Fractional Order Control System

An approach to

Presenting by Sreerag.K.S S2 IDC Roll No: 17

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Guided by Mrs. Radhika.R Asst. Professor RIT, Pampady

Introduction Requirement: Lighter robots that can be driven with less

energy.

Control of flexible light weight manipulators.

Aerospace Industry, mobile robotics.

Different control strategies are available.

Fractional order controllers are introduced.

Better control performance.

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Modeling of the Single Link Flexible Manipulator

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Single Link Flexible Arm

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The dynamics of the flexible link is given by

The transfer function model of the link dynamics is

The dynamics of motor with closed loop current control system is given by

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Design of the Three loops used for modeling

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Inner Loop The inner loop dynamics can be written as

A standard PD controller is designed for this loop so as to have a unity (approximately) transfer function for the inner loop.

In practice motor dynamics can be made fast but it is not negligible.

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Simplifying Loop The tip position is fed back to the input of the inner

loop. The feedback gain is unity and it is a positive

feedback. This reduces the manipulator transfer function to a

double integrator type. The feedback gain value which is set as one is not

critical according to the Nyquist stability criteri0n. It is sufficient to have a gain close to unity.

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Outer loop

The tip position is fed back to the input by the outer loop.

Strain gauge is used to find the coupling torque which is then used to estimate tip position.

The position error will be processed by a fractional order control so as to produce the control law.

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Design Specifications.

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It is required that the tip position should track the reference value with minimum overshoot as possible.

In order to have zero over shoot the over all system should be critically damped.

It is well known that the damping ratio is approx. equal to 0.01 times the phase margin.

So the desired phase margin is set as 76.5o .

Also the desired rise time is around 0.3 sec, with this the desired wgc can be calculated as 6rad/s.

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Design of outer loop controller

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With the inner and simplifying loops the entire system will be reduced to

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Therefore the transfer function can be written as

The controller has two functions To maintain the overshoot as constant as possible for

varying payloads. To avoid the effect of disturbance.

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Condition for Constant PM

For phase margin to be within the limits

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Disturbance Rejection From the final value theorem

This implies that

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1<α

Introduction to fractional calculus and fractional order control

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Why? The controller required for the system is a simple

derivative controller.

The order of derivative should be a non integer between 0 & 1.

Better than integer order control

More parameters can be tuned

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Analog Approximation

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Function for Creating Sa

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function [G]=mod_fod(r,N,wl,wh,b,d) %Finding the modified Oustaloop Approximation % r= Fractional Order % N= order of approximation % wl= lower frequency % wh= higher frequency % b & d are constants. if nargin==4

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b=10;d=9; end k=1:N; wu=sqrt(wh/wl); K=(d*wh/b)^r; wkp=wl*wu.^((2*k-1-r)/N); wk=wl*wu.^((2*k-1+r)/N); G=zpk(-wkp',-wk',K)*tf([d,b*wh,0],[d*(1- r),b*wh,d*r]); end

System specific Design

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The controller is of the form

2162.7926 s (s+0.00123) (s+0.0195) (s+0.309) (s+4.898) (s+77.62) (s+1111) =----------------------------------------------------------------------------------------- (s+0.01288) (s+0.2042) (s+3.236) (s+51.29) (s+812.8) (s+7407) (s+0.000765) Order of Approximation Selected = 5 Lower cut off Frequency Wl =0.001 rad/s Upper cut off Frequency Wh=1000 rad/s

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αSαSαSαS

αS

Simulation Ist Phase Without Controller

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With Control

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Time Schedule

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Week Work

1st, 2nd, 3rd Searching for topic

4th, 5th ,6th Approval and search for reference

6th Modeling of the Flexible arm Manipulator

7th 8th and 9th Modeling of Fractional order controller

Future Work Analysis and modification

References Tip position control of a lightweight flexible manipulator using a

fractional order controller C.A. Monje, F. Ramos, V. Feliu and B.M. Vinagre (The Institution of Engineering and Technology 2007)

Fractional Order Systems Modelling and Control Applications by Riccardo Caponetto, Giovanni Dongola,Luigi Fortuna , Ivo Petráš

Fractional order Systems and Control: Fundamentals and Application by Concepción A. Monje, YangQuan Chen,Blas M. Vinagre , Dingyü Xue , Vicente Feliu

A Fractional Order Proportional and Derivative (FOPD) Motion Controller: Tuning Rule and Experiments HongSheng Li, Ying Luo, and YangQuan Chen

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THANK YOU

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