CONTROL ENGINEERING
CONTROL ENGINEERING
Dr.N.V.Raghavendra Professor & Head Dept. of Mechanical Engineering The National Institute of Engineering, Mysore
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Control Engineering Syllabus Sub Code Hrs / W eek SEE Hrs : 3 Hrs
: ME0457 : 05
CONTROL ENGINEERING
CIE : SEE : Max. Marks:
50 % 50 % 100
Course Prerequisites: None Prerequisites: None Course Outcomes: At the end of the course the student will be able abl e to: 1. Translat ranslate e variou various s contr control ol systems systems into into mathem mathemati atical cal models models and identify identify the similarities. 2. Anal Analyz yze e the the tran transi sien entt and and stea steady dy state state resp respon onse se of mech mechan anic ical al contr control ol systems. 3. Comp Comput ute e tran transf sfer er funct unctio ion n of con control trol sy syst ste ems usin sing Bloc Blockk-di diag agra ram m reduction technique and Mason’s gain formula. 4. Apprai Appraise se the stabili stability ty of the control control systems systems using graphi graphical cal methods methods and recommend improvements. 5. Demonstrat Demonstrate e self self learning learning capabilities. capabilities. 8/30/2015
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Control Engineering Syllabus
CONTROL ENGINEERING
Unit 1: Introduction: Concept of automatic controls, open and closed loop systems, requirements of an ideal control system. Mathematical Models: Models of Mechanical systems, Thermal systems, Hydraulic systems and Electrical circuits. Analogous systems: Force voltage, Force current. Models of DC (armature controlled and field controlled) and AC motors on load. SLE: Modelling of Gear train. 08 Hrs Unit 2: Transient and Steady State Response Analysis : Introduction, first order and second order system response to step input, Concepts of time constant, Accuracy, Error and its importance in speed of response. Characteristics of under damped systems. Types of controllers: Proportional, Integral, Differential, Proportional Integral, Proportional Differential, Proportional Integral Differential controllers. SLE: Study of various controllers in automated machines. 08 Hrs
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Control Engineering Syllabus
CONTROL ENGINEERING
Unit 3: Block Diagrams and Signal Flow Graphs: Transfer Functions definition, block-diagram representation of system elements, and reduction of block diagrams. Signal flow graphs: Mason’s gain formula. SLE: Transfer function of Multiple Input Multiple Output control systems. 08 Hrs Unit 4: Mathematical Concept of Stability: Routh’s-Hurwitz Criterion. Frequency Response Analysis: Polar plots, Nyquist Stability Criterion, Stability Analysis, Relative stability concepts, concept of M and N circles. SLE: Study of various ways of improving phase margin and gain margin. 10 Hrs
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Control Engineering Syllabus
CONTROL ENGINEERING
Unit 5: Root locus plots: Definition of root loci, general rules for constructing root loci, Analysis using root locus plots for open loop transfer functions. Applications of Root Locus Plot. SLE: Importance of poles and zeroes for stability. 08 Hrs Unit 6 Stability Analysis: Bode plots, Relative stability concepts, phase and gain margin. System Compensation and State Variables: Series and feedback compensation, Introduction to state concepts, state equation of linear continuous data system. Matrix representation of state equations, Controllability and Observability, Kalman and Gilberts test. SLE:State equation, and controllability and observability of spring mass 10 Hrs damper system
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Control Engineering Syllabus
CONTROL ENGINEERING
Text Book: 1. Automatic Control Systems by Farid Golnaraghi, Benjamin C. Kuo, John Wiley & Sons, 2010. Reference Books: 1. Feedback Control Systems: Schaum’s series 2001. 2. Control Systems Principles and Design: M. Gopal, TMH, 2000 3. Introduction to Automatic Controls, Howard L Harrison, John G Bollinger, Second Edition July 1970. CIE Assessment: • Written Tests (Test, Mid Semester Exam & Make Up Test) are Evaluated for 25 Marks each. • Best of two of these tests will be considered for CIE.
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What is a control system?
Generally speaking, a control system is a system that is used to realize a desired output or objective. Control systems are everywhere ◦
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They appear in our homes, in cars, in industry, in scientific labs, and in hospital… Principles of control have an impact on diverse fields as engineering, aeronautics ,economics, biology and medicine… Wide applicability of control has many advantages (e.g., it is a good vehicle for technology transfer)
Slides courtesy: Prof. Bin Jiang & Dr. Ruiyun QI 8/30/2015
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A brief history of control
CONTROL ENGINEERING
Two of the earliest examples Water clock (270 BC) Self-leveling wine vessel (100BC) ◦
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The idea is still used today, i.e. flush toilet
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A brief history of control ◦
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Fly-ball governor (James Watt,1769)
the first modern controller • regulated speed of steam engine • reduced effects of variances in load • propelled Industrial Revolution •
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A brief history of control
CONTROL ENGINEERING
Birth of mathematical control theory
G. B. Airy (1840)
J. C. Maxwell (1868)
the first one to discuss instability in a feedback control system the first to analyze such a system using differential equations the first systematic study of the stability of feedback control
E. J. Routh (1877) deriving stability criterion for linear systems A. M. Lyapunov (1892) deriving stability criterion that can be applied to both
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linear and nonlinear differential equations results not introduced in control literature until about 1958 NVR
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A brief history of control
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Birth of classical control design method ◦
H. Nyquist (1932)
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H. W. Bode (1945)
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developed a relatively simple procedure to determine stability from a graphical plot of the loop-frequency response. frequency-response method
W. R. Evans (1948)
root-locus method
With the above methods, we can design control systems that are stable, acceptable but not optimal in any meaningful sense. 8/30/2015
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A brief history of control
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Development of modern control design ◦
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Late 1950s: designing optimal systems in some meaningful sense 1960s: digital computers help time-domain analysis of complex systems, modern control theory has been developed to cope with the increased complexity of modern plants 1960s~1980s: optimal control of both deterministic and stochastic systems; adaptive control and learning control 1980s~present: robust control, H-inf control…
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CONTROL ENGINEERING
Basic components of a control system
Plant Controlled Variable Expected Value Controller Actuator Sensor
Disturbance 8/30/2015
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CONTROL ENGINEERING
Basic components of a control system 1.Plant: a physical object to be Plant
Controlled variable
Expected value
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controlled such as a mechanical device, a heating furnace, a chemical reactor or a spacecraft.
