【正文】 hree terms, the proportional, the integral and the derivative terms are summed to calculate the output of the PID controller. Defining u(t) as the controller output, the final form of the PID algorithm is: and the tuning parameters are 7 Kp: Proportional Gain Larger Kp typically means faster response since the larger the error, the larger the Proportional term pensation. An excessively large proportional gain will lead to process instability and oscillation. Ki: Integral Gain Larger Ki implies steady state errors are eliminated quicker. The tradeoff is larger overshoot: any negative error integrated during transient response must be integrated away by positive error before we reach steady state. Kd: Derivative Gain Larger Kd decreases overshoot, but slows down transient response and may lead to instability due to signal noise amplification in the differentiation of the error. 3. Loop tuning If the PID controller parameters (the gains of the proportional, integral and derivative terms) are chosen incorrectly, the controlled process input can be unstable, . its output diverges, with or without oscillation, and is limited only by saturation or mechanical breakage. Tuning a control loop is the adjustment of its control parameters (gain/proportional band, integral gain/reset, derivative gain/rate) to the optimum values for the desired control response. The optimum behavior on a process change or setpoint change varies depending on the application. Some processes must not allow an overshoot of the process variable beyond the setpoint if, for example, this would be unsafe. Other processes must minimize the energy expended in reaching a new setpoint. Generally, stability of response (the reverse of instability) is required and the process must not oscillate for any bination of process conditions and setpoints. Some processes have a degree of nonlinearity and so parameters that work well at fullload conditions don39。 1 PID controller From Wikipedia, the free encyclopedia A proportional–integral–derivative controller (PID controller) is a generic .control loop feedback mechanism widely used in industrial control systems. A PID controller attempts to correct the error between a measured process variable and a desired setpoint by calculating and then outputting a corrective action that can adjust the process accordingly. The PID controller calculation (algorithm) involves three separate parameters。 the Proportional, the Integral and Derivative values. The Proportional value determines the reaction to the current error, the Integral determines the reaction based on the sum of recent errors and the Derivative determines the reaction to the rate at which the error has been changing. The weightedsum of these three actions is used to adjust the process via a control element such as the position of a control valve or the power supply of a heating tuning the three constants in the PID controller algorithm the PID can provide control action designed for specific process requirements. The response of the controller can be described in terms of the responsiveness of the controller to an error, the degree to which the controller overshoots the setpoint and the degree of system oscillation. Note that the use of the PID algorithm for control does not guarantee optimal control of the system or system stability. Some applications may require using only one or two modes to provide the appropriate system control. This is achieved by setting the gain of undesired control outputs to zero. A PID controller will be called a PI, PD, P or I controller in the absence of the respective control actions. PI controllers are particularly mon, since derivative action is very sensitive to measurement noise, and the absence of an integral value may prevent the system from reaching its target value due to the control action. 2 A block diagram of a PID controller Note: Due to the diversity of the field of control theory and application, many naming conventions for the relevant variables are in mon use. loop basics A familiar example of a control loop is the action taken to keep one39。t work when the process is starting up from noload. This section describes some traditional manual methods for loop tuning. There are several methods for tuning a PID loop. The most effective methods generally involve the development of some form of process model, then choosing P, I, and D based on the dynamic model parameters. Manual tuning methods can be relatively inefficient. The choice of method will depend largely on whether or not the loop can be taken offline for tuning, and the response time of the system. If the system can be taken offline, the best tuning method often involves subjecting the system to a step change in input, measuring the output as a function of time, and using this response to determine the control parameters. Choosing a Tuning Method 8 MethodAdvantagesDisadvantages Manual TuningNo math required. Online experienced personnel. Ziegler–NicholsProven Method. Online upset, some trialanderror, very aggressive tuning. Software ToolsConsistent tuning. Online or offline method. May include valve and sensor analysis. Allow simulation before cost and training involved. CohenCoonGood process math. Offline method. Only good for firstorder processes. Manual tuning If the system must remain online, one tuning method is to first set the I and D values to zero. Increase the P until the output of the loop oscillates, then the P should be left set to be approximately half of that value for a quarter amplitude decay type response. Then increase D until any offset is correct in sufficient time for the process. However, too much D will cause instability. Finally, increase I, if