meng332 systems control - emu academic staff directory 1/meng332... · what is engineering design...

MENG332 SYSTEMS CONTROL

Assoc. Prof. Dr. Qasim Zeeshan ASSOCIATE PROFESSOR

DEPARTMENT OF MECHANICAL ENGINEERING

EASTERN MEDITERRANEAN UNIVERSITY

Office: ME141

Email: [email protected]

Tel: +90 392 6301361

Web: http://me.emu.edu.tr/zeeshan/

https://www.linkedin.com/in/qasim-zeeshan

WEEK 2

INTRODUCTION


What is Engineering ???

The creative application of scientific principles to

design or develop structures, machines, apparatus, or

manufacturing processes, or works utilizing them singly

or in combination; or to construct or operate the same

with full cognizance of their design; or to forecast their

behavior under specific operating conditions; all as

respects an intended function, economics of operation

or safety to life and property.

What is Engineering Design ???

Engineering design is the process of devising a system,

component, or process to meet desired needs.

It is a decision making process (often iterative), in which

the basic sciences, mathematics, and engineering

sciences are applied to convert resources optimally to

meet a stated objective.

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 – 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)

What is a Control System?

What is Control System?

• A system Controlling the operation of another system.

• A system that can regulate itself and another system.

• A Control System is a device, or set of devices to manage, command, direct or regulate the behaviour of other device(s) or system(s).

What is Control Engineering ???

Control Engineering is based on foundations of feedback theory and linear system analysis, also it integrates the concepts of network theory and communication theory.

Control Engineering is not limited to any engineering discipline, but connected to all fields of engineering.

History of Control Systems

Three Eras of Control

• Classical control : 1950 before – Transfer function based methods

• Time-domain design & analysis

• Frequency-domain design & analysis

• Modern control : 1950~1960 – State-space-based methods

• Optimal control

• Adaptive control

• Post modern control : 1980 after – H∞ control

– Robust control (uncertain system)

A brief history of control

• Two of the earliest examples

– Water clock (270 BC)

– Self-leveling wine vessel (100BC)

The idea is still used today, i.e.

flush toilet


– Fly-ball governor (James Watt,1769)

• the first modern controller • regulated speed of steam engine • reduced effects of variances in load • propelled Industrial Revolution


– Fly-ball governor (James Watt,1789)


Birth of mathematical control theory G. B. Airy (1840)

the first one to discuss instability in a feedback control system the first to analyze such a system using differential equations

J. C. Maxwell (1868) 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 linear and

nonlinear differential equations results not introduced in control literature until about 1958


• Birth of classical control design method – H. Nyquist (1932)

• developed a relatively simple procedure to determine stability from a graphical plot of the loop-frequency response.

– H. W. Bode (1945) • 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.

core of classical control design


• Development of modern control design – 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…


– Recent applications of modern control theory include such non-engineering systems as biological, biomedical, economic and socioeconomic systems…

CONTROL

Classical Control •System Modelling

•Transfer Function

•Block Diagrams

•Signal Flow Graphs

•System Analysis

•Time Domain Analysis (Test Signals)

•Frequency Domain Analysis

•Bode Plots

•Nyquist Plots

•Nichol’s Chart

Modern Control •State Space Modelling

•Eigenvalue Analysis

•Observability and Controllability

•Solution of State Equations (state Transition Matrix)

•State Space to Transfer Function

•Transfer Function to State Space

•Direct Decomposition of Transfer Function

•Cascade Decomposition of Transfer Function

•Parallel Decomposition of Transfer Function

INTRODUCTION BASIC COMPONENTS OF A CONTROL SYSTEM


Basic components of a control system

Plant

Controlled Variable

Expected Value

Controller

Actuator

Sensor

Disturbance

Basic concepts of a control system

Plant

1.Plant: a physical object to be controlled such as a

mechanical device, a heating furnace, a chemical reactor or a spacecraft.

Controlled variable

2.Controlled variable: the variable controlled by

Automatic Control System , generally refers to the system output.

Expected value

3.Expected value : the desired value of controlled variable

based on requirement, often it is used as the reference input

Disturbance

7.Disturbance: the unexpected factors

disturbing the normal functional relationship between the controlling and controlled parameter variations.

Controller 4.Controller: an agent that can calculate

the required control signal.

Actuator

5.Actuator: a mechanical device that takes

energy, usually created by air, electricity, or liquid, and converts that into some kind of motion.

Sensor

6.Sensor : a device that measures a physical

quantity and converts it into a signal which can be read by an observer or by an instrument.

DEFINITIONS

System – An interconnection of elements and devices for a desired purpose.

Control System – An interconnection of components forming a system configuration that will provide a desired response.

Process – The device, plant, or system under control. The input and output relationship represents the cause-and-effect relationship of the process.

Process Output Input

Controlled Variable– It is the quantity or condition that is measured and Controlled. Normally controlled variable is the output of the control system.

Manipulated Variable– It is the quantity of the condition that is varied by the controller so as to affect the value of controlled variable.

Control – Control means measuring the value of controlled variable of the system and applying the manipulated variable to the system to correct or limit the deviation of the measured value from a desired value.

DEFINITIONS

Disturbances– A disturbance is a signal that tends to adversely affect the value of the system. It is an unwanted input of the system.

• If a disturbance is generated within the system, it is called internal disturbance. While an external disturbance is generated outside the system.

Controller Output Or Controlled Variable

Input or Set point or reference

Process

Manipulated Variable

DEFINITIONS

More Terminology • A plant performs a particular operation. It is the physical object to be

controlled

• A process is any operation to be controlled. Processes can be chemical, economic, biological, etc.

• A system is a combination of components that act together and perform a certain objective.

• A disturbance is a signal that adversely affects the value of the output of a system. May be internal or external.

