Proposed Proportional-integral-derivative Controller Research Articles

A Study of Two-Wheel Self-Balancing Robot Dynamics for Control Systems Learning

The two-wheeled self-balancing robot (TWSBR), utilizing an inverted pendulum arrangement, exhibits dynamic stability while being statically unstable. Due to this behavior, the TWSBR system has been used to demonstrate fundamental principles of stability, nonlinear dynamics, and control theory. In this work, a computational study of the TWSBR was carried out to develop a mathematical model using Newtonian mechanics that serves as an educational tool in control education for demonstrating the impact of different control algorithms such as Proportional (P), ProportionalDerivative (PD), and Proportional-Integral-Derivative (PID) on system stability. The comparison of P, PD, and PID controllers was undertaken to demonstrate the practical advantages of each controller in improving the robot's stability and responsiveness. The PID controller was designed and optimized using the Root-locus techniques, with a damping ratio equal to 1 which exhibits a fast-settling time with minimum overshoots. When an impulse response was applied to the PID controller in the simulation environment it demonstrated system can reach a dynamic balance within 1.2 seconds demonstrating the effectiveness of the proposed PID controller. The optimal gain parameters K value and Kp, Ki, and Kd parameter values were determined using root-locus analysis, which allowed the system to operate with great stability and minimum settling time. These findings highlight the TWSBR's educational significance as a hands-on tool for teaching practical applications of control theory, as well as providing valuable insights into the design and optimization of control systems for dynamic balance tasks. This study emphasizes the relevance of control algorithms in achieving rapid and stable dynamic behaviors, making it a valuable learning resource for both students and instructors. Keywords: Two-wheeled self-balancing robot, Inverted pendulum, P, PD and PID controllers, Stability analysis, Control Education

Robust adaptive PID control of functional electrical stimulation for drop-foot correction

A robust, adaptive proportional–integral–derivative (PID) control strategy is presented for controlling ankle movement using a functional electrical stimulation (FES) neuroprosthesis. The presented control strategy leverages the structurally simple PID controller. Moreover, the proposed PID controller automatically tunes its gains without requiring prior knowledge of the musculoskeletal system. Thus, in contrast to previously proposed control strategies for FES, the proposed controller does not necessitate time-consuming model identification for each patient. Additionally, the computational cost of the controller is minimized by linking the PID gains and updating only the common gain. As a result, a model-free, structurally simple, and computationally inexpensive controller is achieved, making it suitable for wearable FES-based neuroprostheses. A Lyapunov stability analysis proves uniformly ultimately bounded (UUB) tracking of the joint angle. Results from the simulated and experimental trials indicate that the proposed PID controller demonstrates high tracking accuracy and fast convergence.

Learning From Human Educational Wisdom: A Student-Centered Knowledge Distillation Method.

Existing studies on knowledge distillation typically focus on teacher-centered methods, in which the teacher network is trained according to its own standards before transferring the learned knowledge to a student one. However, due to differences in network structure between the teacher and the student, the knowledge learned by the former may not be desired by the latter. Inspired by human educational wisdom, this paper proposes a Student-Centered Distillation (SCD) method that enables the teacher network to adjust its knowledge transfer according to the student network's needs. We implemented SCD based on various human educational wisdom, e.g., the teacher network identified and learned the knowledge desired by the student network on the validation set, and then transferred it to the latter through the training set. To address the problems of current deficiency knowledge, hard sample learning and knowledge forgetting faced by a student network in the learning process, we introduce and improve Proportional-Integral-Derivative (PID) algorithms from automation fields to make them effective in identifying the current knowledge required by the student network. Furthermore, we propose a curriculum learning-based fuzzy strategy and apply it to the proposed PID control algorithm, such that the student network in SCD can actively pay attention to the learning of challenging samples after with certain knowledge. The overall performance of SCD is verified in multiple tasks by comparing it with state-of-the-art ones. Experimental results show that our student-centered distillation method outperforms existing teacher-centered ones.

