Simulation of a Proportional-Integral-Derivative Control for Continuous Bioreactor

In a continuous bioreactor, feed is added, and the product flow is removed at a constant rate. The objective is to maintain the system at a steady state with high product formation. This can produce a very productive process, with a low operating cost. However, there are operational challenges, especially on an industrial scale, because they require tightly controlled conditions and strong monitoring methods. For long operation, the system suffers a higher risk of contamination. This paper investigated the PID (Proportional integral Derivative) control strategy of a continuous bioreactor. Several tuning methods of PID controller were used for controller parameters determination (i.e., Direct Synthesis, Ziegler-Nichols (Z-N), and Tyreus-Luyben (TLC)). The results of the closed-loop simulation for servo (setpoint tracking) problems are presented in this paper for each method and compared. The results showed that the three method works well qualitatively. However, the process model of the system needs to be modified by introducing 5 hrs time delay, which is useful in obtaining cross over frequency and to make PID possible in the Direct Synthesis method

Model for a Nonlinear Tank System Under Proportional-Integral-Derivative Control

A model (NONLINRK) was developed for a closed tank system under feedback control by an ideal proportional-integral-derivative controller. Under servo action the fluid level in the tank is altered from its equilibrium set point. Under regulatory action the feed pressure to the inlet valve and/or the outlet valve percentage opening are varied from equilibrium settings. The numerical model uses Gill’s fourth-order Runge-Kutta algorithm to solve the system equation. The equation was made separable by approximating an exponential factor by the tangent at the beginning of each time step in the numerical solution. NONLINRK simulation trials exhibited many characteristics of linear system including unequal offset under proportional control for the setpoint changes equal in magnitude but opposite in sign, harmonics in the response to a sine wave input on fluid level setpoint and bounded response in spite of increased gain settings. In addition, further simulation trials showed the system response converges to that of a linear system for sufficiently small setpoint of load variations. A second model using the modeling language TUTSIM provided corroboration of the results produced by NONLINRK. Proportional and proportional-integral control simulations differed by less than .1% and the models showed the same rates of convergence as the time step was decreased. Under PID control TUTSIM simulations developed severe instabilities, but NONLINRK exhibited the expected trends in the increased ability to react to a ramp function disturbance and the decrease in phase lag in response to a sinusoidal setpoint function

LINEAR MATRIX INEQUALITY BASED PROPORTIONAL INTEGRAL DERIVATIVE CONTROL FOR HIGH ORDER PLANT

This study presents the application of Linear Matrix Inequalities (LMI) approach in designing a proportional integral derivative (PID) controller for a high order plant. This work also proposes practical steps in designing the robust controller. To cast this control design problem into the LMI framework, the transfer functions of the system with various payloads are obtained by carrying out nonlinear system identification. Subsequently, the dynamic model is represented into convex formulation which leads to the formulation of system requirement into LMIs representation that can accommodate the convex model. A set of robust PID gains is then obtained by solving the LMIs with desired specifications. For performance assessment, a PID controller is also designed using Ziegler Nichols (ZN) technique for all loading conditions. System responses namely hub angular position and deflection of both links of the flexible manipulator are evaluated in time and frequency domains. The performance of the LMI-PID controller is verified by comparing with the results using the ZN-PID controller in terms of time response specifications of hub angular position and level of deflection in time and frequency domains

Tilt-fractional order proportional integral derivative control for DC motor using particle swarm optimization

Introduction. Recently, the most desired goal in DC motor control is to achieve a good robustness and tracking dynamic of the set-point reference speed of the feedback control system. Problem. The used model should be as general as possible and consistently represent systems heterogeneous (which may contain electrical, mechanical, thermal, magnetic and so on). Goal. In this paper, the robust tilt-fractional order proportional integral derivative control is proposed. The objective is to optimize the controller parameters from solving the criterion integral time absolute error by particle swarm optimization. The control strategy is applied on DC motor to validate the efficiency of the proposed idea. Methods. The proposed control technique is applied on DC motor where its dynamic behavior is modeled by external disturbances and measurement noises. Novelty. The proposed control strategy, the synthesized robust tilt-fractional order proportional integral derivative speed controller is applied on the DC motor. Their performance and robustness are compared to those provided by a proportional integral derivative and fractional order proportional integral derivative controllers. Results. This comparison reveals superiority of the proposed robust tilt-fractional order proportional integral derivative speed controller over the remaining controllers in terms of robustness and tracking dynamic of the set-point reference speed with reduced control energy.Вступ. Останнім часом найбільш бажаною метою керування двигуном постійного струму є досягнення гарної надійності та динамічного відстеження заданої опорної швидкості системи керування зі зворотним зв’язком. Проблема. Використовувана модель має бути якомога загальнішою і несуперечливо представляти різнорідні системи (які можуть містити електричні, механічні, теплові, магнітні тощо). Мета. У цій статті пропонується робастне управління похідною пропорційного інтеграла дробового порядку нахилу. Мета полягає в тому, щоб оптимізувати параметри контролера шляхом вирішення критерію інтегральної абсолютної тимчасової помилки шляхом оптимізації рою частинок. Стратегія управління застосовується до двигуна постійного струму для перевірки ефективності запропонованої ідеї. Методи. Пропонований метод управління застосовується до двигуна постійного струму, динамічна поведінка якого моделюється зовнішніми перешкодами та шумами вимірів. Новизна. Пропонована стратегія управління, синтезований робастний пропорційно-інтегрально-диференціальний регулятор швидкості нахилу дробового порядку застосовується до двигуна постійного струму. Їх продуктивність та надійність порівнюються з показниками, що забезпечуються контролерами пропорційної інтегральної похідної та пропорційної інтегральної похідної дробового порядку. Результати. Це порівняння показує перевагу запропонованого робастного пропорційно-інтегрально-диференціального регулятора швидкості нахилу дробового порядку над іншими регуляторами з погляду робастності та динамічного відстеження заданої опорної швидкості зі зменшеною енергією управління

