PID Control Systems - Proportional Control
Why Not Use A Proportional Controller?
Properties Of Proportional Controllers
Proportional Control Examples
Proportional Control Problems
Implementing Proportional Controllers
You are at: Design Techniques - The PID Family of Controllers - Proportional Controllers

Why Not Use A Proportional Controller?

Of all the controllers you can choose to control a system, the proportional controller is the simplest of them all.

• If you want to implement a proportional control system, it's usually the easiest to implement.
• In an analog system, a proportional control system amplifies the error signal to generatethe control signal.  If the error signal is a voltage, and the control signal is also a voltage, then a proportional controller is just an amplifier.I
• In a digital control system, a proportional control system computes the error from measured output and user input to a program, and multiplies the error by a proportional constant, then generates an output/control signal from that multiplication.

Goals For This Lesson

Proportional control is a simple and widely used method of control for many kinds of systems.  When you are done with this lesson you will need to be able to use proportional control with some understanding.  Your goals are as follows:

Given a system you want to control with a proportional controller,
Identify the system components and their function, including the comparator, controller, plant and sensor.
Be able to predict how the system will respond using a proportional controller - including speed of response, accuracy (SSE) and relative stability.
Be able to use the root locus to make
those predictons.
Be able to use frequency response analysis to make those predictions.

Properties Of Proportional Controllers

Proportional controllers have these properties:

• The controller amplifies the error as shown in the block diagram below.
• So, the actuating signal (the input to G(s)) is proportional to the error.
In the material that follows, we will examine some of the features of proportional control using a proportional controller.

In a proportional controller, steady state error tends to depend inversely upon the proportional gain, so if the gain is made larger the error goes down.

In this system, SSE is given by the expression

SSE = 1/(1 + KpG(0))

As the proportional gain, Kp, is made larger, the SSE becomes smaller.  As the DC loop gain, KpG(0), becomes large, the error approaches becoming inversely proportional to the proportional gain, Kp.  That's true for most of the cases of interest, that is those with small SSE.

• Proportional control has a tendency to make a system faster.
If we think about the root locus for a system with proportional control we can note the following:
• The proportional gain, Kp, is either the root locus gain, or the root locus gain is proportional to Kp.
• The root locus for a first order system will have the form shown below.

• There's one pole.
• The root locus moves to the left from that pole.
• As the pole moves to the left, the time constant becomes smaller.
• Higher order systems will not behave in the same way, but there may be tendencies to speed up the system, at least for some gain values.  Here is the root locus for a second order system.