Linear Proportional Integral Derivative Controller Research Articles

Control Improvement of Low-Cost Cast Aluminium Robotic Arm Using Arduino Based Computed Torque Control

Gravity causes non-linearity in position control of an articulated industrial robotic arm. Especially for a joint position control of a robot’s shoulder and elbow that works parallel with the gravity direction. To overcome the problem, Computed Torque Control algorithm was implemented. This algorithm linearized the feedback, so a regular linear Proportional Derivative controller can be implemented. The contribution of this research is to find an effective controller to control a heavy weight low-cost robotic arm link/body using low-cost controller such as Arduino. A Computed Torque Control was implemented to control the shoulder joint of an articulated robotic arm. This joint is the most affected joint by the gravity. It works along the vertical plane, and loaded by the rest of the arm and the robot’s load. The proposed controller was compared to a Proportional Integral Derivative (PID) Controller and a Cascade PID Controller. The experiment showed that the Computed Torque Controller can control the position of the arm properly both in the direction along or against the gravity. A linear PID controller could not bring the arm to the set point when it moves against the gravity, but it works well when the arm moves in the opposite direction. A Cascade PID controller has an overshot when the arm moves along the gravity. But it works properly when it moves up against the gravity. A Computed Torque Control works well in both directions even in the presence of gravity force because it includes the gravity on its algorithm.

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.

Proportional Integral Derivative Control in Spark Plasma Sintering Simulations.

The prediction of microstructure evolution and densification behavior during the spark plasma sintering (SPS) process largely depends on accurate temperature regulation. A loop feedback control algorithm called proportional integral derivative (PID) control is a practical simulation tool, but its coefficients are often determined by an inefficient “trial and error” method. This paper is devoted to proposing a numerical method based on the principles of variable coefficients to construct an optimal linear PID controller in SPS electro-thermal simulations. Different types of temperature profiles were applied to evaluate the feasibility of the proposed method. Simulation results showed that, for temperature profiles conventionally used in SPS cycles, the PID output keeps pace with the desired profile. Characterized by an imperfect time delay and overshoot/undershoot, the constructed PID controller needs further advancement to provide a more satisfactory temperature regulation for non-continuous temperature profiles. The first step towards a numerical rule for the optimal PID controller design was undertaken in this work. It is expected to provide a valuable reference for the advanced electro-thermal modeling of SPS.

Design of an Intelligent NPID Controller Based on Genetic Algorithm for Disturbance Rejection in Single Integrating Process with Time Delay

The integrating process with time delay (IPTD) is a fundamentally unstable open-loop system due to poles at the origin of the transfer function, and designing controllers with satisfactory control performance is very difficult because of the associated time delay, which is a nonlinear element. Therefore, this study focuses on the design of an intelligent proportional-integral-derivative (PID) controller to improve the regulatory response performance to disturbance in an IPTD, and addresses problems related to optimally tuning each parameter of the controller with a real coded genetic algorithm (RCGA). Each gain of the nonlinear PID (NPID) controller consists of a product of the gains of the linear PID controller and a simple nonlinear function. Each of these nonlinear functions changes the gains in the controller to on line by nonlinearly scaling the error signal. A lead-lag compensator or first-order filter is also added to the controller to mitigate noise, which is a disadvantage of ideal derivative action. The parameters in the controller are optimally tuned by minimizing the integral of time-weighted absolute error (ITAE) using a RCGA. The proposed method is compared with three other methods through simulation to verify its effectiveness.

Estrategias de control no lineal para la regulación de corriente y estabilización de voltaje DC para un Aerogenerador operando en una Microred

