Relay Feedback Tuning of Robust PID Controllers With Iso-Damping Property

HVDC power transmission systems can overcome some limitations inherent with AC power transmission systems such as transmission over long distance and transmission with cable. One aspect of importance is the improvement in stability achieved with AC-DC power transmission. In this paper a methodology for the optimal proportional integral derivative (PID) controller design using the modified genetic algorithm (MGA) is proposed to improve the transient stability of AC-DC power systems after faults. This study consists of the formulation of load-flow calculation, basic controls on HVDC transmission system, mathematical model selection for stability analysis, and supplementary signal control by an optimal PID controller using the MGA. The proposed method is verified using computer simulation. The results show the application of the MGA-PID controller in AC-DC power systems has improved the transient stability. The PID controller design using MGA method has been shown to be advantageous when applied for the AC-DC power systems.

Desalination plants have an important concern regarding controlling the permeate flow rate and pH during operability. This paper proposes the proportional integral derivative (PID) control design using modified Particle Swarm Optimization (PSO) techniques called autonomous groups PSO (AGPSO) in the two-input two-output (TITO) RO desalination plant to control the permeate flow rate and pH. Here, three different versions (AGPSO1, AGPSO2, and AGPSO3) of the AGPSO algorithm are utilized to design PID control for the same TITO plant. In addition, an integral time absolute error (<inline-formula> <tex-math notation="LaTeX">$J_{\mathrm {ITAE}}$ </tex-math></inline-formula>) based objective function is utilized to design a PID controller. The simulation results suggest that the proposed controller designs are flexible, self-tuning, and have stable characteristics, while the AGPSO3-PID control design attained a robust design for optimum tuning compared to existing improved grey wolf optimization PID (IGWO-PID) and other versions of AGPSO based PIDs (AGPSO1-PID, AGPSO2-PID). The design of AGPSO-PID achieved a minimum objective function than existing IGWO-PID and other versions of AGPSO based PIDs &#x007B;AGPSO1-PID, AGPSO2-PID&#x007D;. Finally, the proposed controller designs outperform the existing IGWO-PID design in literature in terms of control performance, demonstrating a precise control for and the improvement of plant performance.

This paper presents the effect of Variable Damping Ratio on design of Proportional Integral Derivative (PID) Controller. This novel method is very useful because of their successful practical application, robustness and simplicity. The most popular and widely used controllers in industries are PID controllers. To find appropriate parameters, many design methods have been proposed for PID controller with having its own merits and demerits. However, it is still not easy to find appropriate parameters for the PID controllers. In this paper, PID having variable Damping ratio is developed to improve the performance of the controller. By using this method there is a 60% saving in settling time as compared to the method proposed by Ziegler Nicholas and 84.6% saving settling time as compared to technique proposed by Salem. Our method is independent of maximum overshoot which is distinguishable advantage which increases the performance of system. Based on the mathematical model of the system, controller is designed and is estimated by the MATLAB version 2013. Data for model estimation is taken from an experimental works, the performance has improved significantly of the PID controller having variable damping ratio compare to conventional PID controller.

Design of Optimal PID Control with a Sensitivity Function for Resonance Phenomenon-involved Second-order Plus Dead-time System

