Fractional order control for the temperature loop in a chemical reactor

C

Improved model reduction and tuning of fractional-order PI(λ)D(μ) controllers for analytical rule extraction with genetic programming

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.Genetic algorithm (GA) has been used in this study for a new approach of suboptimal model reduction in the Nyquist plane and optimal time domain tuning of proportional-integral-derivative (PID) and fractional-order (FO) PI(λ)D(μ) controllers. Simulation studies show that the new Nyquist-based model reduction technique outperforms the conventional H(2)-norm-based reduced parameter modeling technique. With the tuned controller parameters and reduced-order model parameter dataset, optimum tuning rules have been developed with a test-bench of higher-order processes via genetic programming (GP). The GP performs a symbolic regression on the reduced process parameters to evolve a tuning rule which provides the best analytical expression to map the data. The tuning rules are developed for a minimum time domain integral performance index described by a weighted sum of error index and controller effort. From the reported Pareto optimal front of the GP-based optimal rule extraction technique, a trade-off can be made between the complexity of the tuning formulae and the control performance. The efficacy of the single-gene and multi-gene GP-based tuning rules has been compared with the original GA-based control performance for the PID and PI(λ)D(μ) controllers, handling four different classes of representative higher-order processes. These rules are very useful for process control engineers, as they inherit the power of the GA-based tuning methodology, but can be easily calculated without the requirement for running the computationally intensive GA every time. Three-dimensional plots of the required variation in PID/fractional-order PID (FOPID) controller parameters with reduced process parameters have been shown as a guideline for the operator. Parametric robustness of the reported GP-based tuning rules has also been shown with credible simulation examples.This work has been supported by the Department of Science and Technology (DST), Government of India, under the PURSE programme

Novel Robust Control Using a Fractional Adaptive PID Regulator for an unstable system

Recent advances in fractional order calculus led to the improvement of control theory and resulted in potential use of fractional adaptive PID controller in advanced academic and industrial applications as compared to the conventional adaptive PID controller. Basically, a fractional order  adaptive PID  controller  is  an  improved version of classical  integer  order  adaptive PID  controller that outperformed  its classical  counterpart. In case of a closed loop system, a minute change would result in instability of the overall system. An efficient PID controller can be used to control the response of such system.  Among various parameters of an instable system, speed of the system is an important parameter to be controlled efficiently. The current research work presents the speed controlling mechanism for an uncertain instable system by using fractional order adaptive PID controller.To validate the arguments, effectiveness and robustness of the proposed fractional order adaptive PID controller have been studied in comparison to the classical adaptive PID controller using The Criterion of quadratic error. Simulation findings and comparisons demonstrated that the proposed controller has superior control performance and outstanding robustness in terms of percentage overshoot, settling time, rising time, and disturbance rejection

Performance analysis of robust stable PID controllers using dominant pole placement for SOPTD process models

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this recordThis paper derives new formulations for designing dominant pole placement based proportionalintegral-derivative (PID) controllers to handle second order processes with time delays (SOPTD). Previously, similar attempts have been made for pole placement in delay-free systems. The presence of the time delay term manifests itself as a higher order system with variable number of interlaced poles and zeros upon Pade approximation, which makes it difficult to achieve precise pole placement control. We here report the analytical expressions to constrain the closed loop dominant and nondominant poles at the desired locations in the complex s-plane, using a third order Pade approximation for the delay term. However, invariance of the closed loop performance with different time delay approximation has also been verified using increasing order of Pade, representing a closed to reality higher order delay dynamics. The choice of the nature of non-dominant poles e.g. all being complex, real or a combination of them modifies the characteristic equation and influences the achievable stability regions. The effect of different types of non-dominant poles and the corresponding stability regions are obtained for nine test-bench processes indicating different levels of open-loop damping and lag to delay ratio. Next, we investigate which expression yields a wider stability region in the design parameter space by using Monte Carlo simulations while uniformly sampling a chosen design parameter space. The accepted data-points from the stabilizing region in the design parameter space can then be mapped on to the PID controller parameter space, relating these two sets of parameters. The widest stability region is then used to find out the most robust solution which are investigated using an unsupervised data clustering algorithm yielding the optimal centroid location of the arbitrary shaped stability regions. Various time and frequency domain control performance parameters are investigated next, as well as their deviations with uncertain process parameters, using thousands of Monte Carlo simulations, around the robust stable solution for each of the nine test-bench processes. We also report, PID controller tuning rules for the robust stable solutions using the test-bench processes while also providing computational complexity analysis of the algorithm and carry out hypothesis testing for the distribution of sampled data-points for different classes of process dynamics and non-dominant pole types.KH acknowledges the support from the University Grants Commission (UGC), Govt. of India under its Basic Scientific Research (BSR) schem

