Classical Proportional Integral Derivative Controller Research Articles

EFFECT OF RISK-SENSITIVE STOCHASTIC OPTIMAL CONTROL WITH TRACKING IN AN EVAPORATOR

This work presents an application of the Risk-Sensitive (R-S) control with tracking applied to a stochastic nonlinear system which models the operation of an electronic expansion valve (EEV) in a conventional evaporator. A novel dynamical stochastic equation represents the mathematical model of the evaporator system. The R-S stochastic optimal problem consists of the design of an optimal control u(t) such that the state reaches setpoint values (SP) and minimizes the exponential quadratic cost function. The presence of disturbances and errors in the sensor measurements is represented by Gauss white noise in the state equation, with the coefficient v(e/(2?^2 )) . One novel characteristic in this proposal is that the coefficient of the control into the state equation contains the state term. The error and exponential quadratic cost function show that the R-S control has a better performance versus the classical PID (Proportional, Integral Derivative) control. Key Words: Optimal Risk-Sensitive control with tracking, modelling of the evaporator.

A Moth-Flame Optimized Robust PID controller for a SEPIC in Photovoltaic Applications

The paper presents a robust proportional integral derivative (PID) controller improved by the metaheuristic moth-flame optimization (MFO) technique for a DC-DC single-ended primary inductor converter (SEPIC) to achieve aimed user output performance in photovoltaic systems. Having non-linear dynamics, SEPIC with the conventional linear PID controllers possessing constant tuning gains cannot exhibit robust performance under the input and load variations. To confront the problem, a process-adaptive PID controller, whose tuning gains are adjusted by the MFO algorithm to ensure the continuity and stability of output voltage and the power, is designed and simulated. Comparative performance analysis of MFO tuned PID controller compared with the classic PID controller is conducted. The simulation results reveal a substantial performance improvement of the MFO-PID controller over the traditional PID controller in terms of maintaining constant regulated output voltage and having excellent setpoint tracking capability with minimal settling times and overshoot under considerable input and load disturbances.

Design and Implementation of Composed Position/Force Controllers for Object Manipulation

In the design of a controller for grasping objects through a robotic manipulator, there are two key problems: to find the position of the object to be grasped accurately, and to apply the appropriate force to each finger to handle the object properly without causing undesirable movement of it during its manipulation. A proportional-integral-derivative (PID) controller is widely used to grasp objects in robotics; however, its main shortcomings are its sensitivity to controller gains, sluggish response, and high starting overshooting. This research presents three coupled (position/force) controllers for object manipulation using an assembled robotic manipulator (i.e., a gripper attached to a robotic arm mounted on a mobile robot). Specifically, an angular gripper was employed in this study, which was composed of two independent fingers with a piezoelectric force sensor attached to each fingertip. The main contributions of this study are the designs and implementations of three controllers: a classic PID controller, a type-I controller, and a type-II fuzzy controller. These three controllers were used to find an object to be grasped properly (position) and apply an equivalent force to each finger (force).

On-Line Auto-Tuning Robust Nonlinear Neural PID Controller Design for Double-Pipe Heat Exchanger Based on Particle Swarm Optimization

The heat exchanger systems have highly nonlinear features between its variables and time delay. In addition, the parameters of them change constantly during operation. Therefore, the heat exchangers need nonlinear robust controller for obtaining required outlet temperature under all operating conditions.In this paper, a robust nonlinear neural PID (NLNPID) controller is proposed for temperature control of double-pipe heat exchanger. Particle swarm optimization (PSO) technique is used to determine on line auto tuning the optimal parameters of proportional-integral-derivative (PID) controller. Mathematical model of heat exchanger takes into account the changes in the density, thermal conductivity, viscosity, specific heat and convection heat transfer coefficient of the fluid which are resulting from changing in temperatures and the velocities with classical PID control. Simulations results show that the performance of the NLNPID controller produces good responses features and give desired outlet temperature under all operating conditions without over shoot and fluctuating.

