Continuous-time Transfer Function Research Articles

Particle swarm optimization solution for roll-off control in radiofrequency ablation of liver tumors: Optimal search for PID controller tuning.

The study investigates the efficacy of a bioinspired Particle Swarm Optimization (PSO) approach for PID controller tuning in Radiofrequency Ablation (RFA) for liver tumors. Ex-vivo experiments were conducted, yielding a 9th order continuous-time transfer function. PSO was applied to optimize PID parameters, achieving outstanding simulation results: 0.605% overshoot, 0.314 seconds rise time, and 2.87 seconds settling time for a unit step input. Statistical analysis of 19 simulations revealed PID gains: Kp (mean: 5.86, variance: 4.22, standard deviation: 2.05), Ki (mean: 9.89, variance: 0.048, standard deviation: 0.22), Kd (mean: 0.57, variance: 0.021, standard deviation: 0.14) and ANOVA analysis for the 19 experiments yielded a p-value ≪ 0.05. The bioinspired PSO-based PID controller demonstrated remarkable potential in mitigating roll-off effects during RFA, reducing the risk of incomplete tumor ablation. These findings have significant implications for improving clinical outcomes in hepatocellular carcinoma management, including reduced recurrence rates and minimized collateral damage. The PSO-based PID tuning strategy offers a practical solution to enhance RFA effectiveness, contributing to the advancement of radiofrequency ablation techniques.

Fully real-time configurable analogue implementation of continuous-time transfer function: Application on fractional controller

This paper proposes a new electronic analog circuit to realize real-time fully configurable continuous-time transfer function. The proposed circuit serves various purposes, including smart controllers, fractional-order controllers, optimal controllers, anti-aliasing filter, and programmable filters. The input signal of the transfer function is continuous and remains continuous throughout the circuit until the output signal is obtained. The proposed approach decomposes the transfer function into elementary first and/or second-order low-pass filters. A new analog first-order low-pass filter circuit is presented, offering advantages over conventional active first-order low-pass filters circuits. These benefits include DC gain and time constant independent of resistor ohmic values, enabling the use of smaller resistors and capacitors for low frequencies, and an expanded frequency working range. Similarly, a new analog circuit for a second-order low-pass filter is proposed, specifically used to obtain complex conjugate poles. The use of digital potentiometers and digital switches controlled by a micro-controller, makes this analog circuit configurable in real-time. As an application, the new circuit is used to realize fractional integrator controller. The circuit gives good similarity between theoretical and experimental measurements.

Analog real time tunable and configurable fractional order PID controller realization

Fractional-order controllers are modeled using irrational continuous-time transfer functions. Implementing these controllers in analogue form can be challenging, particularly if their parameters need to be adjusted in real-time. This paper presents an analogue implementation of a fractional PID controller that can be adjusted and configured in real-time. The controller can be configured as PIαDf, PIDβ, PIα, PDβ, Iα, Dβ. The signal within the proposed controller’s circuit stays analog and is not converted into discrete values. A prototype of the controller is tested. The results of the frequency and time domain validations indicated similarity between the theoretical, simulated and experimental measurements.

Safe Experimentation Dynamics Algorithm for Identification of Cupping Suction Based on the Nonlinear Hammerstein Model

The use of cupping therapy for various health benefits has increased in popularity recently. Potential advantages of cupping therapy include pain reduction, increased circulation, relaxation, and skin health. The increased blood flow makes it easier to supply nutrients and oxygen to the tissues, promoting healing. Nevertheless, the effectiveness of this technique greatly depends on the negative pressure's ability to create the desired suction effect on the skin. This research paper suggests a method to detect the cupping suction model by employing the Hammerstein model and utilizing the Safe Experimentation Dynamics (SED) algorithm. The problem is that the cupping suction system experiences pressure leaks and is difficult to control. Although, stabilizing the suction pressure and developing an effective controller requires an accurate model. The research contribution lies in utilizing the SED algorithm to tune the parameters of the Hammerstein model specifically for the cupping suction system and figure out the real system with a continuous-time transfer function. The experimental data collected for cupping therapy exhibited nonlinearity attributed to the complex dynamics of the system, presenting challenges in developing a Hammerstein model. This work used a nonlinear model to study the cupping suction system. Input and output data were collected from the differential pressure sensor for 20 minutes, sampling every 0.1 seconds. The single-agent method SED has limited exploration capabilities for finding optimum value but excels in exploitation. To address this limitation, incorporating initial values leads to improved performance and a better match with the real experimental observations. Experimentation was conducted to find the best model parameters for the desired suction pressure. The therapy can be administered with greater precision and efficacy by accurately identifying the suction pressure. Overall, this research represents a promising development in cupping therapy. In particular, it has been demonstrated that the proposed nonlinear Hammerstein models improve accuracy by 84.34% through the tuning SED algorithm.

