Nonlinear PID Research Articles

Nonlinear second order plus time delay model identification and nonlinear PID controller tuning based on extended linearization method

PID control systems based on the first order plus time delay model (FOPTD), which approximate the full system dynamics, are well-accepted for a wide range of linear processes. While such controllers can be applied to overdamped nonlinear processes, they often experience excessive overshoots and oscillations for general nonlinear processes. To overcome this limitation, we propose a novel method to design a nonlinear PID controller based on the second order plus time delay (SOPTD) model. The system nonlinearity requires parameter adjustments of the linearized model across operational ranges. Hence, in this work, it is handled by the extended linearization method (ELM), ensuring local stability under the assumptions of slow and small changes in operating points. Importantly, the model achieves global input-to-output stability even without the above constraints, provided there are no structural and parametric errors. The resulting nonlinear SOPTD model can describe changes in process gain and two time constants as the operation point varies. We demonstrate the applicability of our approach with a polymerization reactor simulation and liquid-level control experiments.

Control of a fixed wing unmanned aerial vehicle using a higher-order sliding mode controller and non-linear PID controller

Unmanned aerial vehicles (UAVs) have seen a rise in use during the last few years. Such aircrafts are now a convenient way to complete dangerous, dirty, and tedious tasks. Given that their operation involves a control problem which is non-linear and coupled, it is difficult to analyse. This paper presents the modeling and control of a fixed-wing unmanned aircraft as a contribution to this field. The system’s flight dynamics is derived using Newton’s second law of motion. The system is designed to have a non-linear Proportional Integral Derivative (NPID) controller and a higher-order sliding mode controller (HOSMC). When simulating the system using MATLAB Simulink software, an external disturbance was added to test the robustness of the controllers. Five performance indices which include mean square error (MSE), integral time square error (ITSE), integral absolute error (IAE), integral time absolute error (ITAE), and integral square error (ISE), were used to compare the controllers performance. These indices are used to provide a numerical assessment of the two controllers’ performance. The outcomes demonstrate that the roll, pitch, and yaw states performed better than the super-twisting sliding mode controller. On the airspeed control, the non-linear PID performed better than the super-twisting sliding mode controller.

Optimized Nonlinear PID Control for Maximum Power Point Tracking in PV Systems Using Particle Swarm Optimization

This paper proposes a high-performing, hybrid method for Maximum Power Point Tracking (MPPT) in photovoltaic (PV) systems. The approach is based on an intelligent Nonlinear Discrete Proportional–Integral–Derivative (N-DPID) controller with the Perturb and Observe (P&O) method. The feedback gains derived are optimized by a metaheuristic algorithm called Particle Swarm Optimization (PSO). The proposed methods appear to present adequate solutions to overcome the drawbacks of existing methods despite various weather conditions considered in the analysis, providing a robust solution for dynamic environmental conditions. The results showed better performance and accuracy compared to those encountered in the literature. We also recall that this technique provides a systematic design procedure in the search for the MPPT in photovoltaic (PV) systems that has not yet been documented in the literature to the best of our knowledge.

Control of quadrotor robot via optimized nonlinear type-2 fuzzy fractional PID with fractional filter: Theory and experiment

This paper presents a novel approach for controlling quadrotor robots. It introduces an optimized nonlinear fractional order type-2 fuzzy system integrated with a Fractional Order Proportional-Integral-Derivative controller, supplemented by a fractional filter in the derivative section. The input scaling factors, which represent the scaling coefficients associated with the input variables of the fuzzy system, are adjusted using nonlinear gains. The proposed controller combines type-2 fuzzy logic, fractional calculus, and nonlinear gains to enhance the control performance of the system. Its purpose is to provide superior control accuracy, robustness, and disturbance rejection capabilities. In order to enhance the performance of the quadrotor, the Bat Optimization Algorithm is utilized to finely adjust the controller parameters and membership function parameters of the fuzzy system. The fuzzy system incorporates Gaussian membership functions and applies the Mamdani min-max method for inference, utilizing the centroid method for defuzzification. The performance of the controller is evaluated in two scenarios: tracking aerial maneuvers in the presence of wind disturbance, and achieving angular stabilization by tracking a pulse function in the Hardware-In-The-Loop real-time test. The findings demonstrate significant improvements compared to traditional PID controllers. These improvements surpass 34 % without a filter and 53 % with a filter, in all directions and scenarios.

Enhancing Artificial Ventilator Systems: A Comparative Analysis of Traditional and Nonlinear PID Controllers

Enhancing Artificial Ventilator Systems: A Comparative Analysis of Traditional and Nonlinear PID Controllers

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.

Comparative performance analysis of fractional-order nonlinear PID controller for complex surge tank system: tuning through machine learning control approach

Comparative performance analysis of fractional-order nonlinear PID controller for complex surge tank system: tuning through machine learning control approach

On designing a configurable UAV autopilot for unmanned quadrotors.

