Why proportional controller steady state error

For examples. Its Steady state value is. Similarly, the error signal can be calculated as:. Steady state value of error signal steady-state error is. Another method to calculate steady-state error is as follows:. If the input is unit ramp input, then. Calculate, Velocity error coefficient K v is. If the input is unit parabolic input, than. Calculate, Acceleration error coefficient K a is.

PI controller Proportional plus integral controller reduces the steady state error e ss , but have negative effect on the stability. PI controller reduces the steady state error, it is an advantage; but PI controller reduces the stability also, it is the disadvantage. PI controller reduces the stability , it means, damping will decrease; peak overshoot and settling time will increase; Roots of characteristics equation poles of closed loop transfer function in left hand side will come closer to the imaginary axis.

Now, we will add one PI controller Proportional Plus Integral controller in system-1 and examine the results. After adding PI controller in system-1, various steady state value are shown in Figure-5, It can be seen that output is exactly equal to reference input.

It is the advantage of PI controller, as it tries to minimize steady state error, so that output will follow the reference input. Transfer function of PI controller can be calculated as. One question can be asked that if input of any transfer function is zero than its output should be zero.

So, in present case input to the PI controller is zero, but output of PI controller is a finite value i. Input is zero, integration of zero is undefined. So output of PI controller may be any finite value. An open loop control system can be represented as follows:. Any closed loop control system feedback control system can be represented as follows:.

Transfer function of plant is fixed. There are two aims of a controller i To maintain stability, i. But if we will try to increase the damping than steady-state error may increase. Optimum designing of controller is a vast research topic. To prevent overshoot, instability, and other Bad Things, you make the gain small. As your plant controlled system gets closer and closer to the desired value, the error gets smaller and smaller. When you multiply a smaller and smaller error by a small gain, eventually the product gets too small to have any effect, and is truncated to zero.

That's your steady state error, the region around the desired output where the product of the error and the gain is too small to register. After whatsisname's downvote, I thought back.

He's right. I was confusing "dead band" with "steady state error". If you have a constant perturbing force for lack of a better term , and you are using a PI controller, there will be some point at which the control signal product of error and gain exactly balances the perturbing force.

At this point, the plant system being controlled experiences zero net force: the perturbing force and the correction cancel each other, and the plant just sits there, with a constant error, the error generating the signal to cancel out the perturbing force.

The first-level fix is to go to a PI controller, one that not only produces a correction based on the error, but also based in the integral over time of the error.

The integral term is what "notices" the steady state error and moves to correct it. Sign up to join this community. The best answers are voted up and rise to the top.

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Add a comment. Active Oldest Votes. The PID controller is widely employed because it is very understandable and because it is quite effective. One attraction of the PID controller is that all engineers understand conceptually differentiation and integration, so they can implement the control system even without a deep understanding of control theory. Further, even though the compensator is simple, it is quite sophisticated in that it captures the history of the system through integration and anticipates the future behavior of the system through differentiation.

We will discuss the effect of each of the PID parameters on the dynamics of a closed-loop system and will demonstrate how to use a PID controller to improve a system's performance. The output of a PID controller, which is equal to the control input to the plant, is calculated in the time domain from the feedback error as follows:. First, let's take a look at how the PID controller works in a closed-loop system using the schematic shown above. The variable represents the tracking error, the difference between the desired output and the actual output.

This error signal is fed to the PID controller, and the controller computes both the derivative and the integral of this error signal with respect to time.

The control signal to the plant is equal to the proportional gain times the magnitude of the error plus the integral gain times the integral of the error plus the derivative gain times the derivative of the error. This control signal is fed to the plant and the new output is obtained. The new output is then fed back and compared to the reference to find the new error signal. The controller takes this new error signal and computes an update of the control input.

This process continues while the controller is in effect. Let's convert the pid object to a transfer function to verify that it yields the same result as above:.

Increasing the proportional gain has the effect of proportionally increasing the control signal for the same level of error. The fact that the controller will "push" harder for a given level of error tends to cause the closed-loop system to react more quickly, but also to overshoot more. Another effect of increasing is that it tends to reduce, but not eliminate, the steady-state error.

The addition of a derivative term to the controller adds the ability of the controller to "anticipate" error. With simple proportional control, if is fixed, the only way that the control will increase is if the error increases.

With derivative control, the control signal can become large if the error begins sloping upward, even while the magnitude of the error is still relatively small. This anticipation tends to add damping to the system, thereby decreasing overshoot. The addition of a derivative term, however, has no effect on the steady-state error. The addition of an integral term to the controller tends to help reduce steady-state error. If there is a persistent, steady error, the integrator builds and builds, thereby increasing the control signal and driving the error down.

A drawback of the integral term, however, is that it can make the system more sluggish and oscillatory since when the error signal changes sign, it may take a while for the integrator to "unwind. The general effects of each controller parameter , , on a closed-loop system are summarized in the table below.

Note, these guidelines hold in many cases, but not all. If you truly want to know the effect of tuning the individual gains, you will have to do more analysis, or will have to perform testing on the actual system.