Control of Nonlinear Uncertain Systems by Extended PID

Since the classical proportional-integral-derivative (PID) controller is the most widely and successfully used ones in industrial processes, it is of vital importance to investigate theoretically the rationale of this ubiquitous controller in dealing with nonlinearity and uncertainty. Recently, we have investigated the capability of the classical PID control for second-order nonlinear uncertain systems, and provided some analytic design methods for the choices of PID parameters, where the system is assumed to be in the form of cascade integrators. In this article, we will consider the natural extension of the classical PID control for high-order affine-nonlinear uncertain systems. In contrast to most of the literature on controller design of nonlinear systems, we do not require such special system structures as normal or triangular forms, thanks to the strong robustness of the extend PID controller. To be specific, we will show that under some suitable conditions on nonlinearity, and uncertainty of the systems, the extended PID controller can semiglobally stabilize the nonlinear uncertain systems, and at the same time the regulation error converges to zero exponentially fast, as long as the control parameters are chosen from an open unbounded parameter manifold constructed in this article.

Hybrid feedback PID-FxLMS algorithm for active vibration control of cantilever beam with piezoelectric stack actuator

FxLMS (Filtered-x Least Mean Square) algorithm and PID (Proportional Integral Derivative) controller have been widely used for AVC (Active Vibration Control). Yet, the convergence rate and vibration suppression performance are restricted by each other for both the classical FxLMS algorithm and the traditional PID controller. A hybrid PID-FxLMS algorithm which combines the feedback FxLMS algorithm and PID controller is proposed, and applied to improve the vibration control efficiency of piezoelectric cantilever beam. In order to conveniently install the piezoelectric stack on the beam structures, a new piezoelectric stack actuator is designed and installed at the root of cantilever beam. Meanwhile, a coupled finite element model of the piezoelectric stack actuator and cantilever beam is established in ABAQUS, and the state-space model of the coupled system is obtained. Subsequently, based on the obtained state-space model, an AVC simulation and experimental system is built to verify the effectiveness of the proposed algorithm. Numerical and experimental results show that convergence rate and vibration suppression performance of the hybrid PID-FxLMS algorithm are much better than that of the classical FxLMS algorithm or traditional PID controller alone, while the hybrid controller also has strong adaptability and anti-noise ability.

Artificial Fuzzy-PID Gain Scheduling Algorithm Design for Motion Control in Differential Drive Mobile Robotic Platforms.

Mobile robots are promising devices which are dedicated to human comfort in all areas. However, the control algorithm of the wheels of mobile robot is entirely challenging due to the nonlinearity. Recently, the classical PID (proportional-integral-derivative) controllers are frequently used in robotics for their high accuracy and the smooth determination of their parameters. A robust approach called fuzzy control which is based on the conversion of linguistic inference sets in a suitable control value is a widely used method in industrial system control in our days. A new challenging method to solve the problem of intelligent navigation of nonholonomic mobile robot is suggested. In this work, the presented methodology is based on three hybrid fuzzy logic PID controllers which are adapted to guarantee target achievement and trajectory tracking. A fuzzy-PID control algorithm is designed with 2 inputs and 3 outputs. By the information given by the system response, error and error derivate can be used to extract and adopt the PID controller parameters: proportional, integral, and derivative gains. Besides, a tuning value A is introduced to improve the resulted response in terms of speeding up and reducing error, overshoot, and oscillation, as well as reducing ISE and IAE values. A modelization of a differential drive mobile robot is presented. The developed algorithm is tested and implemented to this mobile robot model via Simulink/MATLAB.

Variable Bandwidth Adaptive Course Keeping Control Strategy for Unmanned Surface Vehicle

This paper proposes a new and original course keeping control strategy for an unmanned surface vehicle in the presence of modeling error, external disturbance and input saturation. The trajectory linearization control method is used as the basic algorithm to design the course keeping strategy, and the radial basis function neural network and disturbance observer are used to compensate modeling error and external disturbance respectively to enhance the robustness of the control system. Moreover, a robust term is used to compensate various compensation errors to further improve the robustness of the system. In addition, hyperbolic tangent function and Nussbaum function are hired to deal with the potential input saturation problem, and the neural shunting model is adopted to avoid the computational explosion caused by the derivation of virtual control law. Taking the above facts into account will help to further realize engineering practice. Finally, the control strategy proposed in this paper is compared with the classical proportional–integral–derivative control strategy. The simulation results show that the course control results of the proposed control strategy are more robust than proportional–integral–derivative control, regardless of whether the external disturbance is weak or strong.

