The derivative control mode produces an output based on the rate of change of the error. It produces more control action if the error changes at a faster rate; if there is no change in the error, the derivative action is zero. This mode has an adjustable setting called Derivative Time Td. The larger the derivative time setting, the more derivative action is produced. If the derivative time is set too long, however, oscillations will occur and the control loop will be unstable. A Td setting of zero effectively turns off the derivative mode.
Two units of measure are used for the derivative setting of a controller: minutes and seconds. The output of a PID controller is made up of the sum of the proportional, integral, and derivative control actions.
PID control algorithms come in different designs, including the noninteractive algorithm and the parallel algorithm. Both are shown in Figure 3.
In a PID controller, the derivative mode provides more control action sooner than is possible with either P or PI control. This reduces the effect of a disturbance and shortens the time it takes for the level to return to its set point. Figure 4 compares the process heater outlet temperature recovery time after a sudden change in fuel gas pressure under P, PI, and PID control. PID controllers require tuning, but when they first came to market, there were no clear instructions on how to do this.
Tuning was done through trial and error until , when two tuning methods were published by J. Ziegler and N. Nichols from the Taylor Instruments Company. These tuning rules work well on processes with very long time constants relative to their dead times and on level control loops, which contain an integrating process.
They do not work well on control loops that contain self-regulating processes, such as flow, temperature, pressure, speed, and composition. A self-regulating process always stabilizes at some point of equilibrium, which depends on the process design and controller output; if the controller output is set to a different value, the process will respond and stabilize at a new point of equilibrium.
Thus, PI controllers provide a balance of complexity and capability that makes them by far the most widely used algorithm in process control applications. The PI Algorithm While different vendors cast what is essentially the same algorithm in different forms , here we explore what is variously described as the dependent, ideal, continuous, position form:.
The first two terms to the right of the equal sign are identical to the P-Only controller referenced at the top of this article. The integral mode of the controller is the last term of the equation. Its function is to integrate or continually sum the controller error, e t , over time. Some things we should know about the reset time tuning parameter, T i:.
As e t grows or shrinks, the amount added to CO bias grows or shrinks immediately and proportionately. The past history and current trajectory of the controller error have no influence on the proportional term computation. The plot below click for a large view illustrates this idea for a set point response. Below click for a large view is the identical data to that above only it is recast as a plot of e t itself. This plot is useful as it helps us visualize how controller error continually changes size and sign as time passes.
Function of the Integral Term While the proportional term considers the current size of e t only at the time of the controller calculation, the integral term considers the history of the error, or how long and how far the measured process variable has been from the set point over time.
Integration is a continual summing. Integration of error over time means that we sum up the complete controller error history up to the present time, starting from when the controller was first switched to automatic. In the plot below click for a large view , the integral sum of error is computed as the shaded areas between the SP and PV traces. Each box in the plot has an integral sum of 20 2 high by 10 wide. Proportional is just one way to react to an error in the system.
The problem with proportional control is that it can't detect trends and adjust to them. This is the job of integral control. There is another example graph of the error in a system over time on the left of Figure 6. Again, it might be the distance of a robot from an object, or it could be fluid level in a tank, or the temperature in a factory oven. Perhaps the target the robot is following keeps on going away from the robot at a speed that the robot isn't catching up with.
Maybe the oven door seal is worn; maybe the fluid draw from the tank is unusually large. Regardless of the cause, since proportional is not designed to react to trends it can't detect and correct the problem. That's where integral control comes into the picture. Integral measures the area between the error values and the time axis. If the error doesn't return to zero, the area of the error gets larger and larger. The right side of Figure 6 shows how the integral output can react to this kind of trend.
What is a Distributed Control System? What is the Process Time Constant? Expand your knowledge with this featured publication:. Learn more. Stay up to date. Sign up for our newsletter:. These resources offer related content:. Just ask any child.
0コメント