introduction to control theory l.
Skip this Video
Loading SlideShow in 5 Seconds..
Introduction to Control Theory PowerPoint Presentation
Download Presentation
Introduction to Control Theory

Loading in 2 Seconds...

play fullscreen
1 / 38

Introduction to Control Theory - PowerPoint PPT Presentation

  • Uploaded on

Introduction to Control Theory. COMP417 Instructor: Philippe Giguère. Actuators. Earlier lecture presented actuators Electrical motor Now how do we use them in an intelligent manner?. Open-loop?.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
Download Presentation

PowerPoint Slideshow about 'Introduction to Control Theory' - shelly

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
introduction to control theory

Introduction to Control Theory


Instructor: Philippe Giguère

  • Earlier lecture presented actuators
    • Electrical motor
  • Now how do we use them in an intelligent manner?
open loop
  • We want to spin a motor at a given angular velocity. We can apply a fixed voltage to it, and never check to see if it is rotating properly.
  • Called open loop.
open loop4
  • What if there is a changing load on the motor?
    • Our output velocity will change!

speed w

no torque at max speed

stall torque

torque t

closing the loop
Closing the loop
  • Let’s measure the actual angular velocities.
  • Now we can compensate for changes in load by feeding back some information.
control theory
Control Theory
  • Roots in another science: Cybernetics

Cybernetics is the study of feedback and derived concepts such as communication and control in living organisms, machines and organisations.

  • Expression was coined by Norbert Weiner in 1948.
early example of feedback system
Early Example of Feedback System
  • James Watt’s “Centrifugal Governor” in 1788.
  • Regulates the steam engine speed.
other simple examples
Other Simple Examples
  • Body temperature regulation
    • If cold, shiver (muscles produce heat)
    • If hot, sweat (evaporation takes away heat)
  • Maintaining social peace
    • If a crime is found (sensor), the guilty party is punished (actuator).
  • Cruise control in cars
    • You set a speed, CC will increase fuel intake uphill, and decrease it downhill.
  • Etc…
why control theory
Why Control Theory
  • Systematic approach to analysis and design
    • Transient response
    • Consider sampling times, control frequency
    • Taxonomy of basic controllers (PID, open-loop, Model-based, Feedforward…)
    • Select controller based on desired characteristics
  • Predict system response to some input
    • Speed of response (e.g., adjust to workload changes)
    • Oscillations (variability)
  • Assessing stability of system
characteristics of feedback system
Characteristics of Feedback System
  • Power amplification
    • Compare neural signal power (mW) vs muscle power output (tens of W)
    • Means it is an active system, as opposed to passive.
  • Actuator
  • Feedback
    • measurement (sensor)
  • Error signal
  • Controller
controller design methodology
Controller Design Methodology


System Modeling

Controller Design

Block diagram construction

Controller Evaluation

Transfer function formulation and validation

Objective achieved?



Model Ok?




control system goals
Control System Goals
  • Regulation
    • thermostat
  • Tracking
    • robot movement, adjust TCP window to network bandwidth
  • Optimization
    • best mix of chemicals, minimize response times
approaches to system modeling
Approaches to System Modeling
  • First Principles
    • Based on known laws.
    • Physics, Queueing theory.
    • Difficult to do for complex systems.
  • Experimental (System Identification)
    • Requires collecting data
    • Is there a good “training set”?
common laplace transfom
Common Laplace Transfom




Impulse d






Damped Sine

transfer function
Transfer Function
  • Definition: H(s) = Y(s) / X(s)
  • Relates the output of a linear system to its input.
  • Describes how a linear system responds to an impulse… called impulse response
    • (remember! Convolving with impulse yields the same thing. Hence probing a system with and impulse is finding its transfer function…)
  • All linear operations allowed
    • Scaling, addition, multiplication
block diagram
Block Diagram
  • Expresses flows and relationships between elements in system.
  • Blocks may recursively be systems.
  • Rules
    • Cascaded elements: convolution.
    • Summation and difference elements
response of system
Response of System
  • Impulse
  • Step


steady state vs transient
Steady-State vs. Transient
  • Step Response illustrates how a system response can be decomposed into two components:
    • Steady-state part:
    • Transient
second order response
Second Order Response
  • Typical response to step input is:

overshoot -- % of final value exceeded at first oscillation

rise time -- time to span from 10% to 90% of the final value

settling time -- time to reach within 2% or 5% of the final value

effect of controller functions
Effect of Controller Functions
  • Proportional Action
    • Simplest Controller Function
  • Integral Action
    • Eliminates steady-state error
    • Can cause oscillations
  • Derivative Action (“rate control”)
    • Effective in transient periods
    • Provides faster response (higher sensitivity)
    • Never used alone

Control Performance (2nd O), P-type

Kp = 20

Kp = 50

Kp = 500

Kp = 200


Control Performance, PI - type

Kp = 100

Ki = 50

Ki = 200


You’ve been integrated...

Kp = 100

instability & oscillation


Control Performance, PID-type

Kp = 100

Kd = 5

Kd = 2

Ki = 200

Kd = 10

Kd = 20


PID Tuning

How to get the PID parameter values ?

(1) If we know the transfer function, analytical methods can be used (e.g., root-locus method) to meet the transient and steady-state specs.

(2) When the system dynamics are not precisely known, we must resort to experimental approaches.

Ziegler-Nichols Rules for Tuning PID Controller:

Using only Proportional control, turn up the gain until the system oscillates w/o dying down, i.e., is marginally stable. Assume that K and P are the resulting gain and oscillation period, respectively.

Then, use

for P control

for PI control

for PID control

Kp = 0.5 K

Kp = 0.45 K

Kp = 0.6 K

Ziegler-Nichols Tuning for second or higher order systems

Ki = 1.2 / P

Ki = 2.0 / P

Kd = P / 8.0

layered approach to control
Layered Approach to Control
  • Robotic systems often have a layered approach to control:


multiple loops
Multiple Loops

Inner loops are generally “faster” that outer loop.

advanced control topics
Advanced Control Topics
  • Adaptive Control
    • Controller changes over time (adapts).
  • MIMO Control
    • Multiple inputs and/or outputs.
  • Predictive Control
    • You measure disturbance and react before measuring change in system output.
  • Optimal Control
    • Controller minimizes a cost function of error and control energy.
  • Nonlinear systems
    • Neuro-fuzzy control.
    • Challenging to derive analytic results.
rc servo
RC Servo
  • Is a controller + actuator in a small package.
  • Not expensive 10$-100$.
  • Those in 417 will use some of these.
  • PWM -- “pulse width modulation
  • Duty cycle:
    • The ratio of the “On time” and the “Off time” in one cycle.
    • Determines the fractional amount of full power delivered to the motor.
  • Why:
    • Transistor acts as a resistor when partially on.
    • Leads to energy being wasted  heat.