• Feedback control refers to an operation that, in the presence of disturbances, tends to reduce the difference between the output of a system and some reference input and does so on the basis of the difference.

BASIC CONCEPTS

System

Modeling

Analysis

A combination of components acting together to perform a specific objective

A procedure to obtain a model describing important characteristics of system

Investigation of performance of system, whose model is known, under specified conditions

OUTPUT

A variable that we observe and consider important

Measurements/instrumentation

Not necessary what we want to know

STATE A variable that is used to describes the internal system dynamics

A set of states can be used to fully describe system’s current situation.

With two identical sets of initial values of states, performance of a system is the same

Do you get all the states of system ?

INPUT

A variable that excites a system

Inputs are not always known beforehand

Inputs are always responsible for problems in systems

SYSTEM

Lumped System

A System with a finite number of state variables Lumped parameter/ discrete system. Usually an artificial/modeling concept

SYSTEM

Distributed System

A System with infinitely many state variables Continuous elastic structures (beams, shells, and plates)

Fluid systems (ocean and atmosphere)

Can often be approximately described with lumped models (FEM, AMM)

Continuous-time System All the signals are continuous in time

Everything is defined at each instant time

Also called Analog systems Discrete-time Systems

Variables are only defined at discrete times

Also called sampled data systems Hybrid System

Continuous-time + discrete-time

Linear System

Equations describing system are linear

Principle of superposition

Time-invariant System (ideal) The features of system never ever changes Usually a good approximation for most engineering application A good starting point to obtain main features of system Relatively easy to analyze

SYSTEM

Time-varying System (in practice)

The characteristics of system changes with time going

time-varying parameters

time-varying dynamics

Nonlinear System

Linearize it near a operating condition to obtain a linear approximation

Interdisciplinary and System Nature Analogous systems

Models are the same regardless of the physical domain of interest

We only need to understand how to analyze one model, but the results are applicable for four seemingly different types of physical systems!

u y

= = =

)(tuyyy

Voltage

Charge

u

y

Force

displ. Transl.

u

y

Torque

displ.Angular

u

y

Pressure

Volume

u

y

MODELING “Mathematical Modeling is the process of constructing mathematical objects, whose behaviors or properties correspond in some way to a particular real-world system”. - A mathematical object could be a system of

equations, a stochastic process, a geometric or algebraic structure, an algorithm, or even just a set of numbers.

- The term real world system could refer to a physical

system, a financial system, a social system, an economical system, or essentially any other system whose behaviors can be observed.

MODELING Why Modeling???

There are many reasons, but out of all there are two main reasons as under: To gain understanding: Generally speaking, if we have a

mathematical model which accurately reflects some behavior of a real-world system of interest, we can often gain improved understanding of that system through analysis of the model. Furthermore, in the process of building the model we find out which factors are most important in the system, and how different parts of the system are related.

To predict or simulate: Very often we wish to know what a real-world system will do in the future, but it is expensive, impractical, or impossible to experiment directly with the system. Examples include nuclear reactor design, space flight, weather prediction, drug efficiency in human, and so on.

Unfortunately, there is no definite “algorithm” to construct a mathematical model that will work in all situations. Modeling is sometimes viewed as an art. It involves taking whatever knowledge you may have of mathematics and of the system of interest and using that knowledge to create something. Since everyone has a different knowledge base, a preferred bag of tricks, and a unique way of looking at problems, different people may come up with different models for the same system. There is usually plenty of room for argument about which model is ‘best’.

MODELING The Modeling Process


• It is very important to understand at the outset that for any real system, there is no “perfect” model. One is always faced with tradeoffs between:

Accuracy Flexibility Cost

• Increasing the accuracy of a model generally increases cost

and decreases flexibility. The goal in creating a model is usually to obtain a “sufficiently accurate” and flexible model at a low cost.


Physical system

Model

Meta Model

Worl

d

The M

odeling S

pace

xm

m

1

s

1

s

1x x

c

k

xc

kx

f(t)

input

+ - -

x

x

x x(t)

output

)(tfkxxcxm

RS Model

jiiiiiiii xxbxbxbby2

0


• Constructing a model requires:

A clear picture of the goal of the modeling exercise. Exactly which aspects of the system do you wish to understand or predict, and how accurately do you need to do it?

An picture of the key factors involved in the system and how they relate to each other. This often requires taking a greatly simplified view of the system, neglecting factors known to influence the system, and making assumptions which may or may not be correct.

SYSTEM LINEAR SYSTEM

A system is called linear if the principle of superposition applies. “The principle of superposition states that the response produced by the simultaneous application of two different forcing functions in the sum of the two individual responses”. Hence, for the linear system, the response to several inputs can be calculated by treating one input at a time and adding the results. It is this principle that allows one to build up complicated solutions to the linear differential equation from simple solutions.

SYSTEM Linear Time Invariant Systems

& Time Varying Systems

“Dynamical systems that are composed of linear time invariant lumped parameter components may be described by linear time-invariant differential equations-that is , constant co-efficient differential equations. Such systems are called Linear Time Invariant Systems”. “Systems that are represented by differential equations whose coefficients are functions of time are called Linear Time Varying Systems.” Example: The mass of a spacecraft changes due to fuel consumption.

Example Vehicle speed control

MgtfBvvM

MgBvtfvM

e

e

)(

sin)(

MODEL:

ANALYSIS:

t

v speed

Desired

speed

Actual Increasing grade

Vehicle

speed

Actual

-

+ speed

Desired

Controller+

force

incline/Gravity

- CONTROL:

input output

states

linearization

Inertia force

Traction: input, excitation Gravitation: disturbance

Friction: damping

THANK YOU FOR YOUR INTEREST

meng332 systems control - emu academic staff directory 1/meng332... · what is engineering design...

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