Unmanned Aerial Vehicles (UAVs) and quadrotors are being used in an increasing number of applications. The detection and management of forest fires is continually improved by the incorporation of new economical technologies in order to prevent ecological degradation and disasters. Using an inner-outer loop design, this paper discusses an attitude and altitude controller for a quadrotor. As a highly nonlinear system, quadrotor dynamics can be simplified by assuming several assumptions. Quadrotor autopilot is developed using nonlinear feedback linearization technique, LQR, SMC, PD, and PID controllers. Often, these approaches are used to improve control and to reject disturbances. PD-PID controllers are also deployed in the tracking and surveillance of smoke or fire by intelligent algorithms. In this paper, the efficiency using a combined PD-PID controllers with adjustable parameters have been studied. The performance was assessed by simulation using matlab Simulink. The computational study conducted to assess the proposed approach showed that the PD-PID combination presented in this paper yields promising outcomes.

A Nonlinear PID-Incorporated Adaptive Stochastic Gradient Descent Algorithm for Latent Factor Analysis

High-dimensional and incomplete (HDI) data are commonly encountered in various big data-related applications concerning the complex interactions among numerous nodes, such as the user-item iterations in a recommender system. A stochastic gradient descent (SGD)-based latent factor analysis (LFA) model can perform efficient representation learning to such HDI data, thereby extracting useful knowledge from them. However, a standard SGD algorithm updates a latent factor based on the current stochastic gradient only, without the considerations on the past information, making a resultant model suffer from slow convergence. To address this critical issue, this paper proposes an Adaptive Non-linear PID-incorporated SGD (ANPS) algorithm with two-fold ideas: 1) rebuilding the instant learning error when computing the stochastic gradient following the principle of a nonlinear PID controller to incorporate past update information into the learning scheme efficiently, and 2) implementing gain parameter adaptation following the principle of particle swarm optimization (PSO). Experiments on six widely-adopted HDI datasets demonstrate that compared with state-of-the-art LFA models, an ANPS-based LFA model achieves significant advantage in both efficiency and accuracy. Moreover, its flexible gain parameter adaptation mechanism greatly boosts its practicability for real issues. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —In many industrial applications like recommender systems, social network systems, and cloud service systems, people usually encounter numerous nodes and their highly-incomplete relationships. An HDI matrix is commonly adopted to describe such specific relationships. One of the major challenges is to acquire useful knowledge from an HDI matrix efficiently and accurately for various data analysis tasks, e.g., accurate recommendation, community detection, and web service selection. An SGD-based LFA model has been widely adopted to tackle this issue. However, it suffers from slow convergence that leads to considerable time cost on large-scale datasets. This study proposes an ANPS algorithm following the principle of a nonlinear PID controller. With it, an ANPS-based LFA model is achieved, which possesses fast convergence rate on an industrial HDI matrix. The proposed ANPS algorithm can be leveraged for different types of various machine learning models, thereby improving their utility and scalability in practice.

Autonomous navigation and control of magnetic microcarriers using potential field algorithm and adaptive non-linear PID.

Microparticles are increasingly employed as drug carriers inside the human body. To avoid collision with environment, they reach their destination following a predefined trajectory. However, due to the various disturbances, tracking control of microparticles is still a challenge. In this work, we propose to use an Adaptive Nonlinear PID (A-NPID) controller for trajectory tracking of microparticles. A-NPID allows the gains to be continuously adjusted to satisfy the performance requirements at different operating conditions. An in-vitro study is conducted to verify the proposed controller where a microparticle of 100 m diameter is put to navigate through an open fluidic reservoir with virtual obstacles. Firstly, a collision-free trajectory is generated using a path-planning algorithm. Secondly, the microparticle dynamic model, when moving under the influence of external forces, is derived, and employed to design the A-NPID control law. The proposed controller successfully allowed the particle to navigate autonomously following the reference collision-free trajectory in presence of varying environmental conditions. Moreover, the particle could reach its targeted position with a minimal steady-state error of 4 m. A degradation in the performance was observed when only a PID controller was used in the absence of adaptive terms. The results have been verified by simulation and experimentally.

Nonlinear PID Control for Automatic Docking of a Large Container Ship in Confined Waters Under the Influence of Wind and Currents

This study addresses the challenges of maneuvering a large container ship in confined waters under the influence of wind and currents. The proposed guidance, navigation, and control system presents a novel combination of modeling methodologies, control allocation techniques, and nonlinear control systems theory. We consider a docking scenario through a simulation of a realistic, narrow harbor accommodating area-specific currents and global wind forces. Control allocation is solved by utilizing detailed models of the actuators and hydrodynamics in a mixed-integer-like solution for optimal thrust allocation, and an inverse mapping to the control inputs. Furthermore, our approach introduces a modified Wageningen B-Series model, that is capable of modeling propellers with negative pitch dynamics. The complexity of safely docking in environments like the Antwerp harbor, where wind and currents pose significant risks, is tackled using a nonlinear PID control system integrated with Line-Of-Sight (LOS) guidance. This enables precise maneuvering of a fully actuated Roll-On/Roll-Of vessel to its docking position and orientation. Given that few studies on automated docking holistically address the intricate challenges of complex harbor environments and the concurrent impact of multiple external forces, our work proposes a comprehensive solution based on an integrated combination of guidance, navigation, and control systems.

