State Space Control of a Magnetic Suspension System

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# State Space Control of a Magnetic Suspension System - PowerPoint PPT Presentation

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

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
• 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

dx/dt = Ax + Bu

y = Cx + Du

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

y

+

D

+

u

+

B

1/s

C

x’

x

+

A

Steps for State Space Design
• State Matrices
• Controllability and feedback gain
• Observability and observer gain
• Combine both
• Introducing reference input
Equations
• Differential equation for system
• Transfer function
• Canonical forms
• Controllable canonical form
• Observable canonical form
• Jordan canonical form
• Modal canonical form
• Diagonal canonical form
• MatLab
Controllability
• Controllability matrix
• Matrix rank is n or n linearly independent column vectors
• If determinant is non zero system is controllable
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
• K matrix calculated with input set to zero
• Kc input gain
• Kc=(1/(C*(-1/(A-Bk))*B)
Observer
• State variables not always available
• Observer designed to estimate the state variables
• Full state observer
• Reduced state observer
Observability
• Observability matrix
• Matrix rank is n or has

n linearly independent

column vectors

• Determinant is a non

zero value

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
• Part of the Matlab Program
• Used to draw and simulate block diagrams
• Graphs at different points in the system can be plotted
PSpice
• MicroSim Corporation
• Designing and simulating circuits
• Schematic capture or netlist
• Libraries
• Modelling transfer function
• Saves time and money
Hardware
• Building circuit
• Testing circuit
• Fault finding
• Part of circuit already built
Applications
• MagLev train
• Floats above guide way
• Two types
• Reach speeds of 310 mph (500 kph)
• Frictionless bearings