State feedback based fractional order control scheme for linear servo cart system

Fractional order control schemes are being actively investigated for various systems. Fractional order concept is incorporated in integral (I), proportional integral (PI), proportional derivative (PD) or proportional integral derivative (PID) controller to investigate the performance of different state variables of the system. These techniques are often used for the purpose of technology transfer but very scanty research has so far been conducted using state space approach. The current investigation is initiated to observe the effect of fractional order controller using state space approach for the system's performance while tracking the position and regulating the speed of a linear servo cart system. Integer order controller based on proportional derivative (PD) approach is also shown for comparison. Simulation responses are presented and analyzed, in this investigation. The superiority of state space approach based fractional order controller is shown in the results. The paper contains a literature review on several control techniques used to control position and speed of a servo-cart system. An over view of mathematical modeling of servo cart system and a description of a proposed fractional controller is presented in this paper. A brief description of integer order control scheme is also presented. Simulated results are compared and discussed for both fractional order controller and integer order controller at the end of this paper

Proportional-integral-derivative control algorithm with delay compensation for steer-by-wire under network controlled system

Controller Area Network (CAN) is a popular network commonly used in the automotive industry which is an advanced serial bus system designed for real-time control system. This thesis addresses the modelling and controller design for Steer-by-Wire (SbW) system under the influence of a network controlled system. The analysis of the control performance of the SbW system under several CAN configuration setting is discussed in detail. The mathematical model of the SbW system is adopted from previous research works using both steering rack dynamic and the vehicle system dynamic. Proportional-Integral-Derivative (PID) controller that can compensate delay is designed to achieve the desired control performance of the SbW system. The analysis of the control performance is solely based on the simulation conducted in the Matlab/Simulink software environment with Truetime toolbox to simulate the real time performance of the SbW system. The simulation is performed based on nine different cases in the event of several difference in the CAN network properties such as the network speed, sampling periods, scheduling techniques, rate of data losses, interruption by higher priority data and clock drift to evaluate the control performance of the SbW system. The result is found that the SbW system control performance deteriorates by the selection of low network speed, sensor’s sampling periods and the rate of data losses

Applications of Mathematical Models in Engineering

The most influential research topic in the twenty-first century seems to be mathematics, as it generates innovation in a wide range of research fields. It supports all engineering fields, but also areas such as medicine, healthcare, business, etc. Therefore, the intention of this Special Issue is to deal with mathematical works related to engineering and multidisciplinary problems. Modern developments in theoretical and applied science have widely depended our knowledge of the derivatives and integrals of the fractional order appearing in engineering practices. Therefore, one goal of this Special Issue is to focus on recent achievements and future challenges in the theory and applications of fractional calculus in engineering sciences. The special issue included some original research articles that address significant issues and contribute towards the development of new concepts, methodologies, applications, trends and knowledge in mathematics. Potential topics include, but are not limited to, the following: Fractional mathematical models; Computational methods for the fractional PDEs in engineering; New mathematical approaches, innovations and challenges in biotechnologies and biomedicine; Applied mathematics; Engineering research based on advanced mathematical tools

Applicable Solutions in Non-Linear Dynamical Systems

From Preface: The 15th International Conference „Dynamical Systems - Theory and Applications” (DSTA 2019, 2-5 December, 2019, Lodz, Poland) gathered a numerous group of outstanding scientists and engineers who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without great effort of the staff of the Department of Automation, Biomechanics and Mechatronics of the Lodz University of Technology. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our event was attended by over 180 researchers from 35 countries all over the world, who decided to share the results of their research and experience in different fields related to dynamical systems. This year, the DSTA Conference Proceedings were split into two volumes entitled „Theoretical Approaches in Non-Linear Dynamical Systems” and „Applicable Solutions in Non-Linear Dynamical Systems”. In addition, DSTA 2019 resulted in three volumes of Springer Proceedings in Mathematics and Statistics entitled „Control and Stability of Dynamical Systems”, „Mathematical and Numerical Approaches in Dynamical Systems” and „Dynamical Systems in Mechatronics and Life Sciences”. Also, many outstanding papers will be recommended to special issues of renowned scientific journals.Cover design: Kaźmierczak, MarekTechnical editor: Kaźmierczak, Mare

Recent Development of Hybrid Renewable Energy Systems

Abstract: The use of renewable energies continues to increase. However, the energy obtained from renewable resources is variable over time. The amount of energy produced from the renewable energy sources (RES) over time depends on the meteorological conditions of the region chosen, the season, the relief, etc. So, variable power and nonguaranteed energy produced by renewable sources implies intermittence of the grid. The key lies in supply sources integrated to a hybrid system (HS)