Digital control system and function of each block

A digital control system is a feedback control system in which a digital computer (microprocessor, microcontroller or PLC) acts as the controller. The plant is continuous, so signals are converted between analog and digital forms at the controller's input and output.

Block diagram

 r(kT) -->(+)--> Digital  --> D/A --> Hold
           ^ -   computer             (ZOH)
           |                            |
           |                            v
          A/D                       Actuator
           ^                            |
           |                            v
          S/H                         Plant ---> y(t)
           ^                            |
           +-------- Sensor <-----------+

Function of each block

Working

1. The output $y(t)$ is measured by the sensor and gives an analog signal.
2. The S/H samples it at $t = kT$ and the A/D converts it into a digital number $y(kT)$.
3. The computer forms the error $e(kT) = r(kT) - y(kT)$ and solves a difference equation, for example the PID law $u(kT) = K_p e(kT) + K_i \sum e(iT) + K_d [e(kT)-e((k-1)T)]$.
4. The D/A converter and ZOH turn $u(kT)$ into a piecewise-constant analog signal $u(t)$.
5. The actuator applies $u(t)$ to the plant, and the cycle repeats every sampling period.

Types of signals in the loop

• Continuous-time analog: plant output, actuator input.
• Sampled-data (discrete-time analog): S/H output.
• Digital (quantized and coded): inside the computer.

Main features

• The controller is a program, so the control law can be changed easily.
• One computer can handle many loops by multiplexing.
• The sampling period $T$ must be small compared with the plant time constants (normally 8 to 10 samples per cycle of the damped oscillation) to give good performance.
• Quantization and sampling introduce small errors and delays that must be considered in design.

Example: in a DC motor speed control, a tachogenerator measures speed, a microcontroller with built-in ADC runs a PI algorithm, and a PWM output (acting as D/A plus hold) drives the motor through a power amplifier.