Nonlinear PID Controller Research Articles

A novel PID control with fractional nonlinear integral

A nonlinear PID controller for robust tracking of second-order nonlinear systems is proposed, which consists in a classical PD structure plus a fractional-order nonlinear integral action of control (FONLI). This nonlinear integral action of fractional-order induces robustness properties to the closed-loop system in order to withstand for a general class of continuous but not necessarily differentiable disturbances, while inducing a stable sliding motion in finite time, such that, the tracking error converges with exponential rate. The resulting controller is uniformly continuous, preserving the regularity of the control signal. The proposed scheme is extended for higher-order dynamical systems by means of a state-feedback control plus a FONLI, inducing a stable motion in finite time. Numerical results based on simulation are discussed to show the reliability of the proposed scheme.

A nonlinear PID controller based novel maximum power point tracker for PV systems

This paper proposes a novel application of Nonlinear Proportional-Integral-Derivative (NPID) controller to effectively attain Maximum Power Point Tracking (MPPT) in Photovoltaic (PV) systems. The proposed controller is based on the basic structure of the PID controller wherein, its integral term gain is varied at run time according to instantaneous error. The performance of the NPID controller is assessed in terms of undershoot, settling time and ripple which have been evaluated under varying realistic irradiation and temperature profiles. The Teaching Learning Based Optimization (TLBO) tuned NPID controller is found to be superior to TLBO tuned PID, Perturb and Observe and Incremental Conductance classical MPPT methods for all the considered environmental profiles. Therefore, based on the presented comprehensive investigations, it is concluded that the proposed NPID controller is a promising MPPT technique.

Control Algorithm of Six Cable-Driven Parallel Manipulator for FAST

The feed cabin supporting system in a Five-hundred-meter Aperture Spherical Radio Telescope (FAST) project is a large-span cable-driven parallel manipulator (CPM). In this article, the kinematics model of the six CPM was established in the global coordinate O-XYZ. A corresponding difference of cable length between the current position and next position of the feed cabin was determined by controlling the servo motor. A nonlinear adaptive interaction PID (NAIPID) controller was proposed to improve the control performance of the control system. The simulations program of traditional PID and NAIPID were implemented in MATLAB software, respectively. A 3-meter model experiment was carried out to prove the control accuracy of the feed cabin. Both simulation and experimental results showed that the proposed control method had rapid response, and can effectively improve the control performance for the six CPM systems.

Performance Study of Enhanced Non-Linear PID Control Applied on Brushless DC Motor

<span style="color: black; font-family: 'Times New Roman',serif; font-size: 9pt; mso-fareast-font-family: 'Times New Roman'; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA; mso-bidi-font-style: italic;">This paper presents an enhanced nonlinear PID (NPID) controller to follow a preselected speed profile of brushless DC motor drive system. This objective should be achieved regardless the parameter variations, and external disturbances. The performance of enhanced NPID controller will be investigated by comparing it with linear PID control and fractional order PID (FOPID) control. These controllers are tested for both speed regulation and speed tracking. The optimal parameters values of each control technique were obtained using Genetic Algorithm (GA) based on a certain cost function. Results shows that the proposed NPID controller has better performance among other techniques (PID and FOPID controller).</span>

Tuning of Nonlinear PID Controller for TRMS Using Evolutionary Computation Methods

Tuning of Nonlinear PID Controller for TRMS Using Evolutionary Computation Methods

Data-Driven PID Controller and Its Application to Pulp Neutralization Process

The pulp neutralization process is a complex industrial process with strong nonlinearity and time-varying dynamics. In general, this kind of process is hardly controlled by using traditional control techniques such as the proportional-integral-derivative (PID) controller. To resolve this problem, a novel PID control scheme is proposed by integrating a data-driven compensation of unmodeled dynamics and a multistep ahead of optimal control strategy. Essential difference from the classical PID controller lies in the use of unmodeled dynamics, the measured data from the pulp neutralization process is used directly for building the nonlinear PID controller, which plays an important role in control system design. Based on multistep ahead prediction optimal control theory, the controller parameters can be obtained through optimizing a cost function. Some theoretical results on the stability and convergence of the closed-loop system are established. To demonstrate the effectiveness of the proposed control techniques, a simulation model and a cobalt nickel hydroxide pulp neutralization process are employed. Simulations were carried out using data extracted from an actual pulp neutralization process, followed by some industrial experiments. Results from both simulations and experiments indicate that our proposed controller can effectively control the pH value of the pulp neutralization process with promising control performance.

