Classical Proportional Integral Derivative Controller Research Articles

Analytical approach in designing PID controller for complex fractional order transfer function

The study focuses on the fractional complex order plant model, which has gained popularity in applied mathematics, physics, and control systems. A significant contribution of this research lies in discussing the physical phenomena associated with complex plant models and their impact on system stability and robustness. The main purpose of the method presented in this paper is to tune the controller parameters to ensure the stability and robustness of the system. There are methods presented in the literature for this purpose. One of these methods is to keep the phase curve in the system frequency response flat within a certain range. However, this process is based on equating the derivative of the phase value to zero at a certain frequency and adds great mathematical complexity to the calculations. In this study, reliable analytical formulas are presented for the same purpose using a graphical approach. Since the fractional complex order plant model represents the most general mathematical form, it enables easy creation of other plant models, including integer order and fractional order plant. The reason why this plant is chosen is that this structure can be named as the universal plant, which all other structures can be built by making little variations. For instance, a transfer function having integer, real and/or complex number coefficients and/or orders can be obtained by proper determination of the parameters of the universal plant. A time delay can also be added towards researcher's desire. The main inspiration comes from studying on an inclusive plant. The method in this paper intends to tune the well‐known classical Proportional Integral Derivative controller. Thus, effectiveness of the integer order controller on various plants will be shown. This approach provides analytical calculation equations for the physical modifications of plants with integer, fractional, and/or complex coefficients and/or orders. The effectiveness of the method is demonstrated visually with different examples that include these different possible situations. The results observed in the changes of the parameters in the transfer functions were also examined. Thus, pros and cons of the variations of integer, fractional, and complex numbers on system parameters have been shown.

Participation of wind-storage combined system in the secondary frequency regulation control strategy of power grid

Abstract The secondary frequency modulation of the unit, that is, the automatic generation control (AGC), is the process of increasing or decreasing the power of the power generation unit by the power plant unit according to the dispatching command issued by the power grid dispatching center, and then using the frequency modulator to restore the frequency. Based on the principle of AGC, this paper establishes a frequency dynamic response model of the secondary frequency modulation of the traditional unit and the wind storage participation system including load frequency control (LFC) and traditional proportional-integral-derivative (PID) controllers, determines the frequency modulation control strategy of wind storage, and uses the distribution mode based on Area Control Error (ACE) signal to assist in the secondary frequency modulation. In order to solve the parameter optimization problem of the classical PID controller when the wind-storage combined system participates in the secondary frequency modulation under the large load disturbance, a parameter optimization model of the controller with PID was established, and the ITAE evaluation index was finally selected as the fitness function by comparing different fitness evaluation indexes. To overcome the problem that the conventional Particle Swarm Optimization (PSO) is prone to local extremum, the inertia weights and learning factors are adjusted nonlinearly to balance and optimize the global and local optimization capabilities and improve the search efficiency, and the parameters of the PID controller are optimized by the improved PSO algorithm. The simulation results show that the proposed algorithm improves the secondary frequency modulation effect under the background of a high proportion of renewable energy connected to the power grid.

Nonlinear Optimized PID Vibration Control of Thermal-Dependent FG Composite Porous Plates Reinforced by Agglomerated CNTs

This research study aims to delve into the effects of carbon nanotubes (CNTs) agglomeration on the dynamic characteristics of smart functionally graded (FG) porous sandwich plates. The structure of the sandwich plate comprises a core layer that incorporates dispersed CNTs within a polymer matrix. In addition, two layers are equipped with piezoelectric sensors and actuators. The agglomeration of CNTs is mathematically modeled using the Eshelby–Mori–Tanaka approach, accounting for both complete and partial agglomeration states. Moreover, the study takes into account the thermal-dependent behavior of CNTs. Subsequently, an optimal nonlinear proportional-integral-derivative (PID) control scheme based on the Bat optimization algorithm is applied to mitigate vibrations within the composite structure. Unlike the fixed gains of the classical PID, the nonlinear version dynamically adjusts its parameters in real time, ensuring enhanced responsiveness and stability. Furthermore, a comprehensive numerical investigation is conducted to assess the impact of several parameters on the natural frequencies in the frequency domain. These parameters encompass porosity distributions, porosity coefficients, reinforcement patterns, weight fractions of nanofillers, temperature, and the agglomeration of CNTs. The vibration attenuation performance of both nonlinear and classical PID controllers is evaluated through numerical simulations. The findings indicate the robustness and rapid disturbance rejection of the proposed control scheme.

