7/23/2019 Workshop Poster Presentation

1/1

Decentralised Anti-windup design approacheswith application to Quadrotor UAVs

Nkemdilim A Ofodile, Matthew C Turner, Teng D Chollom

Control Research Group, Department of Engineering, University of Leicester, UK

Motivation

Anti-windup (AW) compensatorsimprove performancein both MIMO andSISO systemswhen saturation occurs.

However in practice, MIMO AW compensators are;not as simple as SISO AW , the practical consequences ofL

2performance may be difficult to interpret.

Highly complex, hence problems arise when computational resources arelimited.

not structured. Key featuresAim: Design decentralized AW compensators for a class of MIMO systems

(eg: Quadrotor UAVs fall in this category).The AW must ensure global stability of the entire nonlinear system.

MIMO Plant Description

GD(s) =diag(G1(s), G2(s), . . .Gm(s)) diag(Gi(s)) KD(s) =diag(K1(s), K2(s), . . .Km(s)) diag(Ki(s))

KD GDX1 u

K

r y

G

X

(u)

Figure : MIMO system structure

GD is a diagonal dynamic part of the plant G Xis a non-diagonal but static, invertible matrix. Its inverseX1 can be

interpreted as a contol allocation matrix.Whensaturation inactive, system behaves as m decoupled loopsWhensaturation occurs, decoupling is destroyed,system experiences windup

Typical Anti-Windup (AW) Structure

+

+

-

-

+

+

GDKD XX1r y

GK

u

u

um

ud

yd

Figure : Full anti-windup structure

The AW compensator,(s)has the structure and state-space realisation:

(s) =

M(s) I

N(s)

A + BF BF 0

C + DF D

Ghas right coprime factorisation G(s) = N(s)M1(s). Fis chosen so thatA+BF is Hurwitz.

A stable system with F can be obtained by satisfying the LMI described in [2]

Psuedo-Decentralized AW Features

+

+

-

-

+

+GDKD XX

1r y

ylin

vlin

v

v

vm

vd

yd

(v)

Figure : Decentralized AW structure

Here, the AW, (s) is driven by virtual signal v = v (v). By performing the stability analysis as described in [3], this LMI is obtained

He

ADQD+ BDLD BDXUD 0 0LDX

1 X1UDX1 0

0 0 2

I 0CDQD+ DDLD DDUD 0

2I

0 and V > 0 such thatV = XWXexists, AW

compensators can be designed using the LMI in [2] Result is structured and easy to implement with great practical appeal. Note:

[MD, ND] [diag(Mi(s)), diag(Ni(s))]

Quadrotor UAV Test Platform

System has the same structureas earlier stated MIMO plant

Practical quadrotor used is aModified 2014 3DR Quadrotor

Flight Tests Results

Figure: Pitch angleresponse: From Left; 1st

Nominal response; 2nd

Saturated response noAW;3rd Saturation,decentralized AW; 4th

Saturation,channel-by-channelAW

Note: All plots are not exactly

alike because outdoor flights

conditions are not constant.

1.06 1.08 1.1 1.12 1.14 1.16 1.18 1.2

x105

25

20

15

10

5

0

5

10

15

Time in milliseconds

Pitch

in

degrees

Desired Pitch

NominalPitch

7 7.2 7.4 7.6 7.8 8 8.2 8.4

x104

25

20

15

10

5

0

5

10

15

Time in milliseconds

Pitch

in

degrees

Desired Pitch

ActualPitch Saturated no AW

1.08 1.1 1.12 1.14 1.16 1.18

x 105

25

20

15

10

5

0

5

10

15

Time in milliseconds

Pitch

in

degrees

Desired Pitch

ActualPitch Saturated with AW

2.38 2.4 2.42 2.44 2.46 2.48 2.5

x105

25

20

15

10

5

0

5

10

15

Time in milliseconds

Pitch

in

degrees

Desired Pitch

ActualPitch Saturated with AW

Conclusion

Two approaches proposed for structured AW design. Pseudo-decentralised approach provides a one-step design procedure. Channel-by-channel approach allows independent AW design for each channel

and combines them safely for the MIMO system.

Channel-by-channel AW is preferred due to its transparency, flexibility andease of implementation.

Flight results for both designs show improved performance during saturation.

References

[1] Nkemdilim A Ofodile, Matthew C Turner, and Osichinaka C Ubadike. Channel-by-channelanti-windup design for a class of multivariable systems. In American Control Conference(ACC). IEEE, 2015.

[2] Matthew C Turner, Guido Herrmann, and Ian Postlethwaite. Accounting for uncertainty inanti-windup synthesis. In American Control Conference. IEEE, 2004.

[3] Matthew C Turner and Ian Postlethwaite. A new perspective on static and low order anti-windup synthesis. International Journal of Control, 77(1):2744, 2004.

tp://www2.le.ac.uk/departments/engineering/research/control @le.ac.uk