MAE 691 Special Topic : Modern Control Theory

Dr. Hodge Jenkins

Mechanical Engineering

Fall 2016

Control Background Check • Had a math/engineering course using Laplace

transforms?

• Had a math/engineering course using matrices and linear algebra?

• Have used MATLAB ?

• Have used SIMULINK ?

• Had a dynamics course?

• Had a vibrations course?

• Had an undergraduate course in controls?

• Had a graduate controls course?

Control Basics Function Block Diagrams

Lecture 1

Most Common Control System Has No Electronics

• Tank Liquid Volume Control

Function Block Diagram

• Basic modeling representation of hardware, electronic, or software element (has units).

Input

variable or signal

Output variable or

signal

Block diagram: Control & Feedback Terminology

Feedback Basic Terminology • Process: system or central component whose output is to be

controlled • Actuator: Device that can influence the process and change the

process output • Plant: Combination of Plant and Actuator • Comparator: Computes the difference between Reference and

Output • Controller (or compensator): Device that computes the control

signal/variable : Combination of Comparator and Compensator • Senor: Provides an electrical (or mechanical) output proportional

to variable to be measured • Reference: the desired value for the output of a system,

sometimes called Reference Input or Input or Set point • Output: the process variable of a system to be controlled • Transfer Function: function when multiplied by an Input provides

an Output for the component or system being modeled (usually thought of in terms of Laplace transforms for continuous systems)

What is required to control a system Open Loop (no feedback) ?

• Compensator + Actuator

• Accurate model of system response to control input

What additional is required to control a system via feedback control?

• Output sensor

• Comparator

Temperature Control Function Block

Diagram: Open Loop System

Room

Desired Input Temperature

Fuel Flow Control

TSET

Disturbance Heat flow in/out QDist

Compensator

TActual

Output QIn Plant

Furnace

dV/dt

Fuel Rate

Actuator

Room

Reference Input Temp

TSET

TMeasured

+ _

Error

Disturbance Heat flow in/out QDist

TActual

Temperature Control Function Block

Diagram: Closed-Loop Continuous

System

Temperature Sensor

Output

Fuel Flow Control

QIn

Furnace

dV/dt

Fuel Rate

Compensator Actuator

Function block diagram of a room temperature control system, digital output

Room temperature and furnace output vs. time

Plant and Controller • Plant ~= Actuator + Process

• Controller ~= Comparator + Compensator

Room

Reference Input Temp

TSET

TMeasured

+ _

Error

Disturbance Heat flow in/out QDist

TActual

Temperature Sensor

Output

Fuel Flow Control

QIn

Furnace

dV/dt

Fuel Rate

Compensator Actuator

Plant Controller

Why is feedback needed?

• Disturbances ( weather changes for example)

• Unmodeled plant or actuator characteristics

• Changes plant or actuator

Limitations of Control

• Senor saturation

• Power available

• Component physical limits (stress, temperature, etc.)

Modeling of Systems

• Needed to design an appropriate compensator (whether feedback is used or not)

• Characterize the system performance or best possible performance

Modeling: Dynamic Models

Mechanical 1 DOF Model

Apply Laplace transform to get algebraic equation.

Define output and input. Get transfer function.

Mechanical Systems: Car Suspension

Electro/Mech. Systems : Disk Drive

Segway

Electronic circuits

DC Motor

DC motor

• (a) electric circuit of the armature;

• (b) free-body diagram of the rotor

Fluid systems

Thermal Systems (heat transfer)

Steam Engine + Control

Operating parts of a fly-ball governor