Fuzzy-based nonlinear PID controller and its application to CSTR

This study presents a new design method for a nonlinear variable-gain PID controller, the gains of which are described by a set of fuzzy rules. User-defined parameters are tuned using a genetic algorithm by minimizing the integral of absolute error and the weighted control input deviation index. It was observed in the experimental results on a continuous stirred tank reactor (CSTR) that the proposed controller provided performances: overshoot M p ≤1.25%, 2% settling time t s ≤1.71 s and IAE≤1.26 for set-point tracking, perturbance peak M peak ≤0.05%, 2% recovery time t rcy ≤3.97 s and IAE≤0.10 for disturbance rejection, and M peak ≤0.04%, t rcy ≤2.74 s and IAE≤0.04 for parameter changes. Comparison with those of two other methods revealed that the proposed controller not only led to less overshoot and shorter settling time for set-point tracking and less perturbance peak and shorter recovery time for disturbance rejection, but also showed less sensitivity to parameter changes.

Performance investigations of APSO tuned linear and nonlinear PID controllers for a nonlinear dynamical system

This paper investigates the performance of adaptive particle swarm optimization (APSO) algorithm to find the best optimal gain parameters (Kp, Ki, Kd) in linear PID (L-PID) and nonlinear PID (NL-PID) controllers for the trajectory control of a nonlinear dynamical system (NLDS). Mathematical modeling, stability and performance analysis of a NLDS are being carried out with L-PID and NL-PID controllers. It is found that the APSO based tuning of NL-PID controller provides better tracking of NLDS than L-PID controller in respect of its search domain, premature convergence, and computational efficiency. Simulation analysis of various variables of controllers and system response such as error, cost function, and response of NLDS and their comparison to that of APSO tuned L-PID controller is described.

A kind of nonlinear PID controller for Refrigeration Systems based on Vapour Compression

There are different ways in making nonlinear PID controllers. In this paper, a kind of nonlinear PID controller designed by special usage of nonlinear function is introduced, which is called Han’s nonlinear PID controllers for short according to the name of the original inventor. Typically, a fal function based nonlinear PID controller has been taken as an example for performance verification upon the Benchmark PID 2018 platform. The simulation results prove that, by parameters tuning for the performance of minimal control efforts, the fal function based nonlinear PID controller can achieve the desired cooling goal under more stable operating conditions yet holding nearly the similar quality steady-state performance.

Collective Pitch Control with Active Tower Damping of a Wind Turbine by Using a Nonlinear PID Approach

The present work describes the results obtained from a nonlinear PID control (NPID) approach for the pitch control with top tower active damping of a large wind turbine. The control algorithm is implemented by using a well-known approach based on hyperbolic secant functions. A nonlinear PID controller and a nonlinear P controller are used for the collective pitch control and the active tower damping, respectively. As simulation platform, the 5-MW reference turbine developed by NREL and the software FAST are used. Results show that the NPID approach can provide significant improvements in the control performance in comparison to the classic control approach, in particular when the wind speed goes far from its rated value.