La generación a partir de energías renovables, en especial eólica, se encuentra ocupando cada vez más una mayor participación en el mercado energético a nivel mundial. Debido a la alta dinámica del viento, se presentan variaciones en la magnitud de voltaje y frecuencia del sistema que dificulta integrar estos generadores al sistema eléctrico. Varios trabajos proponen diferentes estrategias de control implementadas en sistemas electrónicos de potencia para solventar este problema. Estos sistemas primero rectifican el voltaje variable del generador creando un acople de corriente directa (DC) y luego convierten el resultado en voltaje con magnitud y frecuencia constante. Los controladores más usados son de tipo proporcional integral derivativo (PID), los cuales presentan un buen desempeño en zonas de operación lineal. Sin embargo, existen propuestas no lineales que presentan amplias ventajas frente a los PIDs, sobre todo en sistemas con dinámicas rápidas y no lineales. En el presente trabajo se implementan controladores PIDs lineales y se proponen dos estrategias de control no lineales, una con una estructura PID y otra con control de modo deslizante (SMC), para regular el suministro de corriente y voltaje en aerogeneradores conectados a un sistema electrónico de potencia. En los controladores propuestos se implementó una ganancia no lineal que se calcula en función del error del sistema y se comparó su desempeño con el de los controladores PIDs lineales. Los resultados mostraron mejoras notables en la velocidad de estabilización del sistema y reducción de oscilaciones ante variaciones repentinas de referencia y perturbaciones externas. Para probar el desempeño de los controladores se simuló una micro red enlazada a una barra infinita en Simulink.

Flower Pollination Optimization Based PID Controller Tuning Scheme With Robust Stabilization of Gain Scheduled CSTR

In the area of chemical and control engineering, Continuous Stirred Tank Reactor (CSTR) has been deliberated as a most important topic in temperature process control and it is a extremely nonlinear process, which displays stability only in definite regions and unsteadiness in other regions. In this CSTR, Proportional Integral Derivative (PID) controller has been used to minimize the Integral SquareError (ISE) by adjustment of control parameters like k_p,k_i and k_d.But, this conventional controller has high computational complexity, so to reduce this, the optimization based tool has been designed for PID and it was conceptually simple.Earlier, the Genetic Algorithm (GA) optimization has been focused, but it was not guarantee for good fitness and global optimal solution. So to overcome this, here, Flower Pollination based Global Optimization Algorithm (FPGOA) with Gain scheduling based PID controller is proposed for CSTR. When a plant is exposing to big changes in its operational state, the Gain scheduling has been used. The FPGOA is used for tuning the parameters of PID controller for each region to reduce the ISE. The fuzzy gain scheduler has been combined with multiple local linear PID controllers to check the stability of loop for entire regions with various levels of temperatures. This scheduling is an exceptional form of fuzzy control, which customs linguistic rules and fuzzy perceptive to establish the controller factor transition strategy for the dynamic plant dependent on high changes in its operational state to improve the optimization. MATLAB results demonstrate that the feasibility of using the proposed PID controller compared than existing controller, and it shows the FPGOA attained better results, due to the effectual fitness and global optimal solution for the dynamical nonlinear control of CSTR. The response curves of these systems has been generated and compared with existing schemes.

Robust PID control of quadrotors with power reduction analysis

This paper presents a novel robust controller applied to a quadrotor vehicle for regulation and trajectory tracking tasks. In the proposed scheme, the quadrotor position is controlled by a proportional integral derivative (PID) controller, while the orientation control is achieved through a model-based controller. The proposed controller is combined with a power reduction methodology, which includes a controller-gains tuning stage using the cuckoo search algorithm, and a minimum jerk trajectory design stage. The performance of the new controller is assessed in a free-disturbance case and under the effect of parametric uncertainty and aero-dynamical disturbances. The new controller is compared against two linear PID controllers and a nonlinear sliding mode-based controller. Numerical simulations demonstrate the superiority of the proposed scheme as well as its robustness against different types of perturbations. Also, it is proven that the power demanded by any controller is reduced when using the power reduction methodology.

Adaptive PID controller based on Q ‐learning algorithm

An adaptive proportional–integral–derivative (PID) controller based on Q-learning algorithm is proposed to balance the cart–pole system in simulation environment. This controller was trained using Q-learning algorithm and implemented the learned Q-tables to change the gains of linear PID controllers according to the state of the system during the control process. The adaptive PID controller based on Q-learning algorithm was trained from a set of fixed initial positions and was able to balance the system starting from a series of initial positions that are different from the ones used in the training session, which achieved equivalent or even better performances in comparison with the conventional PID controller and the controller only uses Q-learning algorithm. This indicates the advantage of the adaptive PID controller based on Q-learning algorithm both in the generality of balancing the cart–pole system from a relatively wide range of initial positions and in the stabilisability of achieving smaller steady-state error.

