山东科技大学学士学位论文 附录
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, i.e. 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 combination of process conditions and setpoints. Some processes have a degree of non-linearity and so parameters that work well at full-load conditions don't work when the process is starting up from no-load. 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 \be taken offline, the best tuning method often involves subjecting the system to
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山东科技大学学士学位论文 附录
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 MethodAdvantagesDisadvantages
Manual TuningNo math required. Online method.Requires experienced personnel.
Ziegler–NicholsProven Method. Online method.Process upset, some trial-and-error, very aggressive tuning.
Software ToolsConsistent tuning. Online or offline method. May include valve and sensor analysis. Allow simulation before downloading.Some cost
and training involved.
Cohen-CoonGood process models.Some math. Offline method. Only good for
first-order processes. 3.1 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 \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 required, until the loop is acceptably quick to reach its reference after a load disturbance. However, too much I will cause excessive response and overshoot. A fast PID loop tuning usually overshoots slightly to reach the setpoint more quickly; however, some systems cannot accept overshoot, in
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山东科技大学学士学位论文 附录
which case an \a P setting significantly less than half that of the P setting causing oscillation. Effects of increasing parameters Parameter Rise Time Kp Ki Kd Decrease Decrease shootSettling Time Increase Increase S.S. Error Small Change Decrease Increase Decrease Eliminate None Small Decrease Decrease 3.2Ziegler–Nichols method
Another tuning method is formally known as the Ziegler–Nichols method, introduced by John G. Ziegler and Nathaniel B. Nichols. As in the method above, the I and D gains are first set to zero. The \the \the oscillation period Pc are used to set the gains as shown:
Ziegler–Nichols method Control Type P PI PID
3.3 PID tuning software
Most modern industrial facilities no longer tune loops using the manual calculation methods shown above. Instead, PID tuning and loop optimization software are used to ensure consistent results. These software packages will gather the data, develop process models, and suggest optimal tuning. Some
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Kp Ki Kd 0.5 Kc - - 0.45Kc 1.2 Kp /Pc - 0.6 Kc 2Kp / Pc KpPc / 8 山东科技大学学士学位论文 附录
software packages can even develop tuning by gathering data from reference changes.
Mathematical PID loop tuning induces an impulse in the system, and then uses the controlled system's frequency response to design the PID loop values. In loops with response times of several minutes, mathematical loop tuning is recommended, because trial and error can literally take days just to find a stable set of loop values. Optimal values are harder to find. Some digital loop controllers offer a self-tuning feature in which very small setpoint changes are sent to the process, allowing the controller itself to calculate optimal tuning values.
Other formulas are available to tune the loop according to different performance criteria.
4 Modifications to the PID algorithm
The basic PID algorithm presents some challenges in control applications that have been addressed by minor modifications to the PID form.One common problem resulting from the ideal PID implementations is integral windup. This can be addressed by:
Initializing the controller integral to a desired value
Disabling the integral function until the PV has entered the controllable region
Limiting the time period over which the integral error is calculated Preventing the integral term from accumulating above or below pre-determined bounds
Many PID loops control a mechanical device (for example, a valve). Mechanical maintenance can be a major cost and wear leads to control
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