Control of coupled nonaffine multiagent stochastic systems by classical PID

AbstractThe classical PID (proportional‐integral‐derivative) control is the most basic and widely used control algorithm in engineering systems by far. Whether PID control can effectively deal with coupled multiagent uncertain nonlinear dynamics is well worth investigating. In this article, a class of PID controlled multiagent stochastic systems with coupled uncertain dynamics is considered, where the control input is nonaffine. Each agent has its own regulation objective, and only has access to its own regulation error information for PID feedback. First, a PID parameter set will be constructed explicitly based on some prior knowledge about the nonlinear functions, such that the overall multiagent system can be stabilized globally in the mean square sense, as long as the PID parameters are chosen from the constructed set. Moreover, the regulation error will be proven to have an upper bound proportional to the noise intensity along the reference signal. Furthermore, it will be shown that the regulation error of each agent can be arbitrarily small by choosing the PID parameters suitably large. Finally, the theoretical results will be verified by simulations.

Design and stabilization of a Coandă effect-based UAV: Comparative study between fuzzy logic and PID control approaches

Recent years have experienced a notable surge in unmanned aerial vehicles (UAV) research, prompting exploration into innovative concepts. This paper introduces a compact UAV harnessing the Coandă effect, an underexplored phenomenon in fluid mechanics. Featuring a single lift motor and two types of flaps, this UAV offers exceptional maneuverability, presenting significant challenges compared to conventional multi-rotor UAVs. To address these challenges, we explore the theoretical study, mechatronic design, and manufacturing complexities of the Coandă UAV. Emphasizing the distinctiveness of our work, we assess a Fuzzy Logic Controller (FLC) for UAV stabilization, marking the first application of such techniques to a Coandă-effect UAV, in contrast to the Proportional-Integral-Derivative (PID) control employed by other researchers. This innovative application of Fuzzy logic, particularly the Sugeno model, proves advantageous, offering faster and more robust control in uncertain or noisy environments. The proposed FLC strategy is systematically compared against a classical PID control approach, formulated based on the Mamdani and Sugeno models, optimized and manually tuned using a genetic algorithm. Our results showcase a significantly improved settling time of 0.417 s with the FLC strategy, surpassing the PID control approach by 35.23%. To substantiate our findings, we present comprehensive experimentation conducted at both software and hardware levels using Matlab® and Simulink for a microcontroller-based UAV. This groundbreaking fusion of novel design and advanced control techniques not only addresses the unique challenges posed by the Coandă UAV's aerodynamics but also contributes significantly to the field of UAV research.

Mathematical Analysis and Real-Time Control of a Novel 5-DOF Robotic System with a Parallel Kinematics Structure for Additive Manufacturing Technologies

The systems that use parallel kinematic structures in additive manufacturing technology are particularly notable for their ability to provide exceptional precision and efficiency in the fabrication of intricate geometrically shaped items. This study introduces a novel system paradigm with five degrees of freedom, specifically developed to tackle existing additive manufacturing issues. In the proposed design, by incorporating rotational motions along the x and z axes, contributions were added to the efficiency of typical three-degrees-of-freedom (3-DOF) systems, resulting in a total of five degrees of freedom. In this way, it is aimed at increasing product durability, improving surface integrity, and saving production time. In this study, the conceptual design of the system was defined. Mathematical analyses were then used to determine the kinematic and dynamic models of the system, and a proposed model-based control technique was revealed. To evaluate the axis movement performance of the system, two different control techniques were used, and real-time test studies were conducted. The first control technique was the proportional–integral–derivative (PID) controller, and the second method was the sliding mode control (SMC) method, which was used to increase the performance of the system during trajectory tracking. The experimental results showed that the SMC method provides a reasonably good trajectory tracking response and a steady-state error compared to the classical PID controller.