Designing of intelligent PID controller for cardiac pacemaker using artificial bee colony algorithm

For real-time patient heart rate management, most widely used biomedical implantable devices in the cardiovascular system is the cardiac pacemaker (CP). A key factor in keeping the patient alive is the development of novel heart pacing techniques which can reduce the risk of cardiac arrhythmia. The present work is inspired to achieve this goal. To achieve an accurate, controlled, and regulated heart rate, a pacemaker with an intelligent proportional integral derivative (PID) controller is considered. The proposed PID controller is an integration of the traditional PID controller with appropriate tuning, that uses a swarm intelligence-based artificial bee colony (ABC) algorithm for handling the bio-electrical signals. To ensure the efficacy of the proposed controller experiments are conducted. MATLAB/Simulink software is used to test and simulate the suggested model and to adjust the controller gains. The simulation is performed in the time and frequency domain. The resulting pulse rate from the ABC-PID controller has a rise time (0.0985 s), settling time (0.3293 s), maximum overshoot (0.111367%), and MSE (0.0040565). External disturbances of various duty cycles are also introduced in the proposed CP control system. The proposed ABC-PID controller for implanted pacemakers reduces the risk of heart rate over-run.

Design of Mixed-Mode Analog PID Controller with CFOAs.

The design of a mixed-mode proportional-integral-derivative (PID) controller circuit using current-feedback operational amplifiers (CFOAs) as active components is proposed. With the same circuit topology, the proposed configuration of three CFOAs, four resistors, and two capacitors is capable of performing the PID controller in each of the following four modes: voltage mode, trans-admittance mode, current mode, and trans-impedance mode. Numerous mathematical analyses are conducted to determine the controller's performance under both ideal and non-ideal conditions. Additionally, the mixed-mode second-order lowpass filter is suggested and also used to examine the workability of the proposed mixed-mode PID controller in a feedback control structure. The proposed PID controller is implemented with the commercially available IC-type CFOA AD844, and the simulation results are presented to illustrate the functionality of the controller and its closed-loop control system. According to the findings, the total power consumption of the proposed PID controller is 0.348 W, with symmetrical supply voltages of ±9 V. It also has a temperature variation of less than 0.2% over the AD844's usable range. Monte Carlo statistical analysis results revealed that the gain responses of the controller exhibited a deviation of no more than 7.72% from the theoretical value. The controlled filter in a closed-loop control system has a 43% faster rise time and peak time than the uncontrolled filter in all four modes of operation. It also has a steady-state error less than 0.2 mV for voltage responses and 0.72 µA for current responses.

Implementing gain scheduling approach to control large-scale production of diethyl oxalate in a catalytic fixed bed multi-tubular reactor

In the large-scale production of Diethyl Oxalate (DEO), numerous control and optimization challenges are faced. These issues are targeted in this study by implementing a gain scheduling approach to control a catalytic fixed bed multi-tubular reactor designed for DEO production. A novel inferential modeling method, developed using Python and response surface methodology, was applied to simulate the dynamics of the reactor, and the inlet coolant temperature was identified as the most influential parameter. An inferential control system was implemented that utilized gain scheduling for Proportional Integral Derivative (PID) controllers. The results showed that the proposed PID controller gains offered fast and stable responses, even at high conversion setpoints. However, minimization of response overshoot at high amplitudes of step changes proved challenging, leading to a decrease in conversion estimator accuracy. The use of a quadratic model from response surface methodology for the regression of the inferential estimator was proposed, showing improved prediction accuracy over the linear model. These findings provide valuable insights and guide future optimization in the design and operation of reactors for large-scale DEO production.

PID and LQG controllers for diabetes system with internal delay: a comparison study

Closed-loop treatment for insulin dependent type 1 diabetes patients is a recent medical practice in insulin delivery (bionic pancreas) which aims to achieve tight control of glucose level in plasma and ensure minimizing risk of hypoglicemia. Among those most popular closed-loop controller strategies, proportional integral derivative (PID) and linear quadratic Gaussian (LQG) controllers are designed and compared for insulin delivery in diabetic patients. The controllers are designed based on individual and nominal model which is to study the ability of each controller in order to maintain blood glucose concentration for similar patient’s dynamic. The comparison is conducted numerically not only for for patients suffering type 1 diabetes mellitus (T1DM), but also type 2 diabetes mellitus (T2DM), and double diabetes mellitus (DDM) in the present of internal delay systems, which causes instability. The responses show that the proposed PID controller is better at maintaining the blood glucose level in the normal range for a longer delay of delay in hepatic glucose production. The patient with longer performing physical exercise has lower oscillation peaks in blood glucose concentration.

