Control system block diagram and closed loop advantages

A control system is an arrangement of physical components connected so as to command, direct or regulate itself or another system to give a desired output. In a closed-loop system the output is measured and fed back, and the error between the desired and actual output drives the system.

                       disturbance d
                            |
 r   +----+  e   +------+ u +---+---+   c
---->| Σ  |----->|Contr-|-->| Plant |----+---->
     +----+      | oller|   +-------+    |
      - ^        +------+                |
        |  b    +-----------------+      |
        +-------| Feedback/sensor |<-----+
                +-----------------+

Function of each block

1. Reference input $r$ (set point): desired value of the output.
2. Error detector / summing point: compares $r$ with feedback $b$ and gives error $e = r - b$.
3. Controller: acts on the error (P, PI, PID) and produces control signal $u$.
4. Actuator: power element (motor, valve, amplifier) that applies $u$ to the plant.
5. Plant / process: the system being controlled; gives the controlled output $c$.
6. Disturbance $d$: unwanted input acting on the plant (load change, noise).
7. Feedback element / sensor: measures $c$ and converts it to $b$, comparable with $r$.

The closed-loop transfer function is $\dfrac{C(s)}{R(s)} = \dfrac{G(s)}{1+G(s)H(s)}$.

Example: in a motor speed control, $r$ = speed set by a potentiometer, controller = amplifier, actuator and plant = DC motor and load, sensor = tachogenerator.

Advantages of closed loop over open loop

1. More accurate: output follows the reference; steady-state error is small (zero with integral action).
2. Less sensitive to parameter changes: $S_G^T = \dfrac{1}{1+GH}$ compared with 1 for open loop, so ageing, temperature and supply variations hardly affect the output.
3. Disturbance rejection: a disturbance at the plant is reduced by $(1+GH)$.
4. Faster response, larger bandwidth: a plant $K/(\tau s+1)$ gets time constant $\tau/(1+K)$.
5. Can stabilize unstable plants (e.g. inverted pendulum, aircraft).
6. Automatic operation: no human operator is needed to watch and correct the output.
7. Reduces non-linear effects and distortion (used in feedback amplifiers).

(Its drawbacks are higher cost, more components, lower overall gain and the possibility of instability if the gain is too high.)