2e1242 project course automatic control - the helicopter
TRANSCRIPT
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2E1242 Project Course Automatic Control
- The Helicopter
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The team
David Höök Henric Jöngren Pontus Olsson Ksenija Orlovskaya Vivek Sharma
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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)
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The challenge
MIMO system under influence of cross-coupling
Modelling Many non directly measurable parameters Subsystems interlinked through many parameters
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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
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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.
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Modelling
Main motor and vertical movement
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Modelling
Tail motor and horisontal movement
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Modelling
Physically derived differential equation model
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Modelling
Black box First approach
subsystem and model are compared
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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
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Simulink model, vertical
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Simulink model, horisontal
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Simulink model,reaction torque
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Simulink model, gyroscopic moment
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Validation, vertical movement
Step response of verticalmovement in model and process
t
1
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Validation, horisontal movement
Step response of horisontal movement in model and process
t
2
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Validation, reaction torque
Response in horisontal movement from step in main motor
t
t
2
1
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Validation, gyroscopic effect
Response in vertical movement from step in tail motor
2
1
t
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Validation, total model
System too unstable to be validated open-loop Two manually tuned PID-controllers are used
Model Process
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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
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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…
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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
+
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Validation, vertical movement
Step response of verticalmovement in model and process
t
1
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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
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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)
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Control
Singular values
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Control
LQ PID
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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
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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.
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THE END…11/5 kl. 03.12