discrete and continuous-time transfer function models as implemented in the CAPTAIN MATLAB® Toolbox were applied to the time series data in order to identify the appropriate model. A discernable F-C model was developed of three parallel pathways: the “quick-route” depletion pathway with a residence time months; a “slow-route” build-up pathway with a residence time months and a direct term component pathway regressed in 9 months. The resulting model showed that it is possible to use the DBM modelling approach to address the problem of representing the potential lag between polluting activity and its effect as well as provide more salient information about the system dynamics. This kind of information (i.e. the residence times and the advective time delays in the system) could prove useful for the catchment managers in making informed decisions including laying out remediation measures. Keywords: Flow-Concentration Modelling, Non-Point Source Pollution, Data Based Mechanistic Modelling, Transfer Function models, Water Quality, Flow Pathways