2.Controlled variable: the variable controlled by Automatic Control System , generally refers to the system output.
3.Expected value : the desired value of controlled variable based on requirement, often it is used as the reference input
Basic components of a control system Controller
CONTROL ENGINEERING
4.Controller: an agent that can calculate the required control signal.
5.Actuator: a mechanical device that Actuator
takes energy, usually created by air, electricity, or liquid, and converts that into some kind of motion.
6.Sensor : a device that measures a Sensor
physical quantity and converts it into a signal which can be read by an observer or by an instrument.
7.Disturbance: the unexpected factors Disturbance 8/30/2015
disturbing the normal functional relationship between the controlling and controlled parameter variations. NVR
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CONTROL ENGINEERING
Block diagram of a control system n r Expected value
e Controller -
Actuator
Error
u
Disturbance
Plant
y Controlled variable
Sensor comparison component (comparison point) : its output equals the algebraic sum of all input signals. “+”: plus; “-”: minus 8/30/2015
The Block represents the function and name of its corresponding mode, we don’t need to draw detailed structure, and the line guides for the transfer route. NVR
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Open-loop control systems
Open-loop control systems: those systems in which the output has no effect on the control action. System input
CONTROL ENGINEERING
CONTROLLER
Control signal
PLANT
System output
The output is neither measured nor fed back for comparison with the input. For each reference input, there corresponds a fixed operating conditions; the accuracy of the system depends on calibration . In the presence of disturbances, an open-loop system will not perform the desired task.
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Open-loop control systems
CONTROL ENGINEERING
Examples ◦
Washing machine
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Traffic signals
Note that control systems that operate on a time basis are open-loop. 8/30/2015
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Open-loop control systems
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Some comments on open-loop control systems ◦
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Simple construction and ease of maintenance. Less expensive than a closed-loop system. No stability problem. Recalibration is necessary from time to time. Sensitive to disturbances, so less accurate.
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Good
Bad
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Open-loop control systems
CONTROL ENGINEERING
When should we apply open-loop control? ◦
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The relationship between the input and output is exactly known . There are neither internal nor external disturbances. Measuring the output precisely is very hard or economically infeasible .
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Closed-loop control systems
CONTROL ENGINEERING
Closed-loop control systems are often referred to as feedback control systems. The idea of feedback: Compare the actual output with the expected value . Take actions based on the difference (error) . ◦
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Expected value
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Error
Control signal CONTROLLER
System output PLANT
This seemingly simple idea is tremendously powerful. Feedback is a key idea in the discipline of control.
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Closed-loop control systems
CONTROL ENGINEERING
In practice, feedback control system and closed-loop control system are used interchangeably Closed-loop control always implies the use of feedback control action in order to reduce system error
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Example 1 : flush toilet Plant: water tank Input: water flow Output: water level h(t ) Expected value: h0 Sensor: float Controller: lever Actuator: piston h0
Controller Lever
water
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piston lever
float
h0
h(t)
Actuator
Plant q (t ) Water Piston 1 Tank
h(t ) threshold
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CONTROL ENGINEERING
Example 2: Cruise control mv bv ueng ueng
k (vdes
uhill
v)
Disturbance
Road grade uhill Desired velocity vdes Reference input
Error
Calculation element Controller
Control signal
Engine ueng
Actuator
Auto body
Actual velocity v
Plant
Sensor Measured velocity 8/30/2015
Speedometer
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Sensor noise
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Example 2: Cruise control
mv bv uengine uengine
k (vdes
uhill
v)
Stability/performance
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v ss
vdes as k
Steady state velocity approaches desired velocity as k Smooth response: no overshoot or oscillations
;
→ ∞
Disturbance rejection
Effect of disturbances (eg, hills) approaches zero as k
→ ∞
Robustness Results don’t depend on the specific values of b, m or k, for k NVR sufficiently large
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Example 2: Cruise control
CONTROL ENGINEERING
Note
In this example, we ignore the dynamic response of the car and consider only the steady behavior. ◦
Dynamics will play a major role in later chapters.
There are limits on how high the gain k can be made. ◦
when dynamics are introduced, the feedback can make the response worse than before, or even cause the system to be unstable.
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