Introduction to Feedback Control Systemsusers.encs.concordia.ca/~shz/elec372/introduction.pdfControl systems are used to regulate variables such as position, ... Block Diagram of a

Control Systems Example History Block Diagrams

Introduction to Feedback Control Systems

S. Hashtrudi ZadDept. of Electrical and Computer Engineering

Concordia University

January 2018

c© Copyright by Shahin Hashtrudi Zad 2015-2018

1 / 17


Control Systems I

Control systems are used to regulate variables such as

◮ position, velocity

◮ temperature, pressure and flow

to track a reference input which can either

◮ have a constant value (set point), or

◮ be a given function of time.

2 / 17


Control Systems II

Examples

◮ Automotive: Cruise control system◮ controlled variable: automobile speed◮ set point: chosen by driver

◮ Aerospace: Airplane autopilot system◮ controlled variable: altitude, heading◮ set point: chosen by pilot

3 / 17


Control Systems III

Examples

◮ Process Control: Flow control system◮ controlled variable: liquid flow◮ set point: chosen by operator

◮ Biology: Human thermoregulation◮ controlled variable: body temperature◮ set point: 37oC (set in hypothalamus)

4 / 17


Cruise Control System I

Let us consider the design and implementation of a cruise controlsystem.◮ process (system to-be-controlled): automobile◮ output (controlled variable): automobile speed (v)

First approach: Open-loop system design◮ Design:

◮ Choose control mechanism: adjust throttle position (x)◮ Drive the car at various speeds.◮ Find out the required throttle position.

◮ Implementation◮ For any cruise speed chosen by driver, use the table to set the

appropriate throttle position.

AutomobileThrottle Speed

v(t)x(t)

5 / 17


Cruise Control System II

Issues:

◮ Disturbance: inputs not manipulated by controller◮ Road grade (flat, uphill and downhill drive)◮ Wind

◮ Process changes or uncertainties◮ Number of passengers◮ Windows open or closed

Throttle

Wind

AuToMobIle

Road grade

Speed

v(t)x(t)

6 / 17


Cruise Control System III

Second approach: Closed-loop (feedback) system design

Throttle Speed

WindRoad grade

AutomobileActuatorControllerDesired Error

Controlsignal

Speed sensor

speedv(t)+

−

x(t)

◮ Controller receives speed measurements.

◮ Controller generates appropriate control signal based on theerror signal.(Error could be due to factors such as disturbance, noise andprocess changes.)

7 / 17


Feedback Control Systems

Block Diagram of a Feedback (Closed-loop) Control System

ControllersignalControl

Actuator

Sensor

ErrorProcess

Disturbance

OutputReference

input

(Command)

+

−

◮ Goals:

◮ Stability◮ Command following: Output ≈ Reference input;

both transient and steady-state behaviors are important(Recall: response (output) = transient resp. + steady-state resp.)

◮ Challenges:

◮ Disturbance◮ Process behavior may change◮ Process modeling uncertainties

8 / 17


History of Feedback Control I

Up to 17th century◮ Feedback systems used in limited scale◮ Based on floater to regulate liquid level and flow

Examples:

◮ Water clocks (Ktesibios, 200s BC)

◮ Wine dispenser (Hero, 50 AD)

◮ Animal drinking trough (Banu Musa,800s AD)

Figure: Water Clock (AbrahamRees “Clepsydra” in Cyclopædia, 1819).

9 / 17


History of Feedback Control II

17th and 18th centuries

◮ Floaters are reinvented

◮ Wider use of feedback mechanisms

Examples:

◮ Thermostats fortemperature control(Drebbel, 17th century)

◮ Windmill speed control(Lee, 1745)

◮ Steam engine controlusing flyball governor(Watt, 1788)

Figure: R. Routledge, “Discoveries & Inventions of theNineteenth Century”, 13th edition, 1900.

