2E1242 Project Course Automatic Control

- The Helicopter

The team

David Höök Henric Jöngren Pontus Olsson Ksenija Orlovskaya Vivek Sharma

Resources

Helicopter with two degrees of freedom (Humusoft) Input voltage to two DC motors driving the main and

tail propellers (MIMO-system) Output horisontal and vertical angles Labview (communicating with process) Matlab (simulation, model validation)

The challenge

MIMO system under influence of cross-coupling

Modelling Many non directly measurable parameters Subsystems interlinked through many parameters

Main objective

The helicopter is supposed to:

Follow a prespecified trajectory that illustrates its performance limitations

Attenuate external disturbances Hair-drier simulating hard wind Change of mass centre - adding a load to helicopter

Modelling

Helicopter divided into subsystems

Main motor and vertical movement Tail motor and horisontal movement

Cross coupling:

Main motor to horisontal movement (reaction torque) Horisontal movement to vertical movement (gyroscopic

moment) Cross coupling from tail motor reaction to vertical

moment and vertical gyro effects neglected.

Modelling

Main motor and vertical movement

Modelling

Tail motor and horisontal movement

Modelling

Physically derived differential equation model

Modelling

Black box First approach

subsystem and model are compared

Modelling

White box / Grey box Measure parameters corresponding to the physical

model. Weight, distances

Determine non directly measurable parameters Frictions, inertias, gyro, reaction torque – iteratively by adjusting

parameters from model to fit responses from process ’ Time constants for motor dynamics

Adjusting curves to static measurement data Functions mapping insignals to pull force, rotor velocity and

reaction torque

Simulink model, vertical

Simulink model, horisontal

Simulink model,reaction torque

Simulink model, gyroscopic moment

Validation, vertical movement

Step response of verticalmovement in model and process

t

1

Validation, horisontal movement

Step response of horisontal movement in model and process

t

2

Validation, reaction torque

Response in horisontal movement from step in main motor

t

t

2

1

Validation, gyroscopic effect

Response in vertical movement from step in tail motor

2

1

t

Validation, total model

System too unstable to be validated open-loop Two manually tuned PID-controllers are used

Model Process

Modelling

Conclusion – what have we learned about modelling?

More difficult than expected Dependent system

Tuning a parameter of one subsystem will affect the behavior of other subsystems.

Must find good balance between the best approximation of the separate subsystems and the performance of the total system.

When is the model good enough? – When it is fulfilling its purpose White box: more insight and understanding of system than Black box Black box: less time consuming than white box

Control

Different controllers

Manually adjusted PID – one for each degree of freedom LQ controller with observer – one for the total system

Is it necessary to spend weeks modelling if a quickly tuned P.I.D. can solve the control problem?

-The manually adjusted PID against the model dependent LQ…

Control

PID_vert G_vert

u_vert(t)e_vert(t)r_vert(t) y_vert(t)

+-

PID_hor G_horu_horizontal(t)

e_hor(t)r_hor(t)

y_hor(t)

+-

K2

Introducing cross gain – elimination of cross coupling

Conclusion…

Cross gainsK1

+

Validation, vertical movement

Step response of verticalmovement in model and process

t

1

Control LQ with observer -

Not all states measureable - introducing state observer

2

1

)()()(

)()()(

vtDutCxty

vtButAxtx

)()()( trtLxtu

))(ˆ)(()()(ˆˆ txCtyKtButxAx

)()(ˆ)( trFtxLtu r

Observer

Helicopter+

-L

Fr

r(t) u(t) y(t)

)(ˆ tx

)()()()(min 21 tuQtuteQte TT

Control

2

1

v

v

212

121

RR

RRT White noise with intensities:

2121

12

,,,

0

RRQQ

R

:Design variables

:No covariance between the noise

•Model linearized by hand•Equilibrium point taken from real process (input voltages and angles)

Control

Singular values

Control

LQ PID

Control PID

Easy and fast to derive and implementPossible to tune without modelling in some casesCompansates for static error caused by hair-drierAble to attenuate static error caused due to change in mass pointDo not reduce cross coupling satisfactory

LQ with observerModel dependent Better performace for a MIMO system with cross couplingLess oscillationsAlmost no overshootCouldn’t attentuate static error caused due to change in mass point very well Many parameter need to be estimated. More complicated to derive and implement

Control

Conclusion – what have we learned about control?- Different regulators: PID, LQ ,close look at

advantages and disadvantages over each other.

- The functions are fulfilling their purposes.

THE END…11/5 kl. 03.12