A novel adaptive fuzzy PID controller based on piecewise PID controller for dynamic positioning of sandglass-type FDPSO

A novel adaptive fuzzy proportional-integral-derivative (PID) controller based on the proposed piecewise PID controller is put forward for the sandglass-type floating, drilling, production, storage and offloading unit (FDPSO). First, on the premise of appropriate positioning accuracy, a piecewise linear PID controller considering the directional characteristic between the motions and environmental loads is proposed to conserve energy of traditional linear PID controller. Then, to improve the stability during the transient process and alleviate oscillation induced by piecewise PID controller, the robust adaptive fuzzy PID controller based on the piecewise PID controller is put forward, whose stability is verified by fuzzy Lyapunov method. The proposed fuzzy output variables are designed including motions in both the horizontal and vertical planes to solve the surge–pitch coupling problem and optimize energy consumption. The time-domain simulations with a complete model of all DP components and external forces are carried out. Therein, the thruster model is improved by introducing a virtual thrust command to decrease the obvious phase lag, response delay and amplitude reduction of the traditional thruster model. In addition, the application of wave filter is discussed, especially when the wave-frequency (WF) motions are more prominent and significant than low-frequency (LF) motions. Finally, comparisons between the proposed adaptive fuzzy PID controller and traditional linear PID controller are made and analyzed. Good control effects of the proposed controllers are demonstrated with the assistance of numerical simulations with a series of control parameters.

Equivalence between Fuzzy PID Controllers and Conventional PID Controllers

This paper proposes the equivalence between fuzzy Proportional-Integral-Derivative (PID) controllers and conventional PID controllers. A well-designed conventional PID controller, with the help of the proposed method, can be rapidly transformed to an equivalent fuzzy logic controller (FLC) by observing and defining the operating ranges of the input/output of the controller. Furthermore, the knowledge base of the proposed equivalent fuzzy PID controller is represented as a cube fuzzy associative memory (FAM), instead of a combination of PD-type and PI-type FLCs in most research. Simulation results show the feasibility of the proposed technique, both in continuous and discrete time. Since the design techniques of conventional linear PID controllers have matured, they can act as preliminary expert knowledge for nonlinear FLCs designs. Based on the proposed equivalence relationship, the designer can further tune the membership functions of fuzzy variables in the control rules to exhibit the nonlinearity of a FLC and yield more satisfactory system responses in an efficient way.

Robust task-space control of an autonomous underwater vehicle-manipulator system by PID-like fuzzy control scheme with disturbance estimator

This paper presents, a robust nonlinear proportional-integral-derivative (PID)-like fuzzy control scheme for a task-space trajectory tracking control of an autonomous underwater vehicle-manipulator system (AUVMS) employed for deep-sea intervention tasks. The effectiveness of the proposed control scheme is numerically demonstrated on a planar underwater vehicle manipulator system (consisting of an underwater vehicle and two link rotary (2R) serial planar manipulator). The actuator and sensor dynamics of the system are also incorporated in the dynamical model of an AUVMS. The proposed control law consists of two main parts: first part uses a feed forward term to reinforce the control activity with extravagance from known desired acceleration vector and carries an estimated perturbed term to compensate for the unknown effects namely external disturbances and unmodeled dynamics and the second part uses a PID-like fuzzy logic control as a feedback portion to enhance the overall closed-loop stability of the system. The primary objective of the proposed control scheme is to track the given end-effector task-space trajectory despite of external disturbances, system uncertainties and internal noises associated with the AUVMS system. To show the effectiveness of the proposed control scheme, comparison is made with linear and nonlinear PID controllers. Simulation results confirmed that with the proposed control scheme, the AUVMS can successfully track the given desired spatial trajectory and gives better and robust control performance.

Genetic Algorithm Based PID Controller Tuning Approach for Continuous Stirred Tank Reactor

Genetic algorithm (GA) based PID (proportional integral derivative) controller has been proposed for tuning optimized PID parameters in a continuous stirred tank reactor (CSTR) process using a weighted combination of objective functions, namely, integral square error (ISE), integral absolute error (IAE), and integrated time absolute error (ITAE). Optimization of PID controller parameters is the key goal in chemical and biochemical industries. PID controllers have narrowed down the operating range of processes with dynamic nonlinearity. In our proposed work, globally optimized PID parameters tend to operate the CSTR process in its entire operating range to overcome the limitations of the linear PID controller. The simulation study reveals that the GA based PID controller tuned with fixed PID parameters provides satisfactory performance in terms of set point tracking and disturbance rejection.