An Adaptive PID Control System for the Attitude and Altitude Control of a Quadcopter

Abstract In adaptive model-based control systems, determining the appropriate controller gain is a complex and time-consuming task due to noise and external disturbances. Changes in the controller parameters were assumed to be dependent on the quadcopter mass, which was the process variable. A nonlinear model of the plant was used to identify the mass, employing the weighted recursive least squares (WRLS) method for online identification. The identification and control processes involved filtration using differential filters, which provided appropriate derivatives of signals. Proportional integral derivative (PID) controller tuning was performed using the Gauss–Newton optimisation procedure on the plant. Differential filters played a crucial role in all the developed control systems by significantly reducing measurement noise. The results showed that the performance of classical PID controllers can be improved by using differential filters and gain scheduling. The control and identification algorithms were implemented in an National Instruments (NI) myRIO-1900 controller. The nonlinear model of the plant was built based on Newton’s equations.

Performance Analysis of Cascade Tank System Using Deep Learning Controller

The conventional proportional–integral–derivative (PID) controller is used in the majority of process industries. Although the most commonly used, the classic PID controller has several drawbacks like variable performance for the non-linear system, multivariable control design is not straightforward; the response is influenced by dead time, no constraints involvement, etc. The field of process control systems has grown quickly, and other controllers have been developed that try to overcome the weakness of PID controllers. Advances in artificial neural networks, specifically deep learning, have widened the application domain of process control systems. In this paper, a cascaded tank system, which is a benchmark problem, has been simulated. The input-output data of the plant has been generated and used to train a deep-learning controller using backpropagation. Several measures, such as time response, frequency response, and signal statics performance indices, are used to evaluate the outcomes of the proposed controller. The proposed model performs better on every assessment criterion than the traditional controller.

Semiglobal stability of PID for uncertain nonaffine systems

Proportional–integral–derivative (PID) controller is the most widely used form of feedback control by far. However, a satisfactory theory is still lacking to explain the rationale of the widespread PID control, and the gap between theory and practice of PID needs to be filled by control scientists. It is worth noting that a recent work (Zhao and Guo, 2022) proved that the classical PID controller has the ability to globally stabilize a basic class of uncertain nonaffine nonlinear systems, while the system nonlinear function is required to have a linear growth rate with respect to the state variables. In this paper, we will consider the more general case where the system nonlinear function may have super-linear growth rates, and show that the classical PID control can always be designed to stabilize such systems in the semiglobal sense, provided that the smallest eigenvalue of the control gain matrix has a positive lower bound. Moreover, a three dimensional parameter set for the stabilizing PID parameters will be constructed. Furthermore, under some additional knowledge about the system uncertain functions, we will propose a simpler PD controller with desired compensation, and show that the proposed controllers can still be designed to achieve semiglobal stability and desired tracking targets.

Neuro-fuzzy system based proportional derivative gain optimized attitude control of CubeSat under LEO perturbations

Prompt attitude stabilization is more challenging in Nano CubeSat due to its minimal capacity, weight, energy, and volume-constrained architecture. Fixed gain non-adaptive classical proportional integral derivative control methodology is ineffective to provide optimal attitude stability in low earth orbit under significant environmental disturbances. Therefore, an artificial neural network with fuzzy inference design is developed in a simulation environment to control the angular velocity and quaternions of a CubeSat by autonomous gain tuning of the proportional-derivative controller according to space perturbations. It elucidates the dynamics and kinematics of the CubeSat attitude model with reaction wheels and low earth orbit disruptions, i.e., gravity gradient torque, atmospheric torque, solar radiation torque, and residual magnetic torque. The effectiveness of the proposed ANFIS-PD control scheme shows that the CubeSat retained the three-axis attitude controllability based on initial quaternions, the moment of inertia, Euler angle error, attitude angular rate, angular velocity rate as compared to PID, ANN, and RNN methodologies. Outcomes from the simulation indicated that the proposed controller scheme achieved minimum root mean square errors that lead towards rapid stability in roll, pitch, and yaw axis respectively within 20 s of simulation time.