The paper brings a comparison of two novel combinations of a relay identification test with a Time Delay System (TDS) model. Namely, the on/off plus saturation relay test and relay transient experiment are introduced. In the former case with more then two unknown model parameters, it is necessary to apply some technique for frequency response multiple-points identification; here, the Autotune Variation Plus (ATV+) procedure introducing an artificial delay is utilized. Limit cycles data are evaluated via an unordinary time-domain approach and using the Discrete Time Fourier Transform (DTFT), respectively. Both methodologies are verified and compared on a model of the circuit heating laboratory system with internal delays. INTRODUCTION By autotuning (i.e. automatic tuning), a set of methods which enable the controller to be tuned automatically on demand from an operator or an external signal is meant (Astrom and Hagglund 1984; Hang et al. 2002). Industrial experience has clearly indicated that this is highly desirable and useful feature. The whole procedure usually consists of two basic steps: Process model parameters identification followed by controller tuning; however, some approaches do not require explicit model identification. The relay feedback autotuning (identification) test performing limit cycle oscillations was successfully applied to the autotuning of PID controllers in (Astrom and Hagglund 1984) and it is widely used and in practice as a well applicable technique. It is robust, easy to implement, timesaving, easy to use and close-loop control which keeps the process close to the setpoint. The classical relay-feedback loop scheme with a symmetrical relay is depicted in Figure 1. If the process is stabilizable and has a phase lag of at least π radians, the process input ( ) t u and output ( ) t y are logged until the system reaches stationary oscillations, the amplitude A of error ( ) t e equals the amplitude of ( ) t y and the phase shift between ( ) t e and ( ) t y is –π. Figure 1: Relay-feedback Test Scheme However, the original relay feedback test sometimes called ATV (Autotune Variation) – see (Luyben 1987; Yu 2006) – has two basic drawbacks. First, due to an approximation, the estimation of the critical point is not accurate enough for some processes, such as those with large time delays (Wang et al. 1999). For example, there is an error of 23% for a first order unstable system with input-output delay. Second, the basic test enables to estimate only single point of the frequency characteristics. Hence, there have been investigated and developed many advanced techniques, which should eliminate the two mentioned deficiencies. Much research has been undertaken in identifying multiple points on the process frequency response, for instance, inserting of an integral or a delay element into the open loop (Scali et al. 1999; Tan et al. 1996). In this paper, the basic on/off relay test is improved by the use of a saturation relay (Shen et al. 1996; Yu 2006) for more accurate model parameters estimation followed by the above mentioned artificial-delay test. This approach is confronted with a technique utilizing the relay transient with DTFT (Hang et al 1995; Wang et al. 1997). The advantage of the latter method is that arbitrarily many points on the Nyquist curve can be estimated by a single test. The novel merit of this contribution is that the two methods are verified and benchmarked on a simulated identification relay experiment for a TDS model of a circuit heating laboratory plant (Dostalek et al. 2008; Pekař et al. 2009). Proceedings 27th European Conference on Modelling and Simulation ©ECMS Webjorn Rekdalsbakken, Robin T. Bye, Houxiang Zhang (Editors) ISBN: 978-0-9564944-6-7 / ISBN: 978-0-9564944-7-4 (CD) RELAY-FEEDBACK TEST Let us concisely describe model parameters estimation from the relay feedback test. Consider a simple feedback with and on/off relay as in Figure 1. If the process is stabilizable and has a phase lag of at least π radians, the process input ( ) t u and output ( ) t y are logged until the system reaches stationary oscillations, the amplitude A of error ( ) t e equals the amplitude of ( ) t y and the phase shift between ( ) t e and ( ) t y is –π. Hence, the ultimate period u T is obtained from oscillations, which gives the information about the critical point, together with the ultimate gain which is approximately given by

A fractional-order fuzzy proportional integral derivative (PID) controller is a controller that combines the benefits of fractional calculus and fuzzy logic with the conventional PID controller. In this paper, a four-stage optimization algorithm is proposed for the design of a Type-2 Fuzzy fractional-order PID controller based on the Fourier Series Method (FSM). Three distinct control structures are introduced: Type-2 fuzzy fractional PD + fractional PI controller, Type-2 fuzzy fractional PID, and Type-2 fuzzy fractional PD + Type-2 fuzzy fractional PI controller. In addition to a modified multi-performance criterion cost function, four integral performance criteria are employed as cost functions for each stage. The suggested algorithm avoids the utilization of the approximation equivalent for the fractional-order system and instead employs FSM. Furthermore, the approach optimizes the nonlinearity within the upper membership function (UMF) and the uncertainty range through the lower membership function, as opposed to arbitrary selection. By considering variations in the membership functions, the outcomes exhibit a superior response compared to previous investigations. The results of the three control structures are compared with the traditional PID controller, and simulation results demonstrate the feasibility of this technique. The findings suggest that by optimizing different integral performance criteria using this design technique, controllers for both integer and fractional-order plants can yield favorable step responses. The proposed algorithm is validated by comparing its step response performance with that of previous research, followed by a discussion on sensitivity analysis and computational requirements.

PID controller has been widely used in many different areas such as power systems, drives control, automotive mechatronics, aerospace, process control, and robotics. Recently, FPGA (field programmable gate array) has become an alternative solution for the realization of digital control algorithm systems. In this paper FPGA-based incremental PID (Proportional, Integral, Derivative) controller is designed and simulated. After the analysis of PID control algorithm, VerilogHDL language is used to design the software programs. Simulation results show the effectiveness and feasibility of the proposed method.

