--- title: "DCS block diagram and S/H tracking/hold modes" subject: "Digital Control System" chapter: 1 key: "semester_6/digital_control_system:dcs-block-diagram-tracking-hold" source: https://www.bctengineer.com/q/semester_6/digital_control_system/dcs-block-diagram-tracking-hold site: BCT Engineering --- # DCS block diagram and S/H tracking/hold modes Digital Control System · Chapter 1: Introduction to Discrete Time Control System - Asked in: 2081 Chaitra, 3+5 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/digital_control_system/dcs-block-diagram-tracking-hold - Whole chapter: https://www.bctengineer.com/md/semester_6/digital_control_system/chapter-1 ## Question With the help of digital block diagram, explain the control system in detail. Define the term tracking mode and hold mode in sample and hold circuit. ## Short answer A digital control system samples the plant output, converts to digital, computes control law in a computer, outputs via D/A and hold (ZOH) to actuator. Tracking mode: S/H switch closed, output follows input. Hold mode: switch open, capacitor holds last sampled value for ADC conversion. ## Answer #### 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. ```text 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 ```text 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. ```text 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. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is the sequence of operations in each period of the digital control loop? A. Hold, compute, convert, sample, output B. Sample, convert, compute, output, hold C. Compute, sample, hold, convert, output D. Output, sample, compute, convert, hold Answer: B. The loop samples, converts, computes u(kT), outputs and holds it. (Key point: Digital control loop sequence) 2. In the S/H control circuit, what do control = 1 and control = 0 mean? A. 1 = hold, 0 = track B. 1 = sample (switch ON, tracking), 0 = hold (switch OFF) C. Both mean tracking D. 1 = convert, 0 = idle Answer: B. A logic 1 turns the switch on for tracking; a logic 0 turns it off to hold. (Key point: S/H control signal) 3. When is the hold command given? A. After end-of-conversion B. At each sampling instant just before the ADC start-of-conversion pulse C. Only at start-up D. Randomly Answer: B. The S/H must be holding before conversion starts; it returns to tracking after end-of-conversion. (Key point: Timing of hold command) 4. What is aperture time? A. Time for the output to settle to the input B. Delay between the hold command and the switch actually opening C. Time to convert D. Rate of voltage fall during hold Answer: B. Aperture time is the delay between hold command and switch opening; droop rate is I_leak/C. 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