Control Mass-Spring-Damper Based on Tuning Trade-off PID Controller

This paper discusses control mass-spring-dumper (MSD) system used in vehicle suspensions. The vehicle suspension consists of mass, coil (spring), and shock absorber (dumper). MSD provided a shock effect when the vehicle was caused by the frictional force on the load. The dificulty to achive the stability of suspension and the following of set point tracking. Therefore, the proportional-integral-derivative (PID) based on tuning 1-degree of freedom (1-DOF) and 2-degree of freedom (2-DOF) were proposed to stability when the disturbance accours. The MSD equation was obtained by using the laplace transform and validated in Matlab Simulink. The result shows that the proposed PID control reduces disturbance rejection by the smaller set point tracking peak amplitude of 0.01, overshoot of 0.68%, rise time of 0.199 seconds. The 1-DOF tuning achieved set point tracking and disturbance rejection with a peak amplitude of 1.13, overshoot 12.9%, rise time 0.134 seconds, and the 2-DOF tuning achived set point tracking and disturbance rejection with peak amplitude of 1.07, overshoot 6.53%, rise time 1.28 seconds. The proposed PID control has the best performance than 1-DOF and 2-DOF controller.

Simple formula for designing the PID controller of a DC-DC buck converter

This paper proposes a simple way to design a proportional integral derivative proportional integral derivative (PID) controller for a DC-DC buck converter. This work concerns getting the formula to calculate Kp, Ki, and Kd parameters from a PID controller easily. The main advantage of this formula is that the tuning process of the K<sub>P</sub>, K<sub>I</sub> and K<sub>D</sub> parameters of the PID controller will be simplified just by entering the R, L, and C component values of the buck converter into the formula. The synthesis process of the formula is explained step by step. State space analysis is used to model the equations and transfer functions of the buck converter. The transfer function of the PID controller and buck converter was analyzed to obtain the Buck Converter system's closed loop transfer function. The formula for calculating the parameters K<sub>P</sub>, K<sub>I</sub> and K<sub>D</sub> of the PID controller is derived from the closed loop transfer function of the buck converter system. Numerical simulations are provided to confirm the effectiveness of the proposed PID controller. The performance of the buck converter controlled by the proposed PID controller was tested under various load conditions.

Load Frequency Control Assessment of a PSO-PID Controller for a Standalone Multi-Source Power System

The performance of load frequency control (LFC) for isolated multiple sources of electric power-generating units with a proportional integral derivative (PID) controller is presented. A thermal, hydro, and gas power-generating unit are integrated into the studied system. The PID controller is proposed as a subordinate controller to stabilize system performance when there is a sudden demand on the power system. The particle swarm optimization (PSO) algorithm is used to obtain optimal gain values of the proposed PID controller. Various cost functions, mainly integral time absolute error (ITAE), integral absolute error (IAE), integral squared error (ISE), and integral time squared error (ITSE) were used to optimize controller gain parameters. Furthermore, the enhancement of the PSO technique is proven by the performance comparison of conventional, differential evolution (DE) algorithm- and genetic algorithm (GA)-based PID controllers for the same system. The results show the PSO-PID controller delivers a faster settled response and the percentage improvement of the proposed technique over the conventional method is 79%, over GA is 55%, and over DE is 24% in an emergency in a power system.

Low‐gain internal model control PID controller design based on second‐order filter

AbstractA design method is proposed for low‐gain internal model control (IMC) proportional‐integral‐derivative (PID) controllers based on the second‐order filter. The PID parameters are obtained by approximating the feedback form of the IMC controller with a Maclaurin series, in which the second‐order filter is applied using the IMC approach to achieve a low‐gain PID controller that is suitable for model mismatch problems. Analytical PID tuning rules based on the second‐order filter are derived for several common‐use process models. The second‐order filter is designed from the desired time domain performances of maximum overshoot and settling time. Furthermore, the robustness of the IMC PID controller based on the second‐order filter is analyzed, and results show that its robustness performance is better than the first‐order filter under certain conditions. Finally, three categories of models divided by the ration of time constant and time delay are presented in the comparative numerical simulations to validate the effectiveness and generality of the proposed PID controller design method.

Novel Voltage-Mode PID Controller Using a Single CCTA and All Grounded Passive Components

A compact voltage-mode proportional-integral-derivative (PID) controller based on the utilization of a single current conveyor transconductance amplifier (CCTA) is presented in this paper. The presented active PID controller is made up of a single CCTA, and four truly grounded passive components, i.e. two resistors, and two capacitors. The design consideration of the controller parameters has been examined. Besides, the crucial sensitivity performances of the controller parameters for ideal and non-ideal conditions have also been discussed. An application on the closed-loop test system is demonstrated to validate the practicability of the proposed PID controller circuit. To confirm the theoretical behavior, the proposed circuit is simulated with the PSPICE program using TSMC 0.35-um CMOS process technology. Experimental test results based on commercially available CFOA AD844 and OTA CA3080 integrated circuits are also provided to demonstrate the practicality of the proposed circuit.