Proportional–Integral–Derivative-Based Learning Control for High-Accuracy Repetitive Positioning of Frictional Motion Systems

Classical proportional-integral-derivative (PID) control is exploited widely in industrial motion systems with dry friction motivated by the intuitive and easy-to-use design and tuning tools available. However, classical PID control suffers from severe performance limitations. In particular, friction-induced limit cycling (i.e., hunting) is observed when integral control is employed on frictional systems that suffer from the Stribeck effect, thereby compromising setpoint stability. In addition, the resulting time-domain behavior, such as rise time, overshoot, settling time, and positioning accuracy, highly depends on the particular frictional characteristic, which is typically unknown or uncertain. On the other hand, omitting integral control can lead to constant nonzero setpoint errors (i.e., stick). To achieve superior setpoint performance for frictional motion systems in a repetitive motion setting, we propose a PID-based feedback controller with a time-varying integrator gain design. To ensure optimal setpoint positioning accuracy, a data-based sampled-data extremum-seeking architecture is employed to obtain the optimal time-varying integrator gain design. The proposed approach does not rely on knowledge on the friction characteristic. Finally, the effectiveness of the proposed approach is evidenced experimentally by application to an industrial nanopositioning motion stage setup of a high-end electron microscope.

Bulanık Mantık Denetleyicisiyle Sürü İnsansız Hava Aracıları (İHA)’nın Rota Takip Performansı

Swarm Unmanned Aerial Vehicles (UAVs) comprise of a group of aircraft that come together to achieve a specific goal. In recent years, the Swarm UAVs have been used in commercial, civil and military fields such as search and rescue operations, cargo transportation, sensitive agricultural practices, and ammunition delivery to war zones. Swarm UAVs can scan large areas in a short time in both military and civilian use. Swarm UAVs, which have the ability to communicate synchronously with each other, can perform complex tasks in a minimum energy and time by collaborating with respect to a single UAV. It is very important that swarm UAVs can follow the desired route with minimum error in order to perform the task in the shortest time and with least energy. In this study, the fuzzy logic controller is proposed for swarm quadrotors to follow the desired route with minimum error. The system modeling and mathematical equations of quadrotor have been developed in simulation environment. The performance of swarm UAVs to follow the rectangular and circular routes with minimum error is analyzed in this simulation. The fuzzy logic controller proposed for route tracking of the swarm UAVs is handled comparatively with the classical proportional-integral-derivative (PID) controller. The fuzzy logic controller developed in this simulation study increases the UAV’s sudden maneuverability and ability to complete the task with minimum energy compared to the classical PID controller. The classical PID and fuzzy controller performance of each UAV in the swarm is analyzed graphically and it is observed that the performance of the fuzzy logic controller to follow the reference route is higher than the classical PID controller.

Application of an adaptive model predictive control algorithm on the Pelton turbine governor control

Traditionally, hydro turbine governor applications mainly rely on classical proportional–integral–derivative controllers. A classical controller can perform optimally only at the operating point chosen during the controller design. Since hydro power plants are highly non-linear systems alternative control approaches based on adaptive parameters are needed. Historically, due to the limited computation capabilities of microprocessors and programmable logic controllers (PLCs) used in hydro turbine governors, adaptive control schemes were not frequently applied. However, the latest generation of microprocessors and PLCs facilitate the application of adaptive control scheme based on predictive control algorithm for plants with faster dynamic behaviour. In that regard, this study introduces an adaptive controller based on model predictive control (MPC) algorithm developed and applied to a non-linear simulation model of a laboratory hydro power plant. The applied MPC algorithm is based on a linear prediction model whose parameters are identified offline for different operating points across the plant's operating range. The adaptive control scheme updates the prediction model parameters depending on the current operating point. Furthermore, the predictive control algorithm applied in this study is set up as a quadratic programming (QP) optimisation problem that is solved online using a QP solver in a form of Hildreth's algorithm.