Frequency instability of an isolated microgrid (IMG) often arises due to load variations and uncertain power outputs of renewable sources. This contribution addresses the frequency instability issue by designing a Padula and Visioli (PV) tuned proportional-integral-derivative (PID) controller for IMG. The considered IMG model is novel due to the integration of eco-friendly generation sources, including a biogas turbine generator (BTG) and a biodiesel engine generator (BEG), along with other distributed generation units (DGUs) and energy storage devices (ESDs). In this contribution, mathematical modeling of considered units is derived as first-order model. Further, an overall transfer function of the IMG system is obtained using first-order transfer functions of IMG components and system dynamics. Thus, the obtained transfer function is then approximated into a first-order plus time delay (FOPTD) model to facilitate a simpler PID control design. PID controller parameters are computed using PV method for set point (SP) and load disturbance (LD) modes, keeping maximum sensitivity as a constraint. Various PID controller i.e. PID-<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PV</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>SP</i>1.4</sub>, PID-<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PV</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>SP</i>2.0</sub>, PID-<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PV</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>LD</i>1.4</sub>, and PID-<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PV</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>LD</i>2.0</sub> is designed for SP and LD modes. The efficacy of PID control design is tested by analyzing its impact on frequency deviation and mitigation of error with acceptable transient response for SP and LD mode. A comparative study is also performed based on tabulated data featuring error indices, time domain indicators, control efforts, and frequency plots to validate PV method-based PID control designs for IMG. Moreover, the real-time simulator, i.e., OPAL-RT, is utilized to further validate the efficacy of the PID controller in frequency error mitigation of the considered IMG model.

The increasing use of battery-powered electronic devices necessitates efficient and fast charging solutions. This research aims to optimize battery charging at a charging station using the Maximum Power Point Tracking (MPPT) method integrated with Proportional Integral Derivative (PID) control. This method is chosen to address overshoot issues and speed up the stabilization process. The study begins with a literature review to understand the basic theory of MPPT optimization and PID control. Subsequently, hardware and software for the battery charging station were designed and developed. An Arduino ATMega328 microcontroller was used as the main controller, with an LCD to display charging information. Tests were conducted on 12V batteries with capacities of 5Ah and 9Ah. The results showed that using PID control in MPPT optimization successfully increased battery charging efficiency. The fastest charging duration was achieved for a 12V 5Ah battery with parameters Kp=6, Ki=9, and Kd=4, where the battery was fully charged in 19 minutes, and for a 12V 9Ah battery with parameters Kp=5, Ki=3, Kd=1, where the battery was fully charged in 27 minutes. Conversely, the longest charging duration occurred for a 12V 5Ah battery with parameters Kp=5, Ki=3, Kd=1, where the battery was fully charged in 34 minutes, and for a 12V 9Ah battery with parameters Kp=2, Ki=5, Kd=1, with a charging time of 38 minutes. The designed system was able to reduce input current and increase input voltage to reach the 14.5V set point, ensuring that there was no excessive voltage and current that could prolong battery life. This research demonstrates that the PID method in MPPT optimization is effective in accelerating and optimizing battery charging. Future research is expected to further develop this method to improve battery charging efficiency and duration. Keywords: MPPT, PID, Optimization, Battery Charger, Optimal, PWM ABSTRAK Penggunaan perangkat elektronik yang bertenaga baterai semakin meningkat memerlukan solusi pengisian yang efisien dan cepat. Penelitian ini bertujuan untuk mengoptimalkan pengisian baterai pada stasiun pengisian dengan menggunakan metode Maximum Power Point Tracking (MPPT) yang diintegrasikan dengan kontrol Proportional Integral Derivative (PID). Metode ini dipilih untuk mengatasi masalah overshoot dan mempercepat waktu menuju keadaan stabil. Penelitian dimulai dengan studi literatur untuk memahami teori dasar optimasi MPPT dan kontrol PID. Selanjutnya dirancang dan dibuat perangkat keras serta perangkat lunak untuk stasiun pengisian baterai. Mikrokontroler Arduino ATMega328 digunakan sebagai pengendali utama dengan LCD untuk menampilkan informasi pengisian. Pengujian dilakukan pada baterai aki 12V dengan kapasitas 5Ah dan 9Ah. Hasil pengujian menunjukkan bahwa penggunaan kontrol PID pada optimasi MPPT berhasil meningkatkan efisiensi pengisian baterai. Durasi pengisian yang paling cepat dicapai baterai 12V 5ah dengan parameter Kp=6 Ki=9 dan Kd=4 dimana baterai terisi penuh dalam waktu 19 menit dan baterai 12V 9ah dengan parameter Kp=5, Ki=3, Kd=1 dimana baterai terisi penuh dalam waktu 27 menit. Sebaliknya durasi pengisian terlama terjadi pada baterai 12V 5ah dengan parameter Kp=5, Ki=3, Kd=1 baterai terisi penuh dalam waktu 34 menit dan baterai 12V 9ah dengan parameter Kp=2 Ki=5, Kd=1 dengan waktu pengisian 38 menit. Sistem yang dirancang mampu mengurangi arus input dan meningkatkan tegangan input untuk mencapai set point 14.5V menjaga agar tidak terjadi tegangan dan arus berlebih yang dapat memperpanjang umur baterai. Penelitian ini menunjukkan bahwa metode PID pada optimasi MPPT efektif dalam mempercepat dan mengoptimalkan pengisian baterai. Penelitian selanjutnya diharapkan dapat mengembangkan lebih lanjut metode ini untuk meningkatkan efisiensi dan durasi pengisian baterai. Kata kunci: MPPT, PID, Optimasi, Charger Baterai, Optimal, PWM