State space construction for continuous time transfer function matrices via Nerode equivalence

AbstractIn this paper, we show that a minimal state space realization in Jordan canonical form for linear multivariable continuous‐time systems described by rational transfer function matrices could be obtained in a natural and basic way by using the concept of Nerode equivalence. While the minimal state space realization is known, the contribution of this note is to provide an alternative realization procedure which is directly introduced in a simple and self‐contained manner. Both scalar and multivariable cases in the continuous‐time setting are discussed. The presentation also provides a concrete construction of rational vector function with preassigned poles to interpolate any 2‐norm bounded analytical vector function in the open left‐half of the complex plane. The basic idea of Nerode equivalence is that the state can be identified with a corresponding equivalence class of inputs. For a linear finite dimensional time‐invariant continuous‐time system, the zero state is identified with the kernel of certain Hankel operator. This characterization via Nerode equivalence class sheds light on the construction of state for general nonlinear input–output systems.

Implementation and Validation of a Simple Direct Identification Method for an Experimental Multi-Span Web Transport System

The industrial processes that require the use of the web require a control system which allows for preserving the properties of the web unaltered, avoiding the risk of wrinkling, tearing, breakage and other defects. This control generally takes place by detecting the tension and the speed in certain points of the system since these variables determine the stress state on the web, which, if altered beyond certain ranges, can lead to the defects mentioned above. The problem of tension and web speed control is very demanding because the system’s dynamic is a function of many process variables that often vary over a wide range. In this study, an experimental system consisting of 12 rollers, four motorised, was analysed. This system was divided into four subsystems according to the logic of decentralised control. The tension of the initial and final subsystems and the speeds of the two central subsystems were monitored. This study proposes estimating continuous-time transfer functions using experimental time-domain data. A nonlinear least-squares search-based method minimises a weighted prediction error norm for directly identifying the mathematical model used to describe the web transport system. To test the performance of the proposed strategy, experimental data were collected in an open-loop configuration with constant voltage given to the four servo motors. The collected data were subsequently processed to define an extremely simple system model composed of a very limited number of parameters representing the system through transfer functions. The model was further validated by comparing the results obtained through simulations with the experimental data obtained with different inputs, and was also validated with some closed-loop tests.

Model Predictive Control for Blending Processes in Cement Plants

In this paper, we discuss model predictive control applied to blending processes. Blending processes are ubiquitous in the chemical process industries since reactants usually need to be mixed before entering a reactor. Many times, the blending is trivial as pure streams of reactants are mixed. We consider non-trivial blending problems in which non-pure streams with the reactants are to be mixed. The motivating example is the blending problem that occurs in cement production. The raw mix for the cement kiln must have a specified chemical composition. This composition is obtained by mixing piles with different chemical compositions and economic value such that the raw mix meets specifications in the cheapest possible way. We formulate the blending problem as a nonlinear optimization problem that can be approximated well as a convex quadratic optimization problem. We implement the corresponding nonlinear and linear model predictive controllers (NMPC, LMPC) using a continuous-time transfer function description that is realized as a discrete-time linear state space model. The controller obtains feedback by combining regularly sampled online measurements and irregularly sampled laboratory measurements using a time variant dynamic Kalman filter with memory. Numerical simulations demonstrate that the NMPC and LMPC have similar performance.

Identification of Dynamical Systems Through the Structure of Auto-regression With Exogenous Variable by Decreasing Gradient and Least Squares

In this article was made the identification of dynamic systems of first and second order more common in electronics such as low and high pass filters of the first order, pass-band filter and direct current motor through the structure of auto-regression with exogenous variable. The proposed dynamical systems are initially modeled by a continuous-time transfer function using physical laws. Subsequently, a step entry signal was applied and the data for the identification process was recorded in discrete time. The estimation of parameters was performed with the method of decreasing gradient and least squares. It was obtained as a result that the least squares method could not find a model for the first-order high-pass filter, but the decreasing grade method allowed to model all the proposed systems.

Quadrotor Attitude Dynamics Identification Based on Nonlinear Autoregressive Neural Network with Exogenous Inputs

ABSTRACT In the case of quadrotors, system identification is a challenging task because quadrotors are inherently unstable exhibit nonlinear behavior and significant coupling. In addition to this, quadrotors’ behavior is greatly influenced by characteristics and coefficients, which are very hard to measure directly or determine analytically. However, all the difficulties listed above are known to be successfully overcome by the use of artificial intelligence. In this paper, two system identification techniques were applied and compared to model quadrotor attitude dynamics. These techniques are Nonlinear Autoregressive Network with Exogenous Inputs (NARX) and continuous-time transfer function.