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

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

Elevation, pitch and travel axis stabilization of 3DOF helicopter with hybrid control system by GA-LQR based PID controller

This research work presents an efficient hybrid control methodology through combining the traditional proportional-integral-derivative (PID) controller and linear quadratic regulator (LQR) optimal controlher. The proposed hybrid control approach is adopted to design three degree of freedom (3DOF) stabilizing system for helicopter. The gain parameters of the classic PID controller are determined using the elements of the LQR feedback gain matrix. The dynamic behaviour of the LQR based PID controller, is modeled and the formulated in state space form to enable utlizing state feedback controller technique. The performance of the proposed LQR based LQR controller is improved by using Genetic Algorithm optimization method which are adopted to obtain optimum values for LQR controller gain parameters. The LQR-PID hybrid controller is simulated using Matlab environment and its performance is evaluated based on rise time, settling time, overshoot and steady state error parameters to validate the proposed 3DOF helicopter balancing system. Based on GA tuning approach, the simulation results suggest that the hybrid LQR-PID controller can be effectively adopted to stabilize the 3DOF helicopter system.

An optimized fuzzy continuous sliding mode controller combined with an adaptive proportional‐integral‐derivative control for uncertain systems

SummaryThis article discusses the design of a hybrid fuzzy variable structure control algorithm combined with genetic algorithm (GA) optimization technique to improve the adaptive proportional‐integral‐derivative (PID) continuous second‐order sliding mode control approach (APID2SMC), recently published in our previous article in the literature. In this article, first, as an improved extension to APID2SMC published recently in the literature, an adaptive proportional‐integral‐derivative fuzzy sliding mode scheme (APIDFSMC) is presented in which a fuzzy logic controller is added. Second, a GA‐based adaptive PID fuzzy sliding mode control approach (APIDFSMC‐GA) is introduced to obtain the optimal control parameters of the fuzzy controller in APIDFSMC. The proposed control algorithms are derived based on Lyapunov stability criterion. Simulations results show that the proposed approaches provide robustness for trajectory tracking performance under the occurrence of uncertainties. These simulation results, compared with the results of conventional sliding mode controller, APID2SMC, and standalone classical PID controller, indicate that the proposed control methods yield superior and favorable tracking control performance over the other conventional controllers.

Reset PID Design for Motion Systems With Stribeck Friction

We present a reset control approach to achieve setpoint regulation of a motion system with a proportional-integral-derivative (PID)-based controller, subject to Coulomb friction and a velocity-weakening (Stribeck) contribution. While classical PID control results in persistent oscillations (hunting), the proposed reset mechanism induces asymptotic stability of the setpoint and significant overshoot reduction. Moreover, robustness to an unknown static friction level and an unknown Stribeck contribution is guaranteed. The closed-loop dynamics are formulated in a hybrid systems framework, using a novel hybrid description of the static friction element, and the asymptotic stability of the setpoint is proven accordingly. The working principle of the controller is demonstrated experimentally on a motion stage of an electron microscope, showing superior performance over classical PID control.

PID Control of Nonlinear Stochastic Systems with Structural Uncertainties

It is widely known that the classical PID (proportional-integral-derivative) controller still plays a dominating role in engineering control systems, and that most of the theoretical studies on PID control focus on linear deterministic systems. In this paper, we will extend the authors recent theoretical investigation by considering additional uncertainties in the input channel, and try to establish a theoretical foundation on the PID control for a class of high-dimensional nonlinear stochastic systems with structural uncertainties consisting of dynamics uncertainty, diffusion uncertainty and input channel uncertainty. We will construct a three dimensional parameter set based on the available information, so that under the classical PID control, the closed-loop control system can be globally stabilized with regulation error tending to zero in the mean square sense, as long as the three PID parameters are chosen from this set. We will further show that global stabilization and asymptotic regulation of a class of multi-agent uncertain nonlinear stochastic systems can also be achieved by uncoupled PID controllers of the agents.

