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% Wheel.vdmrt
\subsubsection{Closing the feedback loop -- the \texttt{Wheel} class}
The \texttt{Wheel} class is used to close the feedback loop in the environment model.
It computes the new acceleration, speed and angular position, whenever the
\texttt{evaluate} operation is called by the environment.
\begin{vdm_al}
class Wheel
values
-- maximum angular acceleration is 20 pi rad/sec^2
MAX_ACC : real = 62.8318531
instance variables
-- the logical name of the wheel
mName : seq of char;
-- link to the environment
mEnvironment : Environment;
-- last evaluated at time step
last : nat := 0;
-- current angular acceleration
public acc : real := 0.0;
-- current angular speed
public speed : real := 0.0;
-- current angular position
public position : real := 0.0
operations
-- constructor for the wheel class
public Wheel: seq of char * Environment ==> Wheel
Wheel (pname, penv) == ( mName := pname; mEnvironment := penv);
private isActuated: () ==> bool
isActuated () ==
return mEnvironment.getValue(mName^"_ACTUATED") = 1;
private getPWM: () ==> real
getPWM () ==
return mEnvironment.getValue(mName^"_PWM");
public evaluate: () ==> ()
evaluate () ==
( dcl pwm : real := if isActuated()
then getPWM()
else 0.0,
old_acc : real := acc,
old_speed : real := speed,
now : nat := time;
-- compute the amount of time passed
def dt = (now - last) / World`SIM_RESOLUTION in
( -- update the current wheel acceleration
acc := MAX_ACC * pwm;
-- update the wheel angular speed (Euler)
speed := speed + 0.5 * dt * (old_acc + acc);
-- update the wheel angular positiom (Euler)
position := position + 0.5 * dt * (old_speed + speed);
-- remember when we where executed
last := now ) )
end Wheel
\end{vdm_al}
The \texttt{evaluate} operation first checks whether the \texttt{Wheel} is
actuated by the controller (it may be running in \texttt{<FREERUNNING>} mode).
If the motor is \texttt{<ACTUATED>}, then it will retrieve the current PWM
value from the environment, which has been set by the controller.
As a simple abstraction, the direct drive motor is considered ideal and a
simple linear response is created. The new acceleration is computed by
multiplying the PWM value with the maximum angular acceleration
of the motor. The angular speed and position are computed by integration
and double integration respectively, using the well-known Euler algorithm.
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