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 objectiveThe 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

ModellingHelicopter 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.

ModellingMain motor and vertical movement

ModellingTail motor and horisontal movement

ModellingPhysically derived differential equation model

Modelling

Black box First approach

subsystem and model are compared

ModellingWhite 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 movementStep response of verticalmovement in model and process

t

1

Validation, horisontal movementStep response of horisontal movement in model and process

t

2

Validation, reaction torqueResponse in horisontal movement from step in main motor

t

t

2

1

Validation, gyroscopic effectResponse 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

ModellingConclusion – 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

ControlDifferent 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_vertu_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 movementStep response of verticalmovement in model and process

t

1

Control LQ with observer -

Not all states measureable - introducing state observer

2

1

)()()()()()(vtDutCxtyvtButAxtx

)()()( trtLxtu

))(ˆ)(()()(ˆˆ txCtyKtButxAx

)()(ˆ)( trFtxLtu r

Observer

Helicopter+

-L

Frr(t) u(t) y(t)

)(ˆ tx

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

Control

2

1

vv

212

121

RRRR

T 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

ControlLQ 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

ControlConclusion – 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