Optimization with two Green Design constraints

We now want to take a look at two quantities of interest, namely the total power PIN that needs to be supplied to the mass and the power dissipated by the mass by friction, PR (the considered mass submodel, MAS004, takes viscous friction phenomenon into account).

PIN is given by the following expression: PIN = PI + PR, where PI denotes the inertial power of the mass, that can be found, with PR, in the variables of the Power, Energy, Activity group, see the figure below, once power calculations have been activated.

Figure 35: power variables in the MAS004 submodel

The figures below show the absolute values of PR and PIN, respectively, that were obtained with the previous optimization.

Figure 36: absolute value of the dissipated power [W] with no Green Design considerations

Figure 37: absolute value of the input power [W] with no Green Design considerations

We now want to add the following Green Design constraints to the previous problem:

• max(|PIN|)<400W. This first constraint is intended to limit the power consumption of the motor.

• max(|PR|)<5W. This second constraint is here to limit the heat produced by the friction of the mass.

The result of this optimization now is:.

The figures below show the new evolutions obtained by specifying these two additional constraints related to Green Design aspects. As we can see, both constraints are satisfied, which ensures that the motor will be working in appropriate conditions and also that the heating due to the friction will be limited.

Figure 38: absolute value of the dissipated power [W] with Green Design considerations

Figure 39: absolute value of the input power [W] with Green Design considerations

We now want to see the consequences of the two constraints, both active, on the overall performance of the control:

Figure 40: cylinder displacement [m] comparisons with or without Green Design

As we can see in this figure, the behavior obtained is a compromise between the previously specified performance objective of the control strategy and the necessity to take green design aspects into account. The resulting performance decrease seems very limited compared to the gains achieved in terms of power consumption.

Remark on the cost of oscillations with respect to green design

In this example, one of the objectives was to minimize the oscillations around the duty cycle position. We will imagine that the oscillations observed with high values of k are said to be acceptable now with respect to the wanted precision (here their amplitude reaches 10% of the duty cycle position, as we can see in the figure above). In this case, the highest possible value of k , namely k = 1000 would have been chosen to get the fastest response. Enabling the calculation of the energy variables allows us to obtain the following curves:

Figure 41: energy lost due to oscillations around the duty cycle position

As we can see, the presence of functionally acceptable small oscillations caused by roughly optimized control strategies can lead to dramatic and costly energy losses, compared to smoother behaviors. For instance here, selecting k = 1000 leads to 30 times more energy consumed than with k = 290.963,the value obtained by minimizing the oscillations. Choosing k = 132.97 effectively leads to 40% additional energy saving, as specified by our second green design constraint. This illustrates well how control strategies can be very influential the on the overall energy consumption of the system.