--- title: "Digital control system and function of each block" subject: "Digital Control System" chapter: 1 key: "semester_6/digital_control_system:dcs-function-of-each-block" source: https://www.bctengineer.com/q/semester_6/digital_control_system/dcs-function-of-each-block site: BCT Engineering --- # Digital control system and function of each block Digital Control System · Chapter 1: Introduction to Discrete Time Control System - Asked in: 2075 Bhadra, 4 marks; 2073 Bhadra, 6 marks; 2071 Magh, 8 marks; 2067 Mangsir, 10 marks (asked 4 times) - Video: [Block Diagram of Digital Control System- Digital Control System- Control system-2](https://www.youtube.com/watch?v=O27Es88sMS0) — Ekeeda - 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-function-of-each-block - Whole chapter: https://www.bctengineer.com/md/semester_6/digital_control_system/chapter-1 ## Question Explain digital control system along with the functions of each block. ## Short answer A digital control system uses a digital computer as the controller. The sensor measures the output, S/H samples and holds it, A/D converts it to binary, the computer computes the control law, D/A converts back to analog, ZOH holds the output, and the actuator drives the plant. ## Answer 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 ```text r(kT) -->(+)--> Digital --> D/A --> Hold ^ - computer (ZOH) | | | v A/D Actuator ^ | | v S/H Plant ---> y(t) ^ | +-------- Sensor <-----------+ ``` #### Function of each block | Block | Function | |---|---| | Sensor/transducer | Measures the plant output and converts it to an electrical signal | | Sample-and-hold (S/H) | Samples the analog signal every $T$ s and holds it during conversion | | A/D converter | Quantizes and codes the held value into a binary number | | Digital computer | Compares with the reference and computes the control signal by the algorithm | | D/A converter | Converts the computed binary number into an analog voltage | | Hold (ZOH) | Keeps the output constant between sampling instants (staircase signal) | | Actuator | Amplifies the signal and drives the plant (motor, valve) | | Plant | The physical process being controlled | | Clock | Fixes the sampling period $T$ and synchronises S/H, A/D and D/A | #### 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. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What makes a system a digital control system? A. The plant itself is digital B. A digital computer (microprocessor, microcontroller or PLC) acts as the controller in a feedback loop, with converters between it and the analog plant C. It has no feedback path D. It uses only op-amps and RC networks Answer: B. The controller is a digital computer, and A/D and D/A conversions link it to the continuous plant. (Key point: Digital control system definition) 2. What is the function of the clock block in the loop? A. It amplifies the actuator signal B. It measures plant output C. It fixes the sampling period T and synchronises the S/H, A/D and D/A D. It stores the control program Answer: C. The clock sets T and keeps the sampling, conversion and output operations in step. (Key point: Function of the clock) 3. What does the digital computer do in each sampling period? A. Forms the error e(kT) = r(kT) - y(kT) and solves a difference equation such as the PID law to get u(kT) B. Quantizes the analog sensor output C. Holds u(kT) constant between samples D. Drives the motor directly with a continuous voltage Answer: A. The computer compares reference and measured value and computes the control signal by the algorithm. (Key point: Computer's task in the loop) 4. What do the D/A converter and ZOH together produce? A. A sampled impulse train B. A piecewise-constant (staircase) analog signal u(t) C. A binary word y(kT) D. A random sampling pattern Answer: B. The D/A converts u(kT) to a voltage and the ZOH keeps it constant until the next update, giving a staircase. (Key point: Role of D/A and ZOH) 5. How small should the sampling period T normally be for good performance? A. Larger than the plant time constants B. Equal to one cycle of oscillation C. Small enough to give about 8 to 10 samples per cycle of the damped oscillation D. As large as possible to save computing time Answer: C. T must be small compared with plant time constants, about 8 to 10 samples per damped oscillation cycle. (Key point: Choice of sampling period) ## Related in Digital Control System - [Digital control system block diagram and advantages](https://www.bctengineer.com/question.md?key=semester_6%2Fdigital_control_system%3Adcs-block-diagram-advantages) — Digital Control System, chapter 1, asked 3× - [Pulse transfer function of digital PID controller](https://www.bctengineer.com/question.md?key=semester_6%2Fdigital_control_system%3Aderive-pid-pulse-tf) — Digital Control System, chapter 3, asked 2× - [Advantages of digital over analog control](https://www.bctengineer.com/question.md?key=semester_6%2Fdigital_control_system%3Adcs-advantages-over-analog) — Digital Control System, chapter 1, asked 3× - [Making the case for digital control](https://www.bctengineer.com/question.md?key=semester_6%2Fdigital_control_system%3Acase-for-digital-control) — Digital Control System, chapter 1 - [Types of signals in digital control](https://www.bctengineer.com/question.md?key=semester_6%2Fdigital_control_system%3Asignal-types-in-dcs) — Digital Control System, chapter 1 - [Closed-loop TF with digital PID, plant 1/(s(s+1))](https://www.bctengineer.com/question.md?key=semester_6%2Fdigital_control_system%3Apid-closed-loop-plant-s1) — Digital Control System, chapter 3, asked 2× ## Related in other subjects - [Block diagram of digital communication system](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Ablock-diagram-digital-comm) — Data Communication, chapter 1, asked 8× - [Closed loop control system block diagram explained](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Awhat-is-cs-bd-closed-loop) — Control Systems, chapter 1, asked 4× - [Control system block diagram and closed loop advantages](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Awhat-is-cs-bd-cl-advantages) — Control Systems, chapter 1 - [Analog and digital system block diagrams; linear and non-linear distortion](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aanalog-digital-block-linear-nonlinear-distortion) — Communication Systems, chapter 1