Classical Proportional Integral Derivative Research Articles

A fast relay feedback auto-tuning tilt-integral-derivative (TID) controller method with the fractional-order Ziegler–Nichols approach

The relay feedback auto-tuning method, which was an early commercialized approach, has maintained its popularity due to its simplicity and robustness. However, the classical proportional integral derivative (PID) controller auto-tuning method often results in unacceptable overshoot, especially for integrating and higher-order processes. By integrating the TID controller with the relay feedback technique, we significantly enhance dynamic control performance without relying on prior knowledge of the system. However, the direct application of the classical auto-tuning method to the TID controller encounters challenges due to the additional fractional-order transfer function s−1n. Therefore, we have developed a fractional-order Ziegler–Nichols (FOZ-N) approach, specifically designed to adjust the parameters of the TID controller. The proposed FOZ-N method is fast, simple, and capable of achieving the desired performance. In contrast to the previous Ziegler–Nichols tuning method, the TID controller parameters Kt and Ki are determined to shift the critical point (−1/Ku,j0) to the FOZ-N point (−0.5,−j0.7) on the Nyquist curve, ensuring system robustness and dynamic performance. The impact of the fractional order parameter s−1n and ratio r is explored through time-domain analysis, where these parameters are determined to ensure optimal dynamic performance. Additionally, we provide a detailed tuning procedure along with a helpful example. To demonstrate the advantages of the proposed auto-tuning TID controller over the Ziegler–Nichols PID controller, Optimal PID controller, simple internal model control (SIMC) PID controller, and Ziegler–Nichols FOPID controller, we present a simulation illustration involving multiple different systems. To validate the practical outcomes of this paper, we present experimental results on the temperature control of a Peltier cell.

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.

Attitude control of a 3-DoF quadrotor platform using a linear quadratic integral differential game approach

In this study, a linear quadratic integral differential game approach is applied to regulate and track the Euler angles for a quadrotor experimental platform using two players. One produces commands for each channel of the quadrotor and another generates the worst disturbance based on the mini-maximization of a quadratic criterion with integral action. For this purpose, first, the attitude dynamics of the platform are modeled and its parameters are identified based on the Nonlinear Least Squares Trust-Region Reflective method. The performance of the proposed controller is evaluated for regulation and tracking problems. The ability of the controller is also examined in the disturbance rejection. Moreover, the influence of uncertainty modeling is studied on the obtained results. Then, the performance of the proposed controller is compared with the classic Proportional Integral Derivative, Linear Quadratic Regulator, and Linear Quadratic Integral Regulator. The results demonstrate the effectiveness of the Game Theory on the Linear Quadratic Regulator approach when the input disturbance occurs.

Attitude modelling and real-time robust control of a 3-DoF quadcopter UAV test bench

Abstract In this work, a three degrees-of-freedom (3-DoF) static quadcopter unmanned aerial vehicle (UAV) test-rig of a pendulum-type configuration is custom-designed, developed, instrumented, and interfaced with a PC. The rig serves as a test bed to develop high-fidelity mathematical models as well as to investigate autopilot designs and real-time closed-loop controllers’ performances. The Simulink Desktop Real-Time software is employed for the quadcopter’s attitude signals acquisition and real-time implementation of closed-loop controllers on a target microcontroller hardware. The mathematical models for pitch, roll, and yaw axes are derived via the first principle and validated with the experimental linear system identification (SI) techniques. Subsequently, employing the multi-parameter root contour technique, the classical proportional integral derivative (PID) controllers are designed and implemented in real-time on the quadcopter UAV test rig. This served as a benchmark controller for comparing it with an integral-based linear quadratic regulator (LQR) controller. Further, to improve the transient response of the LQR controller, a novel robust integral-based LQR controller with a feedforward term (LQR-FF) is implemented, which shows much superior performance than the benchmark and basic LQR controller. This work thus will act as a precursor for a more complex 3-DoF autopilot design of an untethered quadcopter.

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.

Feedback control applied to a low cost ball-in-tube air levitation plant

Commercial educational tools for teaching feedback concepts in control systems engineering and mechatronics are generally expensive, large, complexand sensitive instruments; therefore, it cannot be used in universities with budget constraints, which greatly hinders the teaching of basic concepts of control theory and application. The mathematical tools that are taught in the disciplines of control theory in the undergraduate course are often abstract, especially in terms of practical application in an industrial setting, which makes it necessary to use didactic control plants to complement teaching and hands-on experimentation. This paper presents a low-cost ball and tube air levitation laboratory system as a teaching tool for engineering. Ball and tube laboratory setup is a dynamic benchmark system, designed to control the position of the ball on a vertical upward airflow that counteracts the gravitational force exerted on the ball without mechanical support. A blower feeds airflow, and the position of the ball is measurable by using an ultrasonic distance meter. As the purpose of the article is to serve as support material for undergraduate students who are taking their first steps in the study of control theory and feedback control, detailed modeling by the laws of physics are presented, followed by classic tools for the study of linear control and then a proportional-integral-derivative (PID) control system is developed. A modified structure of the classic PID is used and the results are compared with the classic structure.

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%.