A model predictive control approach towards the energy efficiency of submerged dredging

Autonomous submerged dredging offers numerous benefits, such as reduced ship resistance and lower vacuum requirements for the dredge pumps. However, this method also presents new challenges, such as stability and buoyancy control, which must be addressed to minimize the energy requirements and ensure cost-effectiveness and sustainability. To achieve these goals, this paper proposes a Model Predictive Control (MPC) strategy to minimize control effort and energy requirements. Compared to traditional motion control methods such as proportional–integral–derivative (PID) control, MPC shows great promise in terms of energy efficiency and trajectory-tracking. The Autonomous Low Energy Replenishment Dredger (ALERD) is used as a case study to showcase the potential of the proposed control strategy. A time-domain simulation model is developed, and the ALERD is modeled as an underwater vehicle using a state-space representation. The classic PID control and the proposed MPC framework are compared in terms of trajectory-tracking, energy requirements, and robustness to modeling uncertainties, using sensitivity analysis. The results show that the proposed MPC control framework outperforms PID control in all aspects considered. Furthermore, a comparison between the energy requirements of the ALERD and a conventional dredger, for the same operational profile and hopper volume, indicates that autonomous submerged dredging can potentially decrease total energy requirements by 66%.

Control of Linear Electric Actuator with Hybrid Fuzzy PID Controller

In this study, the actuator, which converts circular motion to linear motion, is controlled with a smart hybrid controller. The model includes the analysis of electrical and mechanical parts. The controller, on the other hand, has a design methodology that cleverly blends classical PID (Proportional Integral Derivative) and fuzzy controllers. In this design methodology, classical PID and fuzzy controller have an error parameter dependent blending mechanism. In order to compare the performance of the hybrid controller, the coefficients of the classical PI and PID controllers were obtained by tuning and the coefficients with the best response were used. For performance comparison of conventional controllers and hybrid controllers; rise time, settling time, maximum overshoot and common performance indices values are used. The hybrid controller showed higher performance in terms of maximum overshoot, settling time, rising time and performance indices. The potential benefits of using a hybrid controller for the control of linear electric actuators were demonstrated by the fact that it performed better than conventional PID controllers on the majority of evaluation criteria.

Feedforward neural network emulation of a PID continuous-time controller for quadcopter attitude digital control

<p>Quadcopters are popular UAVs owing to their compact size and maneuverability. Quadcopters are unmanned aircraft guided by remote control, and the demand for them is increasing due to their widespread surveillance, goods delivery, aerial photography, and defense applications. Nonlinear quadcopter operation makes control system implementation very challenging. In this paper, based on artificial intelligence (AI), we train a feedforward neural network (FFNN) controller of a traditional proportional integral derivative (PID). The conventional (PID) is generally tuned to improve the quadcopter control and performance. FFNN can perform offline learning between the inputs and outputs of the controller to learn its behavior. Once the learning is complete, we replace the PID controller with the neural network controller, to get a controller that can maintain system stability,and overcome the limitations of hardware implementation problems caused by the classical PID controller.</p>

UAV Power Line Tracking Control Based on a Type-2 Fuzzy-PID Approach

A challenge for inspecting transmission power lines with Unmanned Aerial Vehicles (UAVs) is to precisely determine their position and orientation, considering that the geo-location of these elements via GPS often needs to be more consistent. Therefore, a viable alternative is to use visual information from cameras attached to the central part of the UAV, enabling a control technique that allows the lines to be positioned at the center of the image. Therefore, this work proposes a PID (proportional–integral–derivative) controller tuned through interval type-2 fuzzy logic (IT2_PID) for the transmission line follower problem. The PID gains are selected online as the position and orientation errors and their respective derivatives change. The methodology was built in Python with the Robot Operating System (ROS) interface. The key point of the proposed methodology is its easy reproducibility, since the designed control loop does not require the mathematical model of the UAV. The tests were performed using the Gazebo simulator. The outcomes demonstrated that the proposed type-2 fuzzy variant displayed lower error values for both stabilization tests (keeping the UAV centered and oriented with the lines) and the following step in which the trajectory is time-variant, compared to the analogous T1_PID control and a classical PID controller tuned by the Zigler–Nichols method.