Optimal Control of Automatic Voltage Regulator System with Coronavirus Herd Immunity Optimizer Algorithm-Based PID plus Second Order Derivative Controller

Optimal control of the Automatic Voltage Regulator (AVR) system can improve the system behavior with the optimal parameters obtained based on optimization. The design of proposed Proportional Integral Derivative (PID) and Proportional Integral Derivative Plus Second Order Derivative (PIDD2) controllers are stated as an optimization problem including objective and constraint. The optimization problem is solved by using Coronavirus herd immunity optimizer (CHIO) algorithm to find the best controller parameters. In this paper, optimal design of PID and PIDD2 controllers for AVR system are presented with different objectives. The optimal design of controllers modeled as an optimization problem is solved with the help of the CHIO Algorithm. CHIO is inspired herd immunity against COVID-19 disease by social distancing. The performances of CHIO-based controllers in AVR system are compared with some well-known algorithms. Also, the obtained results demonstrate that the CHIO algorithm yields the least objective value in comparison with the other algorithms. When the results of the proposed approach are compared to those of some modern heuristic optimization algorithms, such as the Particle Swarm Optimization (PSO) algorithm, Differential Evolution (DE) algorithm, Artificial Bee Colony (ABC) algorithm etc. and the superiority of the proposed approach is demonstrated.

Observer-based PID control for actuator-saturated systems under binary encoding scheme

In this paper, the observer-based proportional-integral-derivative (PID) control problem is investigated for a class of actuator-saturated systems affected by multiplicative noises under the binary encoding scheme (BES). The communication between the sensors and the observers is implemented via a shared network, in which the measurement signals are transmitted by the BES. During the transmission, random bit errors may occur in the bit string due to the channel noises. The aim of this paper is to design an observer-based PID controller such that the closed-loop system is exponentially mean-square ultimately bounded with the consideration of random bit errors, actuator saturations and multiplicative noises. Sufficient conditions are presented to guarantee the expected performance of the resulted tracking error, and the controller gain matrices are obtained by solving a set of matrix inequalities. Finally, the effectiveness of the proposed PID control scheme is verified by a simulation example.

Current Differencing Buffered Amplifier-Based PID Controller Design

A new voltage mode Proportional-Integral-Derivative (PID) controller employing Current Differencing Buffered Amplifier (CDBA) is presented. The proposed PID controller employs a canonical number of capacitors without requiring any passive components matching conditions. The element values are expressed in terms of PID parameters. Workability of the proposed controller is demonstrated through SPICE simulations for which CDBA is realized using Current Feedback Amplifier (CFA). The simulation results are found in close agreement with the theoretical results.

Quantitative Feedback Design-Based Robust PID Control of Voltage Mode Controlled DC-DC Boost Converter

This brief addresses the problem of instability occurring in the voltage control mode of a non-minimum phase (NMP) DC-DC boost converter. To solve this instability issue in the presence of uncertainties and the external disturbances, quantitative feedback theory (QFT) is adapted to systematically design a robust proportional integral derivative (PID) controller, which is realized using only sensed output voltage as feedback. The advantages of the proposed PID design using the QFT are: (i) it eliminates the burden of tedious and ad-hoc tuning of PID gains using the conventional PID design approaches, (ii) current measurement is not required, (iii) disturbance dynamics (input voltage and load current variations) are included in the design stage itself, which further enhances the disturbance rejection performance of the output voltage, and (iv) it allows direct design for the non-minimum phase boost converter despite the bandwidth limitations. Extensive simulations and experiments are carried out to validate the efficacy of the proposed PID controller in the presence of the external disturbances and compared its superiority over a conventional PID controller.

