Proportional Plus Integral Controller Research Articles

Active control of resistive wall modesin the large-aspect-ratio tokamak

The large-aspect-ratio model for current-driven external kinks is applied to study control of non-axisymmetric resistive wall modes in tokamaks. Comparison with toroidal computations indicates that the cylindrical instabilities react in similar ways to feedback as the pressure-driven toroidal modes, when the feedback and sensor coils are placed on the low-field side of the torus. However, higher gain is required in the cylindrical case. The cylindrical model is used to gain insights into design issues concerning a feedback system for ITER, with a double wall and superconducting coils. Good control performance and acceptable coilvoltages are found in an initial value problem, where the initial conditions correspond to expected noise levels, when sensors for the poloidal field are placed inside the first wall. This can be accomplished with a PI (proportional plus integral) controller from the voltages of the sensor loops to the voltage over the active coils. The two-wall structure of ITER makes control somewhat more demanding than for tokamaks with a single wall. Adequate control can be achieved also when poloidal sensors are placed outside a single wall, but this requires additional derivative action (PID) and the resulting voltages are significantly higher.

多品種生産に対応した抄紙機ワイヤーパートのリテンション制御

A retention control system trial was performed for the wet part of a papermaking machine. By introducing two intelligent pulp and ash (filler) low consistency sensors (Kajaani : RM-200 M) to the stock supply line of head box and the white water (WW) filtrate line of wire part, we can monitor its wet end process conditions continuously. The retention control system using these sensors stabilizes the wet part process by controlling WW consistency, that is by an appropriate action of the retention aid dosage using a gap added PI (Proportional plus Integral) controller. As many grades production is running and grade changes are run frequently in this paper machine, it is difficult to determine the target set value (SV) of WW consistency. So we developed a new algorithm to judge the process stability by itself and to determine the SV target value of WW consistency automatically.

Neural-network-based self-tuning PI controller for precise motion control of PMAC motors

In general, proportional plus integral (PI) controllers used in computer numerically controlled machines possess fixed gain. They may perform well under some operating conditions, but not all. To increase the robustness of fixed-gain PI controllers, we propose a new neural-network-based self-tuning PI control system. In this new approach, a well-trained neural network supplies the PI controller with suitable gain according to each operating condition pair (torque, angular velocity, and position error) detected. To demonstrate the advantages of our proposed neural-network-based self-tuning PI control technique, both computer simulations and experiments were executed in this research. During the computer simulation, the direct experiment method was adopted to better model the problem of hysteresis in the AC servo motor. In real experiments, a PC-based controller was used to carry out the control tasks. Results of both computer simulations and experiments show that the newly developed dynamic PI approach outperforms the fixed PI scheme in rise time, precise positioning, and robustness.

A stable design of PI control for DC-DC converters with an RHS zero

The stability of boost and buck-boost DC-DC power converters under proportional plus integral (PI) control is discussed in this paper. A novel PI control configuration is proposed, which reveals the effect that the right-hand-side zero has on PI control stability. Tuning rules in terms of the converter parameters are derived and illustrated via numerical and experimental simulations.

A fuzzy sliding controller for nonlinear systems

It is well known that sliding-mode control can give good transient performance and system robustness. However, the presence of chattering may introduce problems to the actuators. Many chattering elimination methods use a finite DC gain controller which leads to a finite steady-state error. One method to ensure zero steady-state error is using a proportional plus integral (PI) controller. This paper proposes a fuzzy logic controller which combines a sliding-mode controller (SMC) and a PI controller. The advantages of the SMC and the PI controller can be combined and their disadvantages can be removed. The system stability is proved, although there is one more state variable to be considered in the PI subsystem. An illustrative example shows that good transient and steady-state responses can be obtained by applying the proposed controller.

