Controller and Observer Design (Design of Control

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Controller and Observer Design (Design of Control

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Controller and Observer Design (Design of Control System in State Space) (Design of Control System in State Space by Pole placement) References Dr. Radhakant Padhi, Asstt. Prof, IISC, Bangalore, through NPTEL Modern Control Engineering by

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Controller and Observer Design (Design of Control System in State Space)
(Design of Control System in State Space by Pole placement)

References Dr. Radhakant Padhi, Asstt. Prof, IISC, Bangalore, through NPTEL
Modern Control Engineering by Katsuhiko Ogata, PHI Pvt. Ltd New Delhi

Pole placement
Observer Design

Outline Philosophy of observer design

Full order observer

Reduced (minimum) order observer

Philosophy of Observer Design In practice all the sate variable are not available for feedback. Possible reason include:
Non availability of sensors
Expensive sensors
Available sensors are not acceptable (due to high noise, high power consumption etc)
A device (or a computer program) that estimate or observes state variables is called a state observer or simply an observer.

Philosophy of Observer Design… If the observer observes all state variables of the system, regardless of whether some state variables are available for direct measurement, it is called a full order observer.
If the observer observes only the unmeasurable state variables (n-m, n = no of sates, m= measurable state= no of o/p), it is called a minimum order state observer or reduced order state observer.

State Observer Block Diagram

State Observer Block Diagram..

Observer design concepts

Observer design concepts …

Observer Design (Full Order)

Comparison of controller & observer design

Observer Design as a dual problem ---(1) ---(2)

Observer Design as a dual problem… Hence observer design of a system is nothing but simply doing the controller design of its dual system.
So the methods will be same as for controller design.
Method 1: Direct substitution method (when order of system n≤3)
Method 2: Bass-Gura Approach
Method 3: Ackermann’s formula

Pole Placement Technique

Observer Design by method 1: (n≤3)

Controller Design using Method 2: Bass-Gura Approach

Controller Design using Method 2: Bass-Gura Approach… Step 5: The required matrix is

Controller Design using Method 3:Ackermann’s Formula For an arbitrary positive integer n ( number of states) Ackermann’s formula for the state feedback gain matrix K is given by

Example

Example ..

Example…

Example

Example…

Reduced order design?

Thanks

Controller and Observer Design (Design of Control

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