Fuzzy Adaptive Neurons Applied to the Identification of Parameters and Trajectory Tracking Control of a Multi-Rotor Unmanned Aerial Vehicle Based on Experimental Aerodynamic Data

The propulsion subsystem of multi-rotor Unmanned Aerial Vehicles (UAV) is one of the most complex due to the aerodynamic, aero-elastic and electromechanical elements it comprises. Therefore, accurate models of this subsystem can be difficult to work with. Therefore, simplified models are normally used for the design of control and navigation algorithms. Considering this, the effectiveness of these algorithms is heavily dependent on the identification process used for the estimation of the parameters of the simplified propulsion model. On the other hand, the novel method of fuzzy adaptive neurons (FANs) have interesting characteristics that make them attractive for applications in which a fast response and good precision are required. In this article, the identification of the parameters of the propulsion system and the trajectory tracking of a multi-rotor UAV using FANs is explored. The efficient learning algorithm of the FANs is applied to identify the parameters of a simplified model of the propulsion system and to the self-tuning proportional integral derivative (PID) controllers of the trajectory tracking system. The proposed simplified model with the identified parameters is tested with experimental data obtained with low speed wind tunnels. The proposed PID controllers with self-tuning gains defined by the algorithm of the FANs for trajectory tracking system, are verified with simulations in MATLAB/Simulink® environment. The results showed that the parameter identification and trajectory tracking with PID controllers with self-tuning gains defined by the algorithm of the FANs, are suitable for estimating the parameters of the simplified model and track the trajectory with better error reduction than a classical PID controller.

Optimum Design of PID Controlled Active Tuned Mass Damper via Modified Harmony Search

In this study, the music-inspired Harmony Search (HS) algorithm is modified for the optimization of active tuned mass dampers (ATMDs). The modification of HS includes the consideration of the best solution with a defined probability and updating of algorithm parameters such as harmony memory, considering rate and pitch adjusting rate. The design variables include all the mechanical properties of ATMD, such as the mass, stiffness and damping coefficient, and the active controller parameters of the proposed proportional–integral–derivative (PID) type controllers. In the optimization process, the analysis of an ATMD implemented structure is done using the generated Matlab Simulink block diagram. The PID controllers were optimized for velocity feedback control, and the objective of the optimization is the minimization of the top story displacement by using the limitation of the stroke capacity of ATMD. The optimum results are presented for different cases of the stroke capacity limit of ATMD. According to the results, the method is effective in reducing the maximum displacement of the structure by 53.71%, while a passive TMD can only reduce it by 31.22%.

PSO Tabanlı PID Denetimci kullanarak Zaman Gecikmeli AVR Sisteminin Analizi

In this study, a particle swarm optimization (PSO) algorithm-based Proportional-Integral-Derivative (PID) controller is proposed for the Automatic Voltage Regulator (AVR) system terminal tracking problem in the existence of time-delay and varying loads. AVR is a commonly used electronic device for maintaining generator output terminal voltage at a given reference under time-delays and varying load thus introduces a challenging electrical system problem. Time-delays exist in many real-world systems due to the lags in transmission and transport, in general, they have a negative effect on the stability and control design. In this research, the time delay is approximated by Pade approximation leading to the so-called non-minimum phase system. A nonminimum phase system represents the difficulty of controlling due to its zeroes in the complex right half side of the s-plane. To this aim, we utilize a PID controller, its design and application widely studied in real-time systems, thus it is a suitable selection for the AVR system. The optimal controller gains Kp, Ki, and Kd are optimized with the proposed PSO algorithm based on a commonly used error minimization objective function. The PSO-based optimal PID controller’s performance is analyzed with several methods including root locus, bode analysis, robustness, and disturbance rejection. It is demonstrated that the proposed PID controller improves the reference terminal voltage tracking performance of the AVR system. According to the obtained results, it has been revealed that the proposed PSO-based PID controller improves tracking properties under time-delay and load change thus it can be effectively used for synchronous generator automatic voltage regulator (AVR) system terminal voltage stability.

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

The present study discusses an optimal design method of a proportional integral derivative (PID) control system for a continuous-time second-order plus dead-time system (SOPDT) that includes an under-damping system. The proposed PID control system is designed to minimize the performance index defined as the tracking performance for the set-point or the regulation performance for the disturbance, where the assigned stability margin is also achieved in order to attain robust stability for the modeling error. Because of the relationship between tracking performance and robust stability, the PID parameters are decided such that the tracking performance is optimized subject to the user-specified stability margin. In the proposed design method, in order to obtain the most general optimal PID possible parameters for controlled plants, we discuss a design method based on a normalized plant model. As a result, the PID parameters are seamlessly optimized between over-damping, critical-damping, and under-damping systems. The effectiveness of the proposed method is demonstrated through numerical examples.