Control Design

 

Block Diagram and signal flow graph(Mason)

 

 

partial fraction expansion

 

 

Transfer funciton of poles and zeros

 

TF of poles and zeros

 

 

Periodic signal to Aperiodic signal

periodic to aperiodic

 

Fourier Transform (Continuous -Time)

Fourier transform c

 

 

Laplace Transform

s=σ + jω

Laplace transform

 

 

Input signal:

unit step function,unit ramp function, unit acceleration funciton,unit impluse function;

 

unit step response,unit ramp response, unit acceleration response,unit impluse response;

 

 

 

 

 

Typical Blocks:

 

 

Multiplier

Multiplier

 

 

First order system

First-order-system

 

 

Integrator

Integrator

 

 

Differentiator

Differentiator

 

 

Time delay

Time-delay

 

 

Oscillator

Damped-oscillator

 

 

PID controller

PID-controller

 

 

 

Charactertistic equation (transfer funciton)

 

quadratic formula

 

 

 

 

 

Time domain analysis

Step response

(Figure come from Mordern Control Systems,Richard C and Robert H)

 

  rising time Tr

  peak time Tp

  settling timeTs

  percent overshoot)σ%


Routh-Hurwitz criterion

 

 

The Root Locus Method(linear system)

not directly solve the characteristic equation

On the s-plane (complex plane), where the x-axis is σ(real) ,and y-axis is jω (imaginary)

gain K

 

 

 

 

 

Frequency response Methods

Frequency response G(ω)

Frequency response

 

 

Bode plot

 

 

 

Nyquist Criterion

 

 

 

Non-linear control

Lyapunov stability analysis

 

 

State Variable Models

 

Signal flow gain formula

 

Signal flow gain

 

Pijk= gain of kth path from variable xi to variable xj,

 

Δ= determinant of the graph

 

Δijk=cofactor of the path Pijk

 

 

 

The state variables of a dynamic system

 

State var of dynamic sys

 

State differential equation

State differential equation

 

Output equation

Output equation

 

 

State space

 

 

Four first order differential equations

 

Four first order DE

 

TF numerator is b0

 

TF numerator is b0

 

TF numerator is a polynomial

 

TF numerator is a polynomial

 

 

Phase variable canonical form

 

Phase variable canonical form

 

 

Input feedforward canonical form

 

Input feedforward canonical form

 

 

 

Parallel manipulator: PD controller,augmented PD controller,PC torque controller.