Design Intelligent Model-free Hybrid Guidance Controller for Three Dimension Motor

The minimum rule base Proportional Integral Derivative (PID) Fuzzy hybrid guidance Controller for three dimensions spherical motor is presented in this research. A three dimensions spherical motor is well equipped with conventional control techniques and, in particular, various PID controllers which demonstrate a good performance and successfully solve different guidance problems. Guidance control in a three dimensions spherical motor is performed by the PID controllers producing the control signals which are applied to systems torque. The necessary reference inputs for a PID controller are usually supplied by the system’s sensors based on different data. The popularity of PID Fuzzy hybrid guidance Controller can be attributed to their robust performance in a wide range of operating conditions and partly to their functional simplicity. PID methodology has three inputs and if any input is described with seven linguistic values, and any rule has three conditions we will need 343 rules. It is too much work to write 343 rules. In this research the PID-like fuzzy controller can be constructed as a parallel structure of a PD-like fuzzy controller and a conventional PI controller to have the minimum rule base. Linear type PID controller is used to modify PID fuzzy logic theory to design hybrid guidance methodology. This research is used to reduce or eliminate the fuzzy and conventional PID controller problem based on minimum rule base fuzzy logic theory and modified it by PID method to control of spherical motor system and testing of the quality of process control in the simulation environment of MATLAB/SIMULINK Simulator.

Simulation Analysis of Non-Linear Fuzzy PID Temperature Controller

The objectives of the project are to simulate linear Mamdami type fuzzy temperature controller and non-linear Takegi-Sugeno type fuzzy temperature controllers using MATLAB and Simulink, and to compare the performance between the two controllers. A case study has been created to test the controllers involved a water boiler, where the system is modeled using Joules Law and Law of Thermodynamics. A Proportional-Integral-Derivative (PID) controller was tuned and the PID parameters were then used to obtain the gain of the fuzzy controllers. Simulation results confirmed that non-linear fuzzy controller has smaller overshoot and faster settling time compared to the linear fuzzy controller and PID controller, although an extra derivative gain may be needed for the non-linear fuzzy controller if the integral term is huge enough to affect the stability of the system.

Design Artificial Intelligent Parallel Feedback Linearization of PID Control with Application to Continuum Robot

Refer to this research, an intelligent robust fuzzy parallel feedback linearization estimator for ProportionalIntegral-Derivative (PID) controller is proposed for highly nonlinear continuum robot manipulator. In the absence of robot knowledge, PID may be the best controller, because it is model-free, and its parameters can be adjusted easily and separately. And it is the most used in robot manipulators. In order to remove steadystate error caused by uncertainties and noise, the integrator gain has to be increased. This leads to worse transient performance, even destroys the stability. The integrator in a PID controller also reduces the bandwidth of the closed-loop system. Model-based compensation for PD control is an alternative method to substitute PID control. Feedback linearization compensation is one of the nonlinear compensator. The first problem o f the pure feedback linearization co mpensator (FLC) was equivalent problem in certain and uncertain systems. The nonlinear equivalent dynamic problem in uncertain system is solved by using parallel fuzzy logic theory. To eliminate the continuum robot man ipulator system’s dynamic; Mamdani fuzzy inference system is design and applied to FLC. Th is methodology is based on design parallel fu zzy inference system and applied to equivalent nonlinear dynamic part of FLC. The results demonstrate that the model free fuzzy FLC estimator works well to co mpensate linear PID controller in presence of part ly uncertainty system (e.g., continuum robot).

Experimental Implementation of a Nonlinear Dynamic Inversion Controller with Antiwindup

A recently proposed nonlinear antiwindup compensation scheme is implemented and tested on a scaled BAe Hawk jet trainer wind-tunnel model, mounted in a one degree of freedom configuration. The Hawk is modeled as a nonlinear affine system subject to input amplitude constraints. The primary control system consists of an inner-loop nonlinear dynamic inversion controller and an outer-loop linear proportional integral derivative controller. The input constraints are addressed by supplementing this nominal controller with two types of nonlinear antiwindup schemes: a nonlinear variant of the well-known internal model control scheme and a suboptimal norm-based antiwindup compensator. Wind tunnel results are presented which demonstrate the usefulness of the antiwindup schemes in preventing performance deterioration due to the input constraints and the flexibility of the proposed approach from a practical perspective.