This chapter examines the proportional integral derivative (PID) controller design. It introduces the idea of disturbance estimation that leads to an equivalent PI control system. The mathematical model used in the chapter is a first order model. For systems with higher order transfer functions, approximation is required. To design a PID controller using the estimation based approach, a second order transfer function is considered. The chapter presents the MATLAB tutorial for the implementation of disturbance observer‐based PID controller. This implementation contains the anti‐windup mechanism when the control signal reaches its maximum or minimum values. The embedded PID controller via estimation is used in the simulation studies within the Simulink environment. The chapter also explains resonant controller design and implementation with anti‐windup mechanism using the disturbance estimation approach. It presents an example to illustrate the disturbance observer‐based resonant controller design.

This paper demonstrates the design and analysis of automatic generation control using intelligent genetic algorithm tuned fuzzy based controller. A two area thermal power system simulated for four different scenarios considers a reheat steam turbine in each area with Generator rate constraints. The Integral Time Squared Error (ITSE) employed to get an objective function for the optimization of controller gains. The simulation results compared with the conventional Proportional Integral Derivative (PID) controller, Genetic Algorithm (GA) tuned PID controller and GA tuned Fuzzy PID controller. The proposed GA tuned Fuzzy based PID Controller can generate the best performance for peak overshoot, undershoot and settling time with step load disturbances. Robustness of the performance of the proposed controller provided with system parametric uncertainties.

In this paper, digital proportional-integral-derivative (PID)-type and fuzzy-type controllers are compared for application to the buck and boost dc-dc converters. Comparison between the two controllers is made with regard to design methodology, implementation issues, and experimentally measured performance. Design of fuzzy controllers is based on heuristic knowledge of converter behavior, and tuning requires some expertise to minimize unproductive trial and error. The design of PID control is based on the frequency response of the dc-dc converter. Implementation of linear controllers on a digital signal processor is straightforward, but realization of fuzzy controllers increases computational burden and memory requirements. For the boost converter, the performance of the fuzzy controller was superior in some respects to that of the PID controllers. The fuzzy controller was able to achieve faster transient response in most tests, had a more stable steady-state response, and was more robust under some operating conditions. In the case of the buck converter, the fuzzy controller and PID controller yielded comparable performances.

