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State Space Control of a Magnetic Suspension System. Margaret Glavin Supervisor: Prof. Gerard Hurley. Introduction. Proportional and Derivative Control PWM Control State Space Control Applications of the Suspension System. State Space Background. Developed since 1960’s

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state space control of a magnetic suspension system

State Space Control of a Magnetic Suspension System

Margaret Glavin

Supervisor: Prof. Gerard Hurley

introduction
Introduction
  • Proportional and Derivative Control
  • PWM Control
  • State Space Control
  • Applications of the Suspension System
state space background
State Space Background
  • Developed since 1960’s
  • Modern control theory
  • State variable method of describing differential equations
  • Not one unique set of state variables to describe the state space of the system
state equations
State Equations

dx/dt = Ax + Bu

y = Cx + Du

  • A – State Matrix
  • B – Input Matrix
  • C – Output Matrix
  • D – Direct transmission Matrix
block diagram
Block Diagram

y

+

D

+

u

+

B

1/s

C

x’

x

+

A

steps for state space design
Steps for State Space Design
  • State Matrices
  • Controllability and feedback gain
  • Observability and observer gain
  • Combine both
  • Introducing reference input
equations
Equations
  • Differential equation for system
  • Transfer function
methods to calculate space state matrices from transfer functions
Methods to Calculate Space State Matrices from Transfer Functions
  • Canonical forms
    • Controllable canonical form
    • Observable canonical form
    • Jordan canonical form
    • Modal canonical form
    • Diagonal canonical form
  • MatLab
controllability
Controllability
  • Controllability matrix
  • Matrix rank is n or n linearly independent column vectors
  • If determinant is non zero system is controllable
feedback gain matrix
Feedback Gain Matrix
  • Used to place the poles
  • If controllable poles placed at any location
  • Methods to calculate matrix
    • Direct substitution method
    • Transformation matrix
    • Ackermann’s formula
reference input
Reference Input
  • K matrix calculated with input set to zero
  • Kc input gain
  • Overcomes steady state error
  • Kc=(1/(C*(-1/(A-Bk))*B)
observer
Observer
  • State variables not always available
  • Observer designed to estimate the state variables
  • Full state observer
  • Reduced state observer
observability
Observability
  • Observability matrix
  • Matrix rank is n or has

n linearly independent

column vectors

  • Determinant is a non

zero value

observer gain
Observer Gain
  • Used to place the observer poles
  • Poles two to five times faster than controller poles
  • Same methods of calculation used as for feedback gain matrix
simulink
Simulink
  • Part of the Matlab Program
  • Used to draw and simulate block diagrams
  • Graphs at different points in the system can be plotted
pspice
PSpice
  • MicroSim Corporation
  • Designing and simulating circuits
  • Schematic capture or netlist
  • Libraries
  • Modelling transfer function
  • Saves time and money
hardware
Hardware
  • Building circuit
  • Testing circuit
  • Fault finding
  • Part of circuit already built
applications
Applications
  • MagLev train
    • Floats above guide way
    • Two types
    • Reach speeds of 310 mph (500 kph)
  • Frictionless bearings