Control system design for a rapid thermal processing system

Proposes a control system design for a rapid thermal processing (RTP) system, which has four circular concentric lamp zones and four temperature sensors. The control system consists of a least square feedforward controller and an output feedback proportional plus integral (PI) controller. The goal is to maintain uniform temperature tracking for typical ramp-up and hold-steady profiles. A high-order nonlinear model describing the temperature dynamics of the rapid thermal processing (RTP) system is used for the feedforward controller design. A balanced reduced model, obtained from a linear model around a desired uniform steady-state temperature, is used for the design of the multiinput-multioutput PI controller. The PI controller gain matrices are designed using an LQR-based procedure. Tradeoff between robustness and performance of the system is discussed. Simulation results show the control system designed yields robust temperature tracking with good uniformity for a wide temperature range.

Robust PI controller design for nonlinear systems via fuzzy modeling approach

The design problem of proportional and proportional-plus-integral (PI) controllers for nonlinear systems is studied. First, a Takagi-Sugeno fuzzy model with parameter uncertainties is used to approximate the nonlinear systems. Then a numerically tractable algorithm based on the technique of iterative linear matrix inequalities is developed to design a proportional (static output feedback) controller for the robust stabilization of the system in Takagi-Sugeno fuzzy model. Thirdly, we transform the problem of PI controller design to that of proportional controller design for an augmented system and thus bring the solution of the former problem into the configuration of the developed algorithm. Finally, the proposed method is applied to the design of robust stabilizing controllers for the excitation control of power systems. Simulation results show that the transient stability can be improved by using a fuzzy PI controller when large faults appear in the system, compared to the conventional PI controller designed by using a linearization method around the steady state.

LQR/RPS design of robust controllers for a one‐link robot

In this paper, a design method for robust controllers for a one‐link robot is developed. Based on a linearized model of this nonlinear robot system, the linear quadratic regulator (LQR) design method is incorporated with a reduced parameter sensitivity (RPS) technique to design a robust proportional‐plus‐integral (PI) controller to achieve better performance in position control. This robust controller can tolerate real parameter variations resulting from the mechanical loads of applications. A direction method is further developed and used to evaluate the stability robustness of this controlled system. Combining the direction method with the LQR/RPS method, a robust PI controller can be generated to avoid improper over‐design. Both computer simulation and experimental results demonstrate the feasibility and effectiveness of the proposed approach.

Stochastic Optimal and Suboptimal Control of Irrigation Canals

The Saint-Venant equations of open-channel flow were linearized using the Taylor series and a finite-difference approximation of the original nonlinear, partial differential equations. Using the linear optimal control theory, a proportional-plus-integral (PI) controller was developed for an irrigation canal with five pools. Since the order of the controller gain matrix was large, the Kalman filter was designed to estimate values for the state variables that were not measured. For this problem, there were a total of 45 state and five control variables. With two flow depth measurements per pool, values for the remaining 35 state variables were estimated using the Kalman filter. The simulated canal dynamics with the regional PI controllers along with the local Kalman filter were compared with the performance of the global control algorithms for achieving a constant-volume control and a constant-level control of an example irrigation canal. The performance of the regional constant-volume control algorithm was found to be as good as the performance of the global control algorithm, whereas the performance of the regional constant-level control algorithm was marginally acceptable.

Robust control of a 1.5 MW free turbine engine

This paper describes the robust control design of a 1.5 MW free turbine with complex load. A non-linear model of the engine with load has been developed within Simulink from details previously presented. State space H∞ control designs are performed using a linearized model to represent the key components in the multiloop control configuration. The performance criteria are specified in terms of stability margins, bandwidth and desired response of the engine to a severe load disturbance. The engine is subject to constraints on its manipulated variable (i. e. the throttle valve angle). The H∞ design is simplified to a classical proportional-plus-integral (PI) controller. The results show that the PI control produces results similar to H∞ at low speeds but that H∞, gives better robustness and performance at higher speeds. Non-linear simulations with parameter changes support the conclusion that the design is robust.