An adaptive neuro-fuzzy with nonlinear PID controller design for electric vehicles

In this work, an adaptive neuro-fuzzy (ANF) with a nonlinear proportional integral derivative (NLPID) controller (ANF-NLPID) has been proposed to solve the speed-tracking problem in electric vehicles (EVs) with brushless DC motor (BLDC). The ANF-NLPID controller eliminates the external disturbances caused by environmental or internal issues and uncertainties caused by parameter variations that lead to insufficient speed-tracking performance and increased energy consumption in EVs. An improved particle swarm optimization based on the chaos theory (IPSO-CT) algorithm is introduced to obtain the parameters of the fuzzy logic controller membership function and nonlinear PID controller and present the optimal performance for the EV. Employing the chaos technique with PSO helps to prevent the system from being trapped in the local minimum or optimum problem. The performance of the IPSO-CT algorithm is tested using a numerical comparison with other existing works. The outstanding performance of the ANF-NLPID controller has been evaluated by measuring the speed-tracking performance for the new European driving cycle (NEDC) and circular trajectories. Three case studies have been presented based on measuring the ANF-NLPID controller performance without disturbances, with disturbances, with disturbances, and uncertainties effects, respectively. Furthermore, the ANF-NLPID controller has been employed in different EV models to study the performance of this type of controller. Each of the three cases includes other existing works along with the ANF-NLPID controller to provide an insightful comparison using statistical functions to obtain each controller’s overall objective function value. The other existing works are fuzzy fractional order PID (Fuzzy FOPID), fuzzy integer order PID (Fuzzy IOPID), and integer order PID (IOPID) controllers. A sensitivity analysis has been conducted to test the proposed controller’s ability to present high speed-tracking performance while changing the disturbances and uncertainty rates. The results demonstrate that the ANF-NLPID controller is superior in speed-tracking control regulation for the new European cycle drive (NEDC) and circular speed trajectories and overcomes the external disturbances and uncertainties problem with low error results. In the end, the results reveal that the ANF-NLPID controller is more efficient than the fuzzy FOPID, fuzzy IOPID, and IOPID controllers in each case.

IrisVSA: Infinite-rotation infinite-stiffness Variable Stiffness Actuator towards physical human–robot-interaction

In Human–Robot-Collaboration applications, variable stiffness actuators provide an attractive actuation solution due to their well-established capabilities in ensuring accuracy and safety. Although, several existing VSAs have achieved an infinite-range of stiffness, those are generally relatively bulky, incapable of attaining an infinite-range of rotation, and their stiffness adjustment rate is rather slow. In this paper, we introduce a new infinite-rotation infinite-stiffness Variable Stiffness Actuator (irisVSA). The novelty of this actuator lies in its design topology, where two long-armed torsional springs are mounted on the output link and connected to the input link via a Force Contact Point (FCP). The variation in stiffness is realized by altering the relative distance from the FCP to the joint rotation center (effective arm). This unique topology offers a wide range of stiffness ranging from transparency (0 stiffness) to physically rigid. Moreover, the rate of stiffness adjustment is considerably fast (0.7 sec) through the utilization of a hypocycloid gear train. The working principle, design, prototyping, and characterization process for the irisVSA are detailed here. A Nonlinear Proportional–Integral–Derivative Controller is proposed to ensure the system’s accuracy. The safety of the actuator was evaluated by subjecting it to both impact force criterion experiments as well as Head Injury Criterion.

A COVID-19 Based on Fractional Order Integral-Tilt Derivative Controller for Nonlinear Servomechanism Model

In this research, a new one-axis servomechanism investigation is presented, taking into account parameter fluctuation and system uncertainty. Additionally, a novel method for very effective TID control was created to accurately monitor a chosen profile. A comparative study between the suggested control method and the well-known controllers (PID and Nonlinear PID) is also included. The COVID-19 optimization technique was used to discover the best control parameters. Through the online simulation, the servomechanism system's settings were modified at random within a predetermined range. As nonlinearity resources (friction, backlash, environmental influences), these parameters fluctuate and contribute to system uncertainty. It had been completed and looked at to compare the linear and nonlinear models. The results demonstrate that the suggested controller is capable of tracking the number of operational points with high accuracy, a short rising time, and little overrun.

