Transcript The Helicopter Automatic control – Project course

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.


Determine non directly measurable parameters



Weight, distances
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
1
t
Validation, horisontal
movement
Step response of horisontal movement in model and process
2
t
Validation, reaction torque
Response in horisontal movement from step in main motor
1
t
2
t
Validation, gyroscopic effect
Response in vertical movement from step in tail motor
1
2
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
Introducing cross gain – elimination of cross coupling
u_vert(t)
e_vert(t)
r_vert(t) +
G_vert
PID_vert
-
y_vert(t)
Cross gain
sK1
r_hor(t)
e_hor(t)
+
-
Conclusion…
K2
+
PID_hor
G_hor
u_horizontal(t)
y_hor(t)
Validation, vertical movement
Step response of verticalmovement in model and process
1
t
Control

LQ with observer - min eT (t )Q1e(t ) u T (t )Q2u (t )
x (t )  Ax(t )  Bu(t )  v1
u(t )   Lx(t )  r (t )
y(t )  Cx(t )  Du(t )  v2
Not all states measureable - introducing state observer

u(t )  Lxˆ(t )  Fr r (t )
xˆ  Axˆ (t )  Bu(t )  K ( y(t )  Cxˆ (t ))
r(t)
u(t)
Fr
+
-L
y(t)
Helicopter
xˆ (t )
Observer
Control
•Model linearized by hand
•Equilibrium point taken from real process (input voltages and
angles)
 v1 
v 
 2
White noise with intensities:
 R1 R12 
 RT R 
2
 12
R12  0
:No covariance between the noise
Q1 , Q2 , R1 , R2
:Design variables
Control
Singular values
Control
LQ
PID
Control
PID
LQ with observer
Easy
Model
and fast to derive and
implement
Possible to tune without modelling
in some cases
Compansates for static error
caused by hair-drier
Able to attenuate static error
caused due to change in mass point
Do not reduce cross coupling
satisfactory
dependent
Better performace for a MIMO
system with cross coupling
Less oscillations
Almost no overshoot
Couldn’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