In control system, the error is the difference between input and output. But why are we expecting to get the output same as the input. To get the exact input as output there is no necessary for the system since we have the output available i.e input.
I am not sure I have detailed it correctly but please respond if you get it.
Normally a control system uses a setpoint voltage to amplify power, to achieve a position, velocity or acceleration with feedback to correct the error. There are many situations where power is used to control something and it is best if that feedback uses a sensor to convert from the same units that the voltage represents.
This means having the ability to use linear control to compare without having to integrate and reduce bandwidth, add latency or use phase compensation for stability that may cause overshoot or ringing from disturbances or step changes to the desired input.
Yet often this is not possible and multiple targets are needed like acceleration, velocity, position or direction and multiple sensors are needed.
Let's consider a human driving a car.
simulate this circuit – Schematic created using CircuitLab
Figure 1. The car's human control system.
Note that there is some fancy control calculation going on. Some will be based on experience but you will automatically take into consideration the car's weight to power ratio, the gear you're in, the incline you're on, passenger comfort or load safety, etc.
In a control system (such as cruise control in this case) we have to tune it to obtain the required response. This may be to get to the set point as quickly as possible or at a certain predetermined rate or with minimum overshoot.
To address your questions:
In control system,the error is the difference between input and output.
Correct.
But why are we expecting to get the output same as the input.
We're not. In my example the input is 80 kph but the output is throttle position which might be 34%.
To get the exact input as output there is no necessary for the system since we have the output available i.e input.
No. In the example the throttle isn't calibrated in kph but, if you like, it's calibrated in engine output power. We adjust the power to control the speed. Note also that the car's speed is not proportional to power because, for example, aerodynamic drag increases with the square of the speed.
See if my answer to Understanding the flow of a PI Controller? is of any help.
"To get the exact input as output" : In most control systems, the input is not physically the same as the output. For example, voltage is given as input, but the real output being controlled may be something like position or temperature. But to calculate error (to know if we reached set-point or not), we can't compare voltage to position directly. Like mentioned in the other answers, we then need a feedback system which will translate the controlled variable (position, temperature etc.) into the units of the controlling variable (voltage, pressure etc.).
"error is the difference between input and output" : It doesn't make sense (in physics) to add or subtract things which have different units. So the control system will contain transducers to convert between various parameters with various different units into a common language for the purpose of comparing (adding, subtracting). In electronics, this common language is usually voltage (or current). In pneumatic systems, the common language may be pressure or flow rate.
"error is the difference" : Most common error calculation method may be subtraction, but, it is not the only method. For example, when working with rotations (in a quad-copter control system), the error calculation is a product, not a difference. Even in that case, the input and feedback have the same units (rotation matrices, unit quaternions etc.)
The error is not the difference between the system input and system output, it's the difference between the setpoint (which can be considered a controller input) and the system output.
For example, if you want to bake a nice batch of cookies you might want to set the oven to 375°F (190°C).
190°C is your setpoint.
The controller can work with the difference between the system output (say starting at 20°C) and the setpoint (190°C) and notice that the error is -170°C so turn the heaters on to maximum. As the system approaches the setpoint the heating would be throttled back so that it stabilizes near the desired temperature. When the system output (temperature) equals 190°C the error is zero.
As well as the value of the error, the controller can also look at the rate of change of the error and the integral of the error (PID control).
Of course we might want to look at the absolute temperature and setpoint as well as the error, and maybe even mains voltage, because real systems don't behave linearly, and taking mains voltage variations into account can reduce the variations in temperature because you don't need to wait for the error to appear to (at least partially) correct for the disturbance.
