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Fig. 6. Model of the system to be controlled as a ModelicaML model, composite structure
diagram
be designed to constrain the speed setpoint near the limits so that the setpoint would be
zero at the limit coordinates and it would be reduced already before reaching the limits.
These approaches will be simulated next based on a ModelicaML model of the process
to be controlled and UML AP models of the two control approaches.
To be able to utilize the tools and techniques presented in this paper, the system to be
controlled need to be available as a ModelicaML model. The UML composite diagram
presenting the simplified model of the system is presented in figure 6. The model was
specified with open source Papyrus UML tool, with OpenModelica extensions, and it
consists of 3 ModelicaML components that are instances of ModelicaML classes. The
cart is operated with a motor (CM) that takes its control signal from the IOUnit that col-
lects all measurement and control signals between the process and control system. The
total weight of the cart and motor is assumed to be 20kg ( m total ) and the radius of the
drive wheel 0.1m ( r dw ). The torque (T) and acceleration (a) equations of the motor and
cart based on drive voltage ( V d ) are presented in equations 1, 2 and 3. The numerical
values of the constants of the motor are: R m =0 . 5 , L m =0 . 0015 , K emf =0 . 05 and
K t =0 . 01 . The brake is assumed to be able to decelerate the cart with force of 200N
(Fb). The equations are, thus, simple but sufficient for demonstration purposes.
V d − ω ∗ K emf = L m ∗ dI/dt + R m ∗ I
(1)
T = K t ∗ I
(2)
T/r dw + F b = m total ∗ a
(3)
The UML AP control structure diagram presenting the similar parts of the two control
solutions for the system is depicted in figure 7. The control solution consists of ana-
logue measurements of cart position and speed, an interlock, a PID controller and an
analogue and a binary output for controlling the motor and the brake, respectively. The
two interlocking approaches discussed earlier influence mainly the contents of the in-
terlock. In the first approach, the speed request (setpoint) is not constrained. However,
in order to enable that to be implemented in the second approach, the speed request is
relayed through the interlock AF.
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