DCS block diagram and S/H tracking/hold modes

Digital control system

A digital control system is a feedback system whose controller is a digital computer. Since the plant is analog, it needs A/D conversion at the controller input and D/A conversion at the output.

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

1. Sensor: measures the plant output $y(t)$ as an analog signal.
2. Sample-and-hold: samples the signal every $T$ s and holds it during conversion.
3. A/D converter: quantizes and codes the sample into a binary word.
4. Digital computer: compares with the reference and computes $u(kT)$ by a control algorithm (PID, lead/lag, state feedback) written as a difference equation.
5. D/A converter: converts $u(kT)$ into an analog voltage.
6. Hold (ZOH): holds this voltage constant until the next update (staircase output).
7. Actuator and plant: the actuator applies the control effort to the plant.
8. Clock: sets the sampling period and synchronises all blocks.

In each period the loop does: sample, convert, compute, output, hold. With a small enough $T$ (8 to 10 samples per cycle of oscillation) the system behaves nearly like a continuous one.

Tracking mode and hold mode in S/H

 Vin --[A1]--o/ o--+--[A2]--> Vout
                   |
                  === C
                   |
                  GND

• Tracking mode: the switch is closed; C charges through A1 and the output follows the input.
• Hold mode: the switch is opened at the sampling instant; C keeps its voltage because the open switch and high-impedance buffer A2 draw almost no current, so the output stays at $V_{in}(kT)$ while the ADC converts it.

Control circuit of S/H

The switch is a MOSFET/JFET whose gate is driven by a logic control signal from the controller's timing unit:

• Control = 1 (sample): switch ON, tracking.
• Control = 0 (hold): switch OFF, holding.
• The hold command is given at each sampling instant just before the ADC's start-of-conversion pulse; after end-of-conversion the circuit returns to tracking.

 Control  ‾‾‾|____|‾‾‾‾|____|‾‾‾
           track hold track hold

Important timing terms: aperture time (delay between hold command and switch opening), acquisition time, and droop rate $I_{leak}/C$ during hold.