Now -a-days PID (proportional-integral-derivative) controller is used in every type of small or large industries. For this the digital PID controller is so popular. But it is necessary to design and tune the PID controller in a proper method for applying the plant. The paper represents a method of tuning a digital proportional-integral-derivative (PID) controller. The name of the method is Steepest Gradient Descent Method (SDGM). It is an iterative method. The SDGM method is very simple, easy to use and each iteration is very fast. It is also a guaranteed method to find the minima through numerous times of iterations as long as it exists. By applying this optimization method PID controller is tuned both of digital and analog process. In the paper by applying the method of some plant the comparison result of analog and digital are shown. From the comparison it is found that the digital scheme is preferable than analog scheme. Index Terms—PID controller, SDGM. I. INTRODUCTION The fi rst controllers with proportional, integral, and derivative (PID) feedback control action became commercially available during the 1930s. The 1940s saw widespread acceptance in industry of pneumatic PID controllers, and their electronic counterparts entered the market in the 1950s. Digital hardware has been routinely used since the 1980s with significant impact on process control. Even several decades after three-mode controllers were introduced; the vast majority of controllers used in the chemical process industry are based on PI/PID models (1). The popularity of these controllers has led to research on tuning methods, resulting in hundreds of publications on this topic. Ziegler-Nichols tuning relations and Cohen-Coon tuning rules are among the earliest published methods. Tuning relations based on error criteria are more recent model-based tuning rules, which offer improvements over earlier tuning methods. Tuning rules also exist for unstable processes as well as for tuning in the presence of plant model mismatch (2). Despite the numerous approaches available for controller tuning, surveys indicate that poorly tuned control loops are abundant in industry. In general, the gain scheduling of the PID controllers is an optimization problem. The method of steepest descent (SDGM) is also known as The Gradient Descent, which is basically an optimization algorithm to find the local minimum of a function. By applying the SDGM to the PID controller, the controller is tuned and applied to some conventional plant then the digital and analog results are compared to the paper.

This paper presents a comparison of optimization for vehicle steering controls system simulation using several Artificial Intelligence (AI) for optimizing Proportional Integral Derivative (PID) control parameters to suppress errors on lateral motion and the yaw motion of vehicles. This paper compares five kinds of tuning methods of parameter for PID controller, among other are Firefly Algorithm (FA), Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO), Bat Algorithm (BA) and Imperialist Competitive Algorithm (ICA). The vehicles are represented in the model vehicle with 10 degrees of Freedom of vehicle dynamics system. The simulation results show that the PID control tuned by AI in the vehicle steering control system can adjust the plant output to the desired trajectory so that the stability of the vehicle is maintained. Vehicle yaw error and lateral error can be reduced by using ICA to determine PID parameter. The main advantage of proposed optimization is faster and more accurate compared with PID controller. So the error of the controller is reduced too. The results obtained are of vehicle motion can be maintained in accordance with the desired trajectory with smaller error and was able to achieve higher speeds than with the control system using optimized without parameters. This paper only deals with software simulation to proof the effect of AI optimization. The hardware implementation will be investigated in the next future.

Remote areas need to prioritize the pumping of water for agricultural and drinking purposes. Water pumping is a promising and advantageous application of renewable energy sources, such as hybrid energy sources that combine photovoltaic and wind power. A novel approach to effective flow control in hybrid PV and wind-powered water pumping systems is presented in this research. To optimize a Proportional Integral Derivative (PID) controller that governs motor speed, the proposed approach combines an optimized control algorithm, Unified Power Flow Controller (UPFC), and Fuzzy Q-learning. The main goal is to use UPFC to identify and mitigate Power Quality (PQ) issues. To achieve optimal UPFC operation under a range of solar and wind energy conditions, the Kookaburra Optimization Algorithm (KOA) is utilized. Fuzzy Q-learning provides adaptive parameter tuning based on real-time feedback and system dynamics, enabling the PID controller to be tuned online. Moreover, the detailed models of wind and photovoltaic systems highlight their influence on water pumping technology. A PID controller controlled by the KOA algorithm powers the UPFC, a crucial part of the system. The KOA is applied to optimize PID parameters for the UPFC, resulting in a unique contribution that emulates the hunting behavior of kookaburras for both local and global exploration. The PID controller can be easily adjusted online by the Fuzzy Q-Learning algorithm, which improves system stability when reacting to changing energy and environmental conditions. The combination of the Kookaburra Optimization Algorithm, PID control, and UPFC offers a sophisticated and flexible approach to the best possible operation of water pumping systems. Total Harmonic Distortion (THD) is successfully decreased by the proposed method, indicating better waveform quality and fewer harmonic components in the electrical system. The system’s ability to maintain a high-quality power supply is reflected in the THD value of 3.92% at 50Hz.