Enhanced control of a flexure-jointed micromanipulation system using a vision-based servoing approach

This paper describes a high-precision motion control implementation for a flexure-jointed micromanipulator. A desktop experimental motion platform has been created based on a 3RUU parallel kinematic mechanism, driven by rotary voice coil actuators. The three arms supporting the platform have rigid links with compact flexure joints as integrated parts and are made by single-process 3D printing. The mechanism overall size is approximately 250x250x100 mm. The workspace is relatively large for a flexure-jointed mechanism, being approximately 20x20x6 mm. A servo-control implementation based on pseudo-rigid-body models (PRBM) of kinematic behavior combined with nonlinear-PID control has been developed. This is shown to achieve fast response with good noise-rejection and platform stability. However, large errors in absolute positioning occur due to deficiencies in the PRBM kinematics, which cannot accurately capture flexure compliance behavior. To overcome this problem, visual servoing is employed, where a digital microscopy system is used to directly measure the platform position by image processing. By adopting nonlinear PID feedback of measured angles for the actuated joints as inner control loops, combined with auxiliary feedback of vision-based measurements, the absolute positioning error can be eliminated. With controller gain tuning, fast dynamic response and low residual vibration of the end platform can be achieved with absolute positioning accuracy within ±1 micron.

Modelling, stability analysis and computational aspects of nonlinear fuzzy PID controllers using Mamdani minimum inference

Modelling, stability analysis and computational aspects of nonlinear fuzzy PID controllers using Mamdani minimum inference

Modelling, stability analysis and computational aspects of nonlinear fuzzy PID controllers using Mamdani minimum inference

This paper presents two new mathematical models of the simplest fuzzy PID controller which employ two fuzzy sets (negative and positive) on each of the three input variables (error, change in error and double change in error) and four fuzzy sets (-2, -1, +1, +2) on the output variable (incremental control). L-type, Γ-type and II-type membership functions are considered in fuzzification process of input and output variables. Controller modelling is done via algebraic product AND operation, maximum/bounded sum OR operation, Mamdani minimum inference method, and centre of sums (CoS) defuzzification. The new models obtained in this manner turn out to be nonlinear, and their properties are studied. Since digital controllers are implemented on the digital processors, the computational and memory requirements of the fuzzy controllers and conventional (non-fuzzy) controller are compared. Stability analysis of closed loop systems containing the fuzzy controller models is done using the small gain theorem.

Tracking performance of NPID controller for cutting force disturbance of ball screw drive

The high demand in tracking performance is crucial in machine tools application.Therefore,the purpose of this paper is to design a Nonlinear PID (NPID) controller for improvement of tracking performance via cutting force.The method was then compared with another method which was conventional PID controller.The configuration included different cutting force disturbances of 1500rpm,2500rpm and 3500rpm.The parameters were set to 0.4Hz and 0.7Hz frequency for every 10mm and 20mm of amplitude, respectively.The investigation was centred on a comparative study of these two techniques which focused on x-axis of Googol Tech XY ball screw drive system. Results between the designed controllers were validated based on two types of errors;the maximum tracking error and root mean square error.Results showed that the NPID controller recorded better tracking performance compared to PID controller with an error reduction of about 33%. In addition,the results proved that NPID controller is highly practical and suitable to be used for ball screw drive.The controller can be further improved with the implementation of observer such as disturbance observer to compensate the cutting forces.

Model Identification And Controller Design For An Electropneumatic Actuator System With Dead Zone Compensation

abstract Pneumatic actuator system is inexpensive, high power to weight ratio, cleanliness and ease of maintenance make it’s a choice compared to hydraulic actuator and electromagnetic actuator. Nonetheless, the steady state error of the system is high due to the dead zone of the valve. In this paper, an Auto-Regressive with External Input (ARX) model structure is chosen to represent the pneumatic actuator system. The recursive least square method is used to estimate the model parameters. The poleassignment controller is then developed for position tracking. To cater the problem of high in steady state error, the dead zone compensation is added to the system. The dead zone controller was designed based on the inverse dead zone model and the dead zone compensation designed based on the desired error. The proposed method is then experimentally with varies load and compares with Nonlinear PID controller. The result shows that the proposed controller reduced the overshoot and steady state error of the pneumatic actuator system to no overshoot and 0.025mm respectively.