Tilt-fractional order proportional integral derivative control for DC motor using particle swarm optimization

Introduction. Recently, the most desired goal in DC motor control is to achieve a good robustness and tracking dynamic of the set-point reference speed of the feedback control system. Problem. The used model should be as general as possible and consistently represent systems heterogeneous (which may contain electrical, mechanical, thermal, magnetic and so on). Goal. In this paper, the robust tilt-fractional order proportional integral derivative control is proposed. The objective is to optimize the controller parameters from solving the criterion integral time absolute error by particle swarm optimization. The control strategy is applied on DC motor to validate the efficiency of the proposed idea. Methods. The proposed control technique is applied on DC motor where its dynamic behavior is modeled by external disturbances and measurement noises. Novelty. The proposed control strategy, the synthesized robust tilt-fractional order proportional integral derivative speed controller is applied on the DC motor. Their performance and robustness are compared to those provided by a proportional integral derivative and fractional order proportional integral derivative controllers. Results. This comparison reveals superiority of the proposed robust tilt-fractional order proportional integral derivative speed controller over the remaining controllers in terms of robustness and tracking dynamic of the set-point reference speed with reduced control energy.Вступ. Останнім часом найбільш бажаною метою керування двигуном постійного струму є досягнення гарної надійності та динамічного відстеження заданої опорної швидкості системи керування зі зворотним зв’язком. Проблема. Використовувана модель має бути якомога загальнішою і несуперечливо представляти різнорідні системи (які можуть містити електричні, механічні, теплові, магнітні тощо). Мета. У цій статті пропонується робастне управління похідною пропорційного інтеграла дробового порядку нахилу. Мета полягає в тому, щоб оптимізувати параметри контролера шляхом вирішення критерію інтегральної абсолютної тимчасової помилки шляхом оптимізації рою частинок. Стратегія управління застосовується до двигуна постійного струму для перевірки ефективності запропонованої ідеї. Методи. Пропонований метод управління застосовується до двигуна постійного струму, динамічна поведінка якого моделюється зовнішніми перешкодами та шумами вимірів. Новизна. Пропонована стратегія управління, синтезований робастний пропорційно-інтегрально-диференціальний регулятор швидкості нахилу дробового порядку застосовується до двигуна постійного струму. Їх продуктивність та надійність порівнюються з показниками, що забезпечуються контролерами пропорційної інтегральної похідної та пропорційної інтегральної похідної дробового порядку. Результати. Це порівняння показує перевагу запропонованого робастного пропорційно-інтегрально-диференціального регулятора швидкості нахилу дробового порядку над іншими регуляторами з погляду робастності та динамічного відстеження заданої опорної швидкості зі зменшеною енергією управління