Tuning digital PI controllers for minimal variance in manipulated input moves applied to imbalanced systems with delay

AbstractDetermining the discrete‐time proportional plus integral (PI) controller tuning parameters to achieve the smallest possible variance in the manipulated input moves, for a given variance in the controlled output, is the subject of this article. Previous researchers have developed tuning rules for PI and PI permutated nonlinear controllers to achieve what is commonly referred to as “level‐flow smoothing”, or “averaging level control”, on imbalanced or integrating processes with delay, such as liquid level and gas pressure systems. The intent of this note is to demonstrate a new and simple technique of tuning digital PI controllers which utilizes either open or closed‐loop historical data to estimate the process gain, dead‐time and expected flow disturbance magnitude from which the digital PI tuning constants can be easily derived. By parameterizing the closed‐loop system as a function of the PI tuning constants, we can simultaneously minimize the expected variation in the process input move and output responses while at the same time ensuring nominal stability of the overall system. In order to demonstrate the technique, an illustrative example is included which highlights the new procedure on an oil refinery liquid surge drum level process.

A modified self-organizing controller for real-time process control applications

The paper proposes a systematic approach for an analytic formulation of a modified self-organizing fuzzy logic controller (SOFLC) that can generate control rules on-line and modifies them to changing process conditions. The paper also presents the real-time application of SOFLC for process control and demontrates its ability to operate over a wide range of process variables (nonlinearity and parameter variations). A comparison in terms of steady-state error, setting time and transient response is made with a proportional plus integral (PI) controller, a simple FLC and a modified SOFLC. Experimental results show that modified SOFLC has a performance slightly superior to that of a PI and FLC controllers.

Multiple-page-mapping backpropagation neural network for constant tension control

Constant tension control is widely required in industrial applications. Because of random tension interference, motor running speed vibration usually occurs. Tension control is a way to minimise the effect of random tension interference, however, the tension modification reference is another interference to the speed control system. The rewinding roll drive of a metal-film coating machine is a system with multiple closed loops and multiple input and output variables. Desired speed and tension responses are difficult to achieve by implementing conventional analogue proportional-plus-integral (PI) control. The paper introduces an artificial neural network algorithm that can successfully isolate cross coupling between the speed and tension control loops, and both loops can operate quasi-independently. It overcomes the disadvantages of traditional PI control systems. To handle the variation of the rewinding roll diameter, multiple pages of the network are applied. This technique can treat a dynamic nonlinear system as a quasistatic linear control system. Therefore this method decouples the speed and tension-control paths, and both control paths can independently operate in a quasistatic state. Simulation results show the effectiveness of this control algorithm.

Non-linear Control of the Oscillation Amplitude of a Coriolis Mass-Flow Meter

In a Coriolis mass-flow meter (CMFM) the process fluid (of potentially variable density) flows through a pipe undergoing yawing vibration to generate the required transverse Coriolis acceleration. Reliable control of the amplitude of vibration is necessary for this and other applications employing a deliberately oscillating mass-spring-damper where the mass and damping are subject to variation. The method proposed uses positive feedback of the output velocity to cancel the internal damping, with a gain determined by an outer sampled-data amplitude-control loop. The insertion of two non-linearities into the outer loop is shown to induce overall global linearity. Hence a straightforward proportional-plusintegral control design procedure gives results which are uniformly satisfactory over desired amplitudes spanning several decades, unlike naive methods which are effective for only a limited range of amplitudes. A simple desaturation strategy overcomes potential problems caused by power limits in the actuator. A practical example of successful use of the overall controller on a CMFM indicates the improvement over an existing analogue design.

Multiple-page mapping artificial neural network algorithm used for constant tension control

Constant tension control is widely required in industrial applications such as paper machines, coating machines, rewinding and unwinding machines. In a metal film coating machine, which is a multi-input multi-output system, speed and tension have cross coupling and thus desired speed and tension responses are difficult to achieve by applying conventional analogue proportional-plus-integral (PI) control. This paper introduces a multiple-page mapping artificial neural network with back-propagation training algorithm. This method can successfully decouple the speed and tension control loops and both loops can operate quasi-independently. It overcomes the disadvantages of traditional PI control systems. To handle the variation of the rewinding roll diameter, multiple pages of neural networks are applied. Some simulation results show the effectiveness of this control algorithm.

Synthesis of reinforcement learning, neural networks and PI control applied to a simulated heating coil

An accurate simulation of a heating coil is used to compare the performance of a proportional plus integral (PI) controller to the following schemes for learning improved control: a neural network trained to predict the steady-state output of the PI controller, a neutral network trained to minimize the n-step ahead error between the coil output and the set point, and a reinforcement learning agent trained to minimize the sum of the squared error over time. Although the PI controller works very well for this task, the neural networks showed improved performance. The reinforcement learning agent, when combined with a PI controller, learned to augment the PI control output for the subset of states for which control can be improved.