A deep reinforcement learning algorithm to control a two-wheeled scooter with a humanoid robot

Balancing a two-wheeled scooter is considered a challenging task for robots, as it is a non-linear control problem in a highly dynamic environment. The rapid pace of development of deep reinforcement learning has enabled robots to perform complex control tasks. In this paper, a deep reinforcement learning algorithm is proposed to learn the steering control of the scooter for balancing and patch tracking using an unmodified humanoid robot. Two control strategies are developed, analyzed, and compared: a classical Proportional–Integral–Derivative (PID) controller and a Deep Reinforcement Learning (DRL) controller based on Proximal Policy Optimization (PPO) algorithm. The ability of the robot to balance the scooter using both approaches is extensively evaluated. Challenging control scenarios are tested at low scooter speeds, including 2.5, 5, and 10 km/h. Steering velocities are also varied, including 10, 20, and 40 rad/s. The evaluations include upright balance without disturbances, upright balance under disturbances, tracking sinusoidal path, and path tracking. A 3D model of the humanoid robot and scooter system is developed, which is simulated in a state-of-the-art GPU-based simulation environment as a training and test bed (NVidia’s Isaac Gym). Despite the fact that the PID controller successfully balances the robot, better final results are achieved with the proposed DRL. The results indicate a 52% improvement on average in different speeds with better performance in path tracking control. Controller command evaluation on the real robot and scooter indicates the robot’s complete capability to realize steering control velocities.

Tethered Unmanned Aerial Vehicles—A Systematic Review

In recent years, there has been a remarkable surge in the development and research of tethered aerial systems, thus reflecting a growing interest in their diverse applications. Long-term missions involving aerial vehicles present significant challenges due to the limitations of current battery solutions. Tethered vehicles can circumvent such restrictions by receiving their power from an element on the ground such as a ground station or a mobile terrestrial platform. Tethered Unmanned Aerial Vehicles (UAVs) can also be applied to load transportation achieved by a single or multiple UAVs. This paper presents a comprehensive systematic literature review, with a special focus on solutions published in the last five years (2017–2022). It emphasizes the key characteristics that are capable of grouping publications by application scope, propulsion method, energy transfer solution, perception sensors, and control techniques adopted. The search was performed in six different databases, thereby resulting in 1172 unique publications, from which 182 were considered for inclusion in the data extraction phase of this review. Among the various aircraft types, multirotors emerged as the most widely used category. We also identified significant variations in the application scope of tethered UAVs, thus leading to tailored approaches for each use case, such as the fixed-wing model being predominant in the wind generation application and the lighter-than-air aircraft in the meteorology field. Notably, the classical Proportional–Integral–Derivative (PID) control scheme emerged as the predominant control methodology across the surveyed publications. Regarding energy transfer techniques, most publications did not explicitly describe their approach. However, among those that did, high-voltage DC energy transfer emerged as the preferred solution. In summary, this systematic literature review provides valuable insights into the current state of tethered aerial systems, thereby showcasing their potential as a robust and sustainable alternative to address the challenges associated with long-duration aerial missions and load transportation.

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.

Dynamic characteristics and active vibration control effect for shape memory polymer composites

Shape memory polymer composites (SMPCs) are widely used as a new type of composite material in space expansion structures, which are prone to vibration and resonance in a space environment. A new type of macro fiber composite (MFC) can be used to control the vibration of the structure. Based on Kirchhoff plate theory, the differential equations of motion for composite laminates are derived. Theoretical analysis of SMPC cantilever plates with varying carbon fiber content is carried out. In addition, the effects of local temperature changes on the dynamic characteristics of SMPC with different fiber content are studied. The vibration differential equations of the SMPC cantilever plate were obtained by using the separation variable method and the modal vibration superposition principle. The state-space equations of the system were established based on the transfer function, and the frequency response was determined by sine sweep excitation of the SMPC specimen. The open-loop and closed-loop vibration active control of SMPC specimens was investigated using the classical proportional integral derivative (PID) procedure. Finally, the effect of carbon fiber content on the vibration active control characteristics of SMPC structures was analysed.

Design and Implementation of Adaptive and Artificial Intelligence Controller for Brushless Motor Drive Electric Vehicle

<div>Brushless direct current (BLDC) motor aims to obtain high efficiency when compared to conventional DC motors due to several reasons. But when it comes to the control then its control is much more complicated due to the requirement of a phase supply switching circuit. Usually, the conventional and classical proportional integral derivative (PID) controller is used but it is quite cumbersome to tune its fixed gains. APID controller is used where PID fails to fulfill the objectives in varying situations. So, the adaptive proportional integral derivative (APID) controller is utilized to enhance the results. An artificial neural network (ANN) controller is one of the recent control methods, which gives accurate and precise results and utilizes ANN to give more accurate results. But it lacks fuzzy logic, that is, human tendency, and finally, the artificial neuro-fuzzy inference system (ANFIS) controller is concluded as the best controller to limit the speed of the BLDC motor. ANFIS includes all the advantages of controllers and provides the most accurate results. The mathematical model of all the controllers is discussed and its performance is simulated in MATLAB/Simulink. ANFIS includes all the advantages of controllers and provides the most accurate results.</div>

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.