Modified nondominated sorting genetic algorithm-based multiobjective optimization of a cross-coupled nonlinear PID controller for a Twin Rotor System

This paper presents an innovative nonlinear PID control scheme based on a modified nondominated sorting genetic algorithm validated using a laboratory helicopter model called the Twin Rotor System. The concepts of controlled elitism and dynamic crowding distance are incorporated into the proposed algorithm to progress towards the best solution from the entire population in order to solve the multiobjective optimization problem with good convergence characteristics. The addition of nonlinear functions to the cross-coupled PID controller structure initiates better error tracking and facilitates smooth output under changing input conditions. The design objective is to implement an optimal nonlinear PID control scheme for the angular displacements of the twin-rotor system, with integral square error and control energy taken as the multiobjective problems. The statistical performance of the controller is analyzed by considering the best, worst, mean, and standard deviations of ISE. In this work, simultaneous control of pitch and yaw angles is considered to get rid of the coupling effect between the two rotors. The results indicate the advantage of the MNGSA-based tuning for the two degrees of freedom MIMO control with standard reference trajectories as per the TRMS330-10 model.

Non-Linear PID Control of Fluid Catalytic Cracking Unit

Non-Linear PID Control of Fluid Catalytic Cracking Unit

A Particle Swarm Optimization tuned nonlinear PID controller with improved performance and robustness for First Order Plus Time Delay systems

The Proportional, Integral, and Derivative (PID) controller is a ubiquitous controller within industry. The conventional PID controller can struggle to provide a satisfactory response for the nonlinear systems faced by industry. In addition, conventional PID controllers have a trade-off between performance and robustness, where they cannot compensate for both without compromising stability or speed. In this paper, a novel Nonlinear gains Proportional, Integral, and Derivative (NLPID) control algorithm is proposed as a practical control strategy that shows improvements in the simultaneous set-point tracking and disturbance rejection, to control nonlinear systems. The paper shows the performance and robustness of the proposed controller for the case of a First Order Plus Time Delay (FOPTD) system, which heavily exists in industry. The Particle Swarm Optimization (PSO) algorithm is used to tune the proposed NLPID controller. The performance of the proposed NLPID controller is simulated and compared against established controllers in literature such as conventional PID, two degree of freedom PID, and Smith Predictor PID controllers in MATLAB/Simulink for an FOPTD system, with various uncertainties and disturbances. This study shows that the proposed NLPID controller maintains faster settling and rise time, with no overshoot and excellent disturbance rejection, without compromising stability or speed, and is robust against parametric, additive, and multiplicative uncertainties.

Designing a Secure Mechanism for Image Transferring System Based on Uncertain Fractional Order Chaotic Systems and NLFPID Sliding Mode Controller

A control method for the robust synchronization of a class of chaotic systems with unknown time delay, unknown uncertainty, and unknown disturbance is presented. The robust controller was designed using a nonlinear fractional order PID sliding surface. The Lyapunov method was used to determine the update laws, prove the stability of the proposed mechanism, and guarantee the convergence of the synchronization errors to zero. The simulation was performed using MATLAB software to evaluate the performance of the proposed mechanism, and the results showed that it was efficient. Finally, the proposed method was combined with a secure communication application to encrypt images, and the results obtained were favorable regarding the standard criteria of correlation, NPCR, PSNR, and information entropy.

Modelling, control and development of GUI-based simulator for a quadcopter using nonlinear PID control

Modelling, control and development of GUI-based simulator for a quadcopter using nonlinear PID control

Performance evaluation of a non linear PID controller using chaotic gravitational search algorithm for a twin rotor system

AbstractA novel strategy using a chaotic gravitational search algorithm (CGSA) based nonlinear PID control scheme, which is validated through a laboratory helicopter model called the twin rotor system, is presented in this paper. In this work, CGSA is used as a stochastic based global optimization algorithm for controller design in the twin rotor system adopted. The fine chaotic search process used in CGSA obtains the optimal solution in the iterative process based on the current best solution. The goal of the controller design in this paper is to stabilize the twin rotor system with considerable cross couplings to reach the selected position and follow the desired trajectory effectively. The addition of nonlinear functions to the PID controller structure initiates better error tracking and facilitates smooth output under changing input conditions. The design objective is to implement a nonlinear PID control scheme for the angular displacements of the twin rotor system with minimization of the integral square error (ISE) as the fitness function in the algorithm. The statistical performance of the controller is analyzed by considering the best, worst, mean, and standard deviations of ISE. In this work, simultaneous control of pitch and yaw angles is considered to get rid of the coupling effect between the two rotors. From the simulation results it is observed that the proposed work shows better performance than the other evolutionary computation techniques. The results also indicate the advantage of the proposed CGSA based tuning for the two degree of freedom MIMO control with standard reference trajectories as per the TRMS330‐10 model.