Optimization of Energy Consumption of Industrial Robots Using Classical PID and MPC Controllers

Industrial robots have a key role in the concept of Industry 4.0. On the one hand, these systems improve quality and productivity, but on the other hand, they require a huge amount of energy. Energy saving solutions have to be developed and applied to provide sustainable production. The purpose of this research is to develop the optimal control strategy for industrial robots in order to minimize energy consumption. Therefore, a case study was conducted for the development of two control strategies to be applied to the RV-2AJ Mitsubishi robot arm with 5 DOF, where the system is a nonlinear one. The first examined controller is the classical linear proportional integral derivative (PID) controller, while the second one is the linear model predictive control (MPC) controller. In our study, the performances of both the classical PID model and the linear MPC controller were compared. As a result, it was found that the MPC controller in the execution of the three defined reference trajectories [(1) curve motion, (2) N-shaped motion, and (3) circle motion] was always faster and required less energy consumption, whereas in terms of precision the PID succeeded in executing the trajectory more precisely than the MPC but with higher energy consumption. The main contribution of the research is that the performances of the two control strategies with regard to a complex dynamic system were compared in the case of the execution of three different trajectories. The evaluations show that the MPC controller is, on the one hand, more energy efficient; on the other hand, it provides a shorter cycle time compared to the PID controller.

Adaptive charge control for the space inertial sensor

Inertial sensors are key components of gravitational wave observations and Earth geodesy missions. An inertial sensor includes an isolated free-floating test mass (TM) surrounded by capacitive electrodes and a housing frame (EH) to perform the relative-position measurement and control the TM in six degrees of freedom. Owing to galactic cosmic rays and solar energetic particles, many additional accelerations are introduced through the Coulomb interaction between charged TMs and their surrounding conducting surfaces. Thus, the TM charge control is critical in space-based missions. A contact-free and ultraviolet light-based charge management system (CMS) was developed to reduce charge-induced noises acting on the TMs and minimize force disturbances that can perturb measurements or interrupt science tasks. However, the operating environment for space charge control is full of uncertainties and disturbances. Physical parameters in the discharging process are rarely measured and will vary owing to changes in solar activity, temperature, and so on. The unpredictability and variability of these parameters affects the CMS performance in long-term space missions and must be evaluated or eliminated. This paper presents a simplified physical model for the discharge process based on electron exchange between the TM and the opposing EH. Subsequently, a model reference adaptive control (MRAC) is proposed for the CMS with parametric uncertainties to maintain the TM charge below a certain level and improve its robustness. The simulation results show that the MRAC can automatically adjust control parameters to eliminate the effect of the variability of the aforementioned physical parameters, and the control precision can reach 0.1 mV under uncertainties, which is superior to that of a classic proportional–integral–derivative controller. This study demonstrated the effects of adaptive charge control and its potential for actual applications.

Fuzzy Logic Aided PID Controller for Induction Motor Speed Control

This paper presents design of intelligent based controller for speed control of induction motor. The proposed system integrates a classical proportional-integral-derivative (PID) controller and intelligent algorithm based on fuzzy logic control (FLC). This scheme takes advantages of classical PID and FLC to improve the speed response performance of induction motor analysed in terms of transient and steady state time domain characteristics. The FLC designed was implemented using the fuzzy block of MATLAB/Simulink based on Mamdani model and comprises 9 fuzzy variables and 49 logic (intelligent) rules that define the system behaviour. The FLC takes the loop error and its rate of change to manipulate the input command to the PID control so that the response speed signal matches with the desired speed signal resulting in reduced rise time, peak time, settling time, overshoot, and improved steady state error. The designed intelligent aided PID controller was implemented and the simulation result provided a rise of time of 0.8354 second, peak time of 4.9615 seconds, settling time of 1.2240 seconds, final value (actual speed) of 1724.9 rpm, steady state error 0.1 rpm. Simulation comparison with conventional PID controller showed that the PID yielded a rise time of 1.6723 seconds, peak time of 4.5475 seconds, peak overshoot of 0.6913 %, settling time of 2.9646 seconds, final value (actual speed) 1736.1 rpm, and steady state error of 11.1 rpm. Generally, simulation results indicated that the intelligent (FLC) aided classical PID control improve the system performance and achieved the rated speed of the motor.