Adaptive fuzzy power control for CDMA mobile radio systems

Introduces a new application of fuzzy-logic control (FLC) to power control in a DS/CDMA cellular system over mobile fading radio channels. The conventional feedback power control algorithms allow the base station to send a power command to raise/lower each user transmitting signal power level by a fixed power step and then keep the received powers almost equal. The fixed-step approach is actually an integral control whose power increment is determined according to the bang-bang-like control policy. However, this control scheme suffers from several disadvantages. To tackle these difficulties, a fuzzy proportional-plus-integral (PI) control, whose input variables are the received power error and error change, is introduced to determine each user's transmitting power in order to maintain simultaneously all users' signal power received at the base station nearly equal and to achieve better system stability and control performance. The derivation of the fuzzy PI control has been carried out by analyzing both the closed-loop steady state behavior and transient response of the system with a priori knowledge of the dynamics of the CDMA mobile fading channels. In fuzzy control, linguistic descriptions of actions in controlling a process are represented as fuzzy rules. This fuzzy-rule base is used by an inference mechanism in conjunction with some knowledge of the states of process in order to determine control actions. These actions would lead to the fast rise time, minimum overshoot, and small root-mean-squared (rms) tracking error. Additional advantages of fuzzy PI control over conventional control theories are discussed.

Adaptive fuzzy proportional integral power control for a cellular CDMA system with time delay

We investigate the use of fuzzy logic control techniques for adaptive power control in a direct-sequence code-division multiple-access (DS/CDMA) cellular system over the mobile fading radio channels with propagation time delay. A fuzzy PI (proportional-plus-integral) control whose input variables are the received power error and error change is introduced to determine each user transmitting power in order to simultaneously equalize all users' signal powers received at the base station and achieve better system stability and control performance. This control strategy can ensure long loop transmission delays without causing the system to become unstable. According to the well-known phase-plane method, the derivation of the fuzzy PI control has been carried out by analyzing the response areas, cross-over, and extreme points of the system step response with apriori knowledge of the dynamics of the CDMA mobile fading channels. For a long time-delay fading process, a methodology is developed to modify the rule base to contain the delay information for reducing the deadtime effects of the process. Moreover, the additional advantages of fuzzy PI control over conventional control theories are: increased robustness in spite of interference and the ability to handle the time-delay process whose parameters are not accurately known. Simulation results show that a good performance can be achieved both in RMS tracking error and traffic capacity by use of fuzzy PI power control, especially in poor interuser interference and long time delay conditions.

Development and Testing of a Simple Carbon Dioxide Enrichment Controller for Growth Chambers

Proportional and proportional plus integral (PI) computer algorithms were implemented with a low cost pulse width modulated injection system to control CO2 in a 7.8 m3 growth chamber. Experimental studies with plants in the growth chamber showed that average CO2 concentrations over 12 h were within 3 and 1 mmol mol1 of set point for the proportional and PI controllers, respectively. The positive offset in CO2 concentration found for the proportional control was attributed to sampled measurements and pulse width modulated CO2 injection, and discussion was presented on how true errors differ from measured error estimates for pulse width modulated injection with long sampling periods relative to injection periods.

An active vertical-direction gravity compensation system

To perform simulations of partial or microgravity environments on Earth requires some method of compensation for the Earth's gravitational field. This paper discusses an active compensation system that modulates the tension in a counterweight support cable in order to minimize state deviation between the compensated body and the ideal weightless body. The system effectively compensates for inertial effects of the counterweight mass, viscous damping of all pulleys, and static friction in all parts of the gravity compensation (GC) system using a hybrid PI (proportional plus integral)/fuzzy control algorithm. The dynamic compensation of inertia and viscous damping is performed by PI control, while static friction compensation is performed by the fuzzy system. The system provides a very precise gravity compensation force, and is capable of nonconstant gravity force compensation in the case that the payload mass is not constant. >