Adaptive fuzzy proportional-integral-derivative control for micro aerial vehicle

With multiple industries employing Micro Aerial Vehicles (MA V) to accomplish various tasks comprising agricultural spraying, package delivery and disaster monitoring, the MA V system has attracted researchers towards resolving its stability issue as emerged from external disturbances. Disruptions caused by both wind and payload change disturbances have prevailed as natural mishaps which degrade performance of the quadrotor MA V system at the horizontal and vertical positions in the aspects of overshoot (OS), rise time (Tr), settling time (Ts)and steady-state error (ess)· Such adversities then cause increased error between the system's desired and actual positions, with a longer rise time and settling time towards reaching its steady-state condition. Adopting the rotary wing quad-rotor MAV system with 'X' configuration as the groundwork, the current study has especially set to explore a new approach for the system's robust positional control in the concurrent presence of wind and payload change disturbances. Earlier literatures have simultaneously suggested the adoptions of linear, nonlinear and hybrid approaches towards handing stability challenge of the quad-rotor MA V. Notably, most hybrid approaches are unable to account for current changes in the system's environment, whilst incapable of concomitantly handle multiple disturbances. An instance being the Fuzzy-PID (FPID) method which merely adjusts the Proportional-Integral-Derivative (PID) gains ensuing discovered positional error from emergence of system's overshoot. Acknowledging such incompetency, this research further proposed Adaptive Fuzzy-PlD (AFPID) controller as the contemporary hybrid approach that includes adaptability function for overcoming nonlinearity of the quad-rotor MA V system, while maintaining the system's robust performance facing current environmental changes from simultaneous wind and payload change disturbances. With the proposed adaptive fuzzy control being adopted to adjust the PID gains in accordance to surrounding changes, undertaken improvement is hereby targeted to eliminate the effect of wind and payload change disturbances amidst stabilizing the employed system. In return, encountered error on both the quad-rotor MA V's horizontal and vertical positions is expected to decline despite concurrent bombardment of multiple external disturbances, following a decrease to the system's overshoot (OS), rise time (Tr), settling time (Ts)and steady-state error (ess). In simulation, performance of the proposed AFPID controller on the horizontal, y position as studied under circumstances of different incoming wind velocities and water flow rates with respect to OS, Tr, Ts and e55 is placed in comparison to the performance of the PID and FPID methods. Improvement is observed in the system's ess for the AFPID controller on the horizontal, y position amid disruption of combined disturbances, with respective reductions of0.93 x 10-3 % and 1.35 X 10-3 % over the performances of PID and FPID controllers. Obtained results then confirm corresponding decline of 27.5% and 21.70% in OS for the AFPID controller over the PID and FPID controllers. A decline of 13 7.50 s and 13.40 s in Ts is further recorded for the AFPID controller as compared to the respective PID and FPID controllers. Accumulated findings, thus, validate AFPID as an effective controller for minimized positional error, smaller overshoot (OS) and steady-state error (esJ, as well as shorter settling time (Ts) and rise time (Tr) as compared to the earlier PID and FPID controllers when faced with uncertain situations of wind and payload change disturbances

Autonomous open-source electric wheelchair platform with internet-of-things and proportional-integral-derivative control

This study aims to improve the working model of autonomous wheelchair navigation for disabled patients using the internet of things (IoT). A proportional-integral-derivative (PID) control algorithm is applied to the autonomous wheelchair to control movement based on position coordinates and orientation provided by the global positioning system (GPS) and digital compass sensor. This system is controlled through the IoT system, which can be operated from a web browser. Autonomous wheelchairs are handled using a waypoint algorithm; ESP8266 is used as a microcontroller unit that acts as a bridge for transmitting data obtained by sensors and controlling the direct current (DC) motors as actuators. The proposed system and the autonomous wheelchair performance gave satisfactory results with a longitude and latitude error of 1.1 meters to 4.5 meters. This error is obtained because of the limitations of GPS with the type of Ublox Neo-M8N. As a starting point for further research, a mathematical model of a wheelchair was created, and pure pursuit control algorithm was used to simulate the movement. An open-source autonomous IoT platform for electric wheelchairs has been successfully created; this platform can help nurses and caretakers

Analysis and Simulation of Proportional Derivative and Proportional Integral Derivative Control Systems Using Xcos Scilab

PID (Proportional Integral Derivative) control is a popular control in the industry and aims to improve the performance of a system. This control has controlling parameters, namely Kp, Ki, and Kd which will have a control effect on the overall system response. In this research, P, PD, and PID control simulations with the transfer function of the mass-damper spring as a plant using Xcos Scilab. The method used is the trial and error method by setting and varying the values of the control constants Kp, Ki, and Kd to produce the desired system response. The value adjustment of system control parameters is carried out with several variations, namely Kp control variation, Kp variation to constant Kd, Kd variation to constant Kp, Kp variation to Ki, constant Kd, variation of Ki to Kp, constant Kd and variation of Kd to Kp, Ki constant. The second method is automatic tuning which is done through mathematical calculations to obtain PID control constants, namely Zieglar Nichols PID tuning with the oscillation method. From the system simulation results, the best parameter is obtained through the Zieglar Nichols PID tuning process based on the results of the transient response analysis, namely when the proportional gain value (Kp) is 50. The system performance characteristics produced in the tuning process are 3.994 seconds of settling time at 2.36 seconds research time. resulting in a maximum overshoot value of 3.6% and a peaktime value of 3.994 second