Tuning FPID Controller for an AVR System Using Invasive Weed Optimization Algorithm

In this paper, a design method to determine the optimal fractional proportional integral derivative (FPID) controller’s parameters is proposed for automated voltage regulator (AVR). The AVR model has been obtained utilizing two model reduction techniques, i.e., particle swarm optimization (PSO) and biogeography-based optimization (BBO) with the assistance of MATLAB and Simulink software package. For tuning the FPID controller, invasive weed optimization (IWO) algorithm is used with four unique performance indices: integral square error (ISE), integral time square error (ITSE), integral absolute error (IAE) and integral time weighted absolute error (ITAE). The results show that the IWO-designed FPID - compared to the classical proportional integral derivative controller (PID) - offers a better performance in terms of overshoot, rise time and settling time.

Active Queue Management Supporting TCP Flows Using Disturbance Observer and Smith Predictor

Active queue management (AQM) is a technique to avoid serious congestion of the transmission control protocol (TCP) flows at a router. AQM based on control theory, which utilizes congestion controllers such as proportional-derivative (PD) controller or proportional-integral-derivative (PID) controller, has been previously proposed. In addition, disturbance observer (DOB) has been utilized to compensate for modeling error of a TCP/AQM congestion control system. However, the DOB-based controllers cannot cope with a large time delay in TCP/AQM networks. Although one of the effective time delay compensators is Smith predictor (SP), the implementation of the DOB and SP in an integrated manner has not been accomplished, because of saturation due to the input limit of packet drop probability. In this paper, a novel TCP/AQM congestion control system with the DOB and SP considering the saturation function is proposed to compensate for the modeling error and time delay simultaneously. Simulation results show that the proposed controller provides better throughput and goodput than conventional controllers. One of the simulations assume that the propagation delay and bottleneck link capacity are set to 100 ms and 100 Mbps, respectively. Under this assumption, it is confirmed that the proposed controller achieves a goodput of 99.55 Mbps whereas the classical PID controller and PD controller with DOB achieve 99.23 Mbps and 99.24 Mbps, respectively.

Comparison of MATLAB Simulink application with PLC application of real-time classical PID controllers in laboratory

Process control is a common area of study for different engineering disciplines. Controllers working ‎with ‎the ‎proportional–integral–derivative (PID) method are generally used in process control. ‎Parameters like ‎level, ‎flow, position, pressure, and temperature are controlled in-process control. PID ‎algorithm can be ‎formed ‎with different microprocessor-based devices. Process control is ‎implemented by using analog input ‎and ‎outputs terminals of PLCs (Programmable logic controller) ‎which is recently the most commonly used ‎in ‎industries. Also, a real-time PID method can be ‎implemented by using a computer-based ‎MATLAB ‎ ‎program in the laboratory.‎ The liquid level and flow control in the laboratory has been done by using PID algorithms and ‎PLC ‎device ‎and MATLAB real-time interface by using an experimental set. Necessary connections ‎and ‎configurations have ‎been prepared to perform process control. (SIMATIC Manager Step7) is ‎used for ‎programming in PLC. ‎Besides, the MATLAB simulation program is configured to implement ‎real-time ‎control to be ‎compatible with the MF624 data acquisition card. Liquid level and fluid flow ‎control ‎experiments were ‎performed separately for the same PID algorithms formed on two different ‎devices, then ‎liquid level ‎detection and liquid flow control results have been collected and ‎investigated. Based on these ‎results, a total ‎of four experiments were compared with both devices ‎considering the ease and difficulties of ‎using PLC and ‎MATLAB.‎

Control of Position, Velocity and Acceleration of Actuators Using Optimal State Estimation

Abstract In order to improve performance of closed loop control and achieve highly accurate reference trajectory tracking, motion controllers have to utilize the advanced control and system state estimation algorithms. Classical PID (Proportional-Integral-Derivative) controller includes calculation of derivation of a process value in order to achieve system desired performance of a system. This paper presents Kalman filter as an optimal estimation algorithm on the model of a hydraulic actuator which is equally applicable to any other application that involves calculating derivations of noisy measurements. Alternative form of Kalman filter, suitable for implementation on a PLC (Programmable Logic Controller) or any other embedded system is also presented.