The welding tracking technology of an underwater welding robot based on sliding mode active disturbance rejection control

PurposeA welding robot is a complicated system with uncertainty, time-varying, strong coupling and non-linear system. It is more complicated if it is used in an underwater environment. It is difficult to establish an accurate dynamic model for an underwater welding robot. Aiming at the tracking control of an underwater welding robot, it is difficult to achieve the control performance requirements by the classical proportional integral derivative control method to realize automatic tracking of the seam. The purpose of this paper is to suggest a novel method to deal with these issues.Design/methodology/approachTo combine the advantages of active disturbance rejection control (ADRC) and sliding mode control (SMC) to improve the shortcomings of a single control method, a hybrid control method for an underwater welding robot trajectory tracking based on SMC_ADRC is proposed in this research work.FindingsThe simulation experiment of the proposed approach is carried out by Matlab/Simulink, and the welding experiment is recorded. The seam gets plumper and smoother, with better continuity and no undercut phenomenon.Originality/valueThe proposed approach is effective and reliable, and the system’s tracking performance is stable, which can effectively reduce chattering and improve system robustness.

Thermocapillary-driven dynamics of a free surface in microgravity: Control of sloshing

Numerical simulations are used to analyze the dynamics of a free surface excited by thermal modulations at the lateral boundaries that generate a time-dependent thermocapillary flow. Fluid parameters are selected to be representative of 5 cSt silicone oil. Following the work of Gligor et al. [“Thermocapillary-driven dynamics of a free surface in microgravity: Response to steady and oscillatory thermal excitation,” Phys. Fluids 34, 042116 (2022)], the response of the free surface to oscillatory thermal excitation is characterized by the displacement of the contact points, and a frequency sweep is used to obtain a Bode-type diagram that reveals a resonance peak in the vicinity of the first sloshing mode. The ability of the thermocapillary flow to excite this sloshing mode suggests a control strategy that uses thermal modulations to dampen sloshing motion. After the response of the isothermal surface to a generic pulse-like inertial perturbation is measured, a classical proportional integral derivative control is implemented and the effect of its gains is considered separately. The efficacy of the controller is characterized by the decay time of the contact point oscillations and by a cost function. The effect of possible delays in the control loop is accounted for. Finally, a controller with a derivative gain is selected and used to dampen the motion induced by a reboosting maneuver of the International Space Station.

Adaptive second-order sliding-mode control for a pressurized water nuclear reactor in load following operation with Xenon oscillation suppression

This study proposes an adaptive second-order sliding mode control based on a twisting algorithm to control nuclear reactor core power during load-following power maneuvers. The control system was designed based on the concept of an extended equivalent control. The control technique does not require knowledge of the uncertainty or upper bound of the disturbance in the system. Additionally, the gain of the control system is a dynamic gain that increases or decreases according to the system requirements within a specified period. Consequently, chattering was attenuated. Chattering excites high-frequency dynamics and causes wear out of the control mechanism, making chattering a severe challenge in sliding-mode control. A nuclear reactor is a time-varying, complex, nonlinear, and constrained system. The characteristics of a nuclear reactor are a function of its operating power level, fuel burnup, and aging. In addition, the load-following mode of operation causes Xenon oscillation, which can further cause instability in the core. Therefore, the non-base load operation of the system, including load following, further aggravates uncertainty and disturbances in the system. To this end, an adaptive second-order sliding mode control that does not require knowledge of the uncertainty or the upper bound of the disturbance in the system was designed. The reactor core was modelled using an experimentally verified and validated multi-point kinetic model with four nodes. Simulation experiments were conducted using a multi-point kinetics model and an adaptive second-order sliding mode control. The results of the simulation experiments indicated that reactor core integrity is guaranteed, and the core is protected against peak power densities, such as linear heat generation rates (LHGRs) and lower departure from nucleate boiling ratios (DNBR). Moreover, the control system achieved the load-following objective and suppressed Xenon oscillation. The performance of the proposed control system was further compared with that of a twisting control system and classical proportional integral derivative control system to validate the effectiveness and reliability of the adaptive twisting second-order sliding mode control system.