Simplified Realization of Zero Phase Error Tracking

Abstract Zero phase error tracking (ZPET) control has gained popularity as a simple yet effective feedforward control method for tracking time varying desired trajectories by the plant output of a continuous time transfer function of relative order greater than or equal to two. In this paper, we will note that the sampling zeros of the zero-order hold equivalent of chain of integrators, 1/sn, are configured for natural realization of zero phase error tracking. This property is exploited to realize a simplified realization of zero phase error tracking control for chain of integrators. The property can also be utilized for general transfer functions when the sampling period for digital control is small. The effectiveness of the proposed approach for general transfer functions is demonstrated by simulations.

Detection of Meniscal Tear Effects on Tibial Vibration Using Passive Knee Sound Measurements.

To evaluate whether non-invasive knee sound measurements can provide information related to the underlying structural changes in the knee following meniscal tear. These changes are explained using an equivalent vibrational model of the knee-tibia structure. First, we formed an analytical model by modeling the tibia as a cantilever beam with the fixed end being the knee. The knee end was supported by three lumped components with features corresponding with tibial stiffnesses, and meniscal damping effect. Second, we recorded knee sounds from 46 healthy legs and 9 legs with acute meniscal tears (n = 34 subjects). We developed an acoustic event ("click") detection algorithm to find patterns in the recordings, and used the instrumental variable continuous-time transfer function estimation algorithm to model them. The knee sound measurements yielded consistently lower fundamental mode decay rate in legs with meniscal tears ( 16 ±13 s - 1) compared to healthy legs ( 182 ±128 s - 1), p < 0.05. When we performed an intra-subject analysis of the injured versus contralateral legs for the 9 subjects with meniscus tears, we observed significantly lower natural frequency and damping ratio (first mode results for healthy: [Formula: see text]injured: [Formula: see text]) for the first three vibration modes (p < 0.05). These results agreed with the theoretical expectations gleaned from the vibrational model. This combined analytical and experimental method improves our understanding of how vibrations can describe the underlying structural changes in the knee following meniscal tear, and supports their use as a tool for future efforts in non-invasively diagnosing meniscal tear injuries.

Identification of cardiac afterload dynamics from data

The prospect of ex vivo functional evaluation of donor hearts is considered. Particularly, the dynamics of a synthetic cardiac afterload model are compared to those of normal physiology. A method for identification of continuous-time transfer functions from sampled data is developed and verified against results from the literature. The method relies on exact gradients and Hessians obtained through automatic differentiation. This also enables straightforward sensitivity analyses. Such analyses reveal that the 4-element Windkessel model is not practically identifiable from representative data while the 3-element model underfits the data. Pressure–volume (PV) loops are therefore suggested as an alternative for comparing afterload dynamics.

The Multivariable Control of Carbon Dioxide Absorption System using the Proportional Integral Plus (PIP) Controller

The present article investigates the implementation of non-minimal state space (NMSS) representation with proportional-integral-plus (PIP) controller for the carbon dioxide absorption process of Shiraz petrochemical ammonia unit. The PIP controller is a logical extension of conventional PI/PID controllers with additional dynamic feedback and input compensators. PIP controller is used for multivariable control without limitation on the number of controlled variables. A Multi Input - Multi Output (MIMO) square model was extracted from step response test. In this way, input water flow rate to carbon dioxide absorption system, the heat duty of input absorbent cooler to tray (1) of absorption tower and re-boiler heat duty of stripping tower are chosen as manipulated variables (inputs), while carbon dioxide mole fraction in absorption tower vapor product, the water mole fraction in absorption tower liquid product and tray temperature No. 36 of stripping tower are determined as controlled ones (outputs). The system identification is performed with three input and three output variables using step response test. As a result, continuous and discrete time transfer function matrices and suitable NMSS model for PIP controller are reported. Finally, in order to evaluate the PIP control performance, the feed flow rate increases by 2%. The results show the proper performance of designed PIP controller for both disturbance rejection and set point tracking.

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.

