Closed loop configuration, advantages and disadvantages

A closed-loop control system measures the output with a sensor, compares it with the desired value and uses the error to drive the plant.

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

Major components

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 output relation is $C(s) = \dfrac{G(s)}{1+G(s)H(s)}R(s)$.

Advantages

1. High accuracy: output follows the reference; with integral action the steady-state error to a step is zero.
2. Low sensitivity to parameter changes: $S_G^T = 1/(1+GH)$.
3. Disturbance rejection: load or noise effects are cut by $(1+GH)$.
4. Faster response, wider bandwidth: time constant $\tau/(1+K)$.
5. Stabilizes unstable plants and reduces the effect of non-linearities.
6. Automatic operation without human supervision.

Disadvantages

1. More complex and costly: sensors, comparators and controllers are needed.
2. Reduced overall gain: gain falls from $G$ to $G/(1+GH)$; extra amplification is needed.
3. Possible instability: high loop gain can cause oscillation or instability (e.g. $K/[s(s+1)(s+2)]$ is unstable for $K > 6$).
4. Sensor noise and errors enter the loop directly; output accuracy depends on the accuracy of the feedback element ($C/R \approx 1/H$).
5. More careful design and maintenance are required.

Example: the automatic voltage regulator of a generator senses terminal voltage and adjusts field current, holding voltage constant despite load changes, but needs careful tuning to avoid voltage oscillation.