Global PID Control of Robot Manipulators Equipped with PMSMs

AbstractThis paper is concerned with PID position regulation of robot manipulators actuated by permanent magnet synchronous motors (PMSMs). We present a global asymptotic stability proof when the electric dynamics of these actuators is taken into account. Our controller is so simple that it differs from standard field oriented control (SFOC) of PMSMs in only three simple nonlinear terms that have to be added and a nonlinear PID controller which is used instead of a classical PID controller. Thus, our proposal represents the closest result to SFOC of PMSMs provided with a formal global asymptotic stability proof. We present an advancement, if modest, towards presenting a global stability proof for SFOC when used in robotics.

유압식 계선윈치의 로프 장력 제어

Maintaining stable tension of mooring winch ropes on-board a ship under waves, tides and draft change is very important for the safety of the ship. Hydraulic mooring winches, used for pulling or hauling ropes, are in general highly nonlinear and time varying systems due to the compressibility and varying viscosity of the fluid, oil leakage and disturbances from the load. This paper presents a design method of a nonlinear PID (NPID) controller, combining the linear PD actions and nonlinear I action, for constant rope tension control of a hydraulic mooring winch. The gain of the I term is continuously changed according to the error during the operation for achieving good control effort under the changing external environment and implemented by Takagi-Sugeno type fuzzy rules. The NPID controller parameters are tuned by a genetic algorithm (GA). Effectiveness of the proposed method is verified through a set of simulation works.

Stabilization of nonlinear inverted pendulum system using MOGA and APSO tuned nonlinear PID controller

An inverted pendulum system (IPS) is a highly nonlinear dynamical open loop unstable system, typically used as a benchmark to verify the performance of controllers. The IPS emulates the behaviour o...

Motion Control of An Autonomous Mobile Robot using Modified Particle Swarm Optimization Based Fractional Order PID Controller

This paper presents a comparison between two nonlinear PID controllers, the first is the Neural based controller and the second is the nonlinear fractional order PID controller (FOPID) for a trajectory tracking control of a non-holonomic two wheeled mobile robots (2-WMR). A modified particle swarm optimization (MPSO) has been proposed in this work to tune the parameters of the nonlinear FOPID controller to design the controller so that the 2-WMR follows exactly a predefined continuous track. The kinematic model of a differential drive 2-WMR has been derived to simulate the behavior of the 2-WMR and it is used in the design and simulations of the proposed FOPID controller. From simulation and results, it can be seen that the efficiency of the proposed nonlinear FOPID controller outperforms the nonlinear integer order PID controller; this is proved by the minimized tracking error and the speed control signals obtained.

Nonlinear adaptive fractional order fuzzy PID control of a 2-link planar rigid manipulator with payload

The main objective of this paper is to demonstrate that fractional order operators (differentiator/integrator) can increased the robustness of an intelligent controller. In this paper, a nonlinear adaptive fractional order fuzzy proportional integral derivative (NLA – FOFPID) controller is presented to control a nonlinear, coupled, multi-input and multi-output and uncertain system i.e. a 2-link planar rigid robotic manipulator with payload. The NLA – FOFPID controller is realized using non-integer order differentiator and integrator operators in nonlinear adaptive fuzzy proportional integral derivative (NLA – FPID) controller. The control objective is to track a reference trajectory in virtual industrial environment and under model uncertainties by minimizing the combination of integral of time weighted absolute error and integral of time weighted absolute change in controller output. The industrial environment was simulated by incorporating measurement noise, sinusoidal disturbance and model uncertainties. The gains of NLA – FPID and NLA – FOFPID controllers are optimized using recently reported Backtracking Search Algorithm. Intensive simulations were performed to assess the performances of NLA – FPID and NLA – FOFPID controllers for servo and regulatory mode. It has been observed that NLA – FOFPID controller outperforms NLA – FPID controller by offering much better performance. Particularly in uncertain environment it offered very robust behavior as compared to NLA – FPID controller. The sufficient stability conditions are also established for bounded-input and bounded-output stability of overall closed loop system by using small gain theorem.