Grey wolf optimizer for identification of liquid slosh behavior using continuous-time hammerstein model

This paper presents the identification of liquid slosh plant using the Hammerstein model based on Grey Wolf Optimizer (GWO) method. A remote car that carrying a container of liquid is considered as the liquid slosh experimental rig. In contrast to other research works, this paper consider a piece-wise affine function in the nonlinear function of the Hammerstein model, which is more generalized function. Moreover, a continuous-time transfer function is utilized in the Hammerstein model, which is more suitable to represent a real system. The GWO method is used to tune both coefficients in the nonlinear function and transfer function of the Hammerstein model such that the error between the identified output and the real experimental output is minimized. The effectiveness of the proposed framework is assessed in terms of the convergence curve response, output response, and the stability of the identified model through the bode plot and pole zero map. The results show that the GWO based method is able to produce a Hammerstein model that yields identified output response close to the real experimental slosh output.

Modified Sine Cosine Algorithm for Identification of Liquid Slosh based on Continuous-time Hammerstein Model

This paper presents the identification of liquid slosh plant using the Hammerstein model based on modified Sine Cosine Algorithm (mSCA). A remote car that carries a container of liquid is considered as a liquid slosh experimental rig. In contrast to other research works, this paper considers a piece-wise affine function in a nonlinear function of the Hammerstein model, which is more generalized function. Moreover, a continuous-time transfer function is utilized in the Hammerstein model, which is more suitable to represent a real system. The mSCA method is used to tune both coefficients in the nonlinear function and the transfer function of the Hammerstein model such that the error between the identified output and the real experimental output is minimized. The effectiveness of the proposed framework is assessed in terms of the convergence curve response, output response, and the stability of the identified model through the pole-zero map. The results show that the mSCA based method is able to produce a Hammerstein model that yields identified output response closes to the real experimental slosh output with 82.12 % improvement of sum of quadratic error.

Identification of continuous-time systems utilising Kautz basis functions from sampled-data

In this paper we address the problem of identifying a continuous-time deterministic system utilising sampled-data with instantaneous sampling. We develop an identification algorithm based on Maximum Likelihood. The exact discrete-time model is obtained for two cases: i) known continuous-time model structure and ii) using Kautz basis functions to approximate the continuous-time transfer function. The contribution of this paper is threefold: i) we show that, in general, the discretisation of continuous-time deterministic systems leads to several local optima in the likelihood function, phenomenon termed as aliasing, ii) we discretise Kautz basis functions and obtain a recursive algorithm for constructing their equivalent discrete-time transfer functions, and iii) we show that the utilisation of Kautz basis functions to approximate the true continuous-time deterministic system results in convex log-likelihood functions. We illustrate the benefits of our proposal via numerical examples.

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.

Data-based mechanistic modelling and forecasting globally averaged surface temperature

The main objective of this paper it to model the dynamic relationship between global averaged measures of Total Radiative Forcing (RTF) and surface temperature, measured by the Global Temperature Anomaly (GTA), and then use this model to forecast the GTA. The analysis utilizes the Data-Based Mechanistic (DBM) approach to the modelling and forecasting where, in this application, the unobserved component model includes a novel hybrid Box-Jenkins stochastic model in which the relationship between RTF and GTA is based on a continuous time transfer function (differential equation) model. This model then provides the basis for short term, inter-annual to decadal, forecasting of the GTA, using a transfer function form of the Kalman Filter, which produces a good prediction of the ‘pause’ or ‘levelling’ in the temperature rise over the period 2000 to 2011. This derives in part from the effects of a quasi-periodic component that is modelled and forecast by a Dynamic Harmonic Regression (DHR) relationship and is shown to be correlated with the Atlantic Multidecadal Oscillation (AMO) index.

Optimal design of fractional order low pass Butterworth filter with accurate magnitude response

The design of (1+α) order, 0<α<1, low pass Butterworth filter approximated in terms of an integer order continuous-time transfer function using a nature-inspired optimization technique called Gravitational Search Algorithm (GSA) is presented in this paper. While approximations of the non-integer order Laplacian operator sα in terms of second order rational function using the continued fraction expansion method for the design of fractional order low pass Butterworth filters (FOLBFs) is recently reported in literature, however, such a design technique is non-optimal. In this work, the metaheuristic global search process of GSA efficiently explores and intensely exploits the nonlinear, non-uniform, multidimensional, and multimodal FOLBF design problem error landscape. At the end of the iterative search routine of GSA, the optimal values of the coefficients in terms of the third order rational approximations are achieved which accurately approximate the magnitude response of the ideal FOLBF. The proposed GSA based FOLBFs consistently achieve the best solution quality with the fastest convergence rate as compared with the designs based on Real coded Genetic Algorithm (RGA) and Particle Swarm Optimization (PSO). Comparison with the recent literature also demonstrates the superiority of the proposed designs. SPICE simulations justify the design feasibility of the proposed FOLBF models.