Intelligent Robust Feed-forward Fuzzy Feedback Linearization Estimation of PID Control with Application to Continuum Robot

Refer to this paper, an intelligent-fuzzy feed- forward computed torque estimator for Proportional- Integral-Derivative (PID) controller is proposed for highly nonlinear continuum robot manipulator. In the absence of robot knowledge, PID may be the best controller, because it is model-free, and its parameters can be adjusted easily and separately and it is the most used in robot manipulators. In order to remove steady- state error caused by uncertainties and noise, the integrator gain has to be increased. This leads to worse transient performance, even destroys the stability. The integrator in a PID controller also reduces the bandwidth of the closed-loop system. Model-based compensation for PD control is an alternative method to substitute PID control. Computed torque compensation is one of the nonlinear compensator. The main problem of the pure computed torque compensator (CTC) was highly nonlinear dynamic parameters which related to system's dynamic parameters in certain and uncertain systems. The nonlinear equivalent dynamic problem in uncertain system is solved by using feed-forward fuzzy inference system. To eliminate the continuum robot manipulator system's dynamic; Mamdani fuzzy inference system is design and applied to CTC. This methodology is based on design feed-forward fuzzy inference system and applied to CTC. The results demonstrate that the model base feed-forward fuzzy CTC estimator works well to compensate linear PID controller in presence of partly uncertainty system (e.g., continuum robot).

Tritium breeding control within liquid metal blankets

A key requirement for DEMO is the on-site breeding of tritium. In order to do this, a robust control system must be employed to ensure enough tritium is being bred to sustain the fusion reactor, whilst not breeding an amount which would exceed the plant's tritium inventory license. A tritium breeding method which is cost effective and reduces radioactive waste for disposal is that of the liquid metal breeder such as those based around LiPB and FLiBe. This paper focuses on the modeling of a simplified fusion reactor design with a LiPb blanket with linked radiation transport, nuclide burn-up and control theory. Two simple models were simulated using the FATI code which incorporated a PID (proportional integral derivative) controller that adjusted the Li6/Li7 ratio in order to increase/decrease tritium production based on the difference between the measured excess tritium inventory and the desired excess inventory. The modelling has initially demonstrated that a linear PID controller has the capability to manage tritium production within a LiPb liquid blanket.

Comparative Performance of Decoupled Input–Output Linearizing Controller and Linear Interpolation PID Controller: Enhancing Biomass and Ethanol Production in Saccharomyces cerevisiae

A decoupled input-output linearizing controller (DIOLC) was designed as an alternative advanced control strategy for controlling bioprocesses. Simulation studies of its implementation were carried out to control ethanol and biomass production in Saccharomyces cerevisiae and its performance was compared to that of a proportional-integral-derivative (PID) controller with parameters tuned according to a linear schedule. The overall performance of the DIOLC was better in the test experiments requiring the controllers to respond accurately to simultaneous changes in the trajectories of the substrate and dissolved oxygen concentration. It also exhibited better performance in perturbation experiments of the most significant parameters q (S,max), q (O2,max), and k ( s ), determined through a statistical design of experiments involving 730 simulations. DIOLC exhibited a superior ability of constraining the process when implemented in extreme metabolic regimes of high oxygen demand for maximizing biomass concentration and low oxygen demand for maximizing ethanol concentration.

A cultural algorithm based particle swarm optimization approach to linear brushless DC motor PID controller

This paper presents a new hybrid Cultural Algorithm (CA) based particle swarm optimization (PSO) that converges to a significantly more accurate solution then existing particle swarm optimization and which has also been applied to the linear brushless DC motor PID controller design. The utility of hybrid CA based PSO is demonstrated by determining the optimal proportional-integral-derivative (PID) controller parameters for speed control of a linear brushless DC motor and then compared with basic PSO method. The proposed hybrid approach has superior features including stable convergence characteristic and good computational efficiency, reducing the steady-state error (Ess), rise time (Tr), settling time (Ts) and maximum overshoot (Mp) in speed control of a linear brushless DC motor. The comparative experimental results has demonstrated the feasibility and effectiveness of the proposed novel approach. Key words: Proportional-integral-derivative controller, cultural algorithm, particle swarm optimization, DC motor, step response.