10 / 17


History of Feedback Control III

19th up to mid 20th century

◮ Improved feedback mechanisms

◮ Analysis and design methods

Application domain Issue Solution (Method)Steam engines Error Integral controller Siemens (1846)

Stability Stability analysis using Maxwell (1868),(“hunting”) differential equation Routh (1877),

(time-domain method) Hurwitz (1895)Ship steering Slow response Powered steering Gray (1866)(servomechanism) with feedback

Disturbance PID controller Sperry (1911)Electronic amplifiers Component drift Negative feedback Black (1927)

High-order Frequency-domain Nyquist (1932),differential eq. design methods Bode (1940)

◮ Other notable application domains: Electric machinary,Process industries, Anti-aircraft guns

11 / 17


History of Feedback Control IV

Mid 20th century onwards

◮ More advanced methods◮ Digital computer control◮ Multi-input-multi-output methods◮ State-space methods (sets of first order diff. eq.)◮ Nonlinear methods◮ Optimal control◮ Stochastic methods

◮ New perspectives◮ Cybernetics (N. Wiener): Control and communication in the

animal and the machine

◮ New applications◮ Guided missiles, Spacecraft (e.g. Apollo program)◮ Automotive◮ Robotics◮ Unmanned Aerial Vehicles (UAV)

12 / 17


Building Block Diagrams for Feedback Control Systems I

ControllerErrorReference

input

(Command)

Actuator

Outputoutput

Actuator

Sensor

signal

Control

Disturbance

Process+

−

To build a block diagram for a feedback control system, identify

◮ Output (variable to-be-controlled)

◮ Sensor (measuring device)

◮ Controller

◮ Actuator

◮ Actuator output (input to the process to-be-controlled)

◮ Disturbance (inputs not manipulated by the controller)

13 / 17


Building Block Diagrams for Feedback Control Systems II

Example: Automatic Insulin Delivery SystemAfter food is eaten and digested, sugars (mainly glucose) are absorbed into thebloodstream. Normally, the pancreas secretes insulin into the bloodstream tometabolize the sugar. The pancreas of a diabetic person secretes insufficientinsulin to metabolize blood sugar and as a result, blood sugar levels couldbecome higher than normal. This could result in damage to body organs.

Automatic insulin delivery systems have been developed for diabetics. Thesystem which contains a tiny insulin reservoir and a pump is implanted in thebody. The system measures the blood sugar (glucose) level and compares itwith the level of a normal individual and sends appropriate commands to thepump to adjust insulin delivery from the reservoir to the body.

Draw a block diagram for the insulin delivery system. Identify the signals in theblock diagram and the function of each block.

14 / 17






◮ Output: sugar level

14 / 17







◮ Actuator: pump

14 / 17







◮ Actuator: pump

◮ Actuator output: insulin from reservoir

14 / 17







◮ Actuator: pump

◮ Actuator output: insulin from reservoir

◮ Disturbance (from control system’s perspective): insulin from pancreas

14 / 17


Building Block Diagrams for Feedback Control Systems III

Example: Automatic Insulin Delivery System

Sensor

Insulinfrom

reservoir

Insulin from pancreas

sugar level

Bodymetabolism

Sugar levelPumpControllerDesired +

−+

+

15 / 17


Summary

Benefits of feedback systems

16 / 17


Summary


◮ Improve stability

16 / 17


Summary



◮ Improve response to input commands (both transient andsteady-state responses)

16 / 17


Summary




◮ Reduce effects of disturbance

16 / 17


Summary





◮ Reduce sensitivity to process behavior and process model(Enhances robustness)

16 / 17


Summary






◮ Enhance functionalityExample: Warm-blooded animals (with thermoregulation)compared with cold-blooded animals (withoutthermoregulation)◮ can perform more vigorous activities◮ live and remain active in a wider range of temperatures.

16 / 17


Summary






◮ Enhance functionalityExample: Warm-blooded animals (with thermoregulation)compared with cold-blooded animals (withoutthermoregulation)◮ can perform more vigorous activities◮ live and remain active in a wider range of temperatures.

(However the cost (energy) is higher:

◮ For a human at 20oC: metabolic rate = 1300 to 1800 kcal per day

◮ For an American alligator at 20oC: metabolic rate = 60 kcal per day)

16 / 17


To Probe Further

◮ Otto Mayr, “The origins of feedback control,” Scientific

American, vol. 223, no. 4, pp. 110-118, Oct. 1970.

◮ Stuart Bennett, “A brief history of automatic control,” IEEE

Control Systems, vol. 16, no. 3, pp. 17-25, June 1996.

17 / 17

Documents

Introduction to Feedback Control Systemsusers.encs.concordia.ca/~shz/elec372/introduction.pdfControl systems are used to regulate variables such as position, ... Block Diagram of a