Strange behavior: gain bocks which integrate step inputs

Hi all!

I have the following problem. I have three signals which pass into some Compare to constant block. The Compare to constant blocks clearly output a boolean value. Let's call these boolean variable A,B and C. Now, depending on the values of A,B,C I should select an appropriate input of a 4-port switch. Therefore, I need to a function that takes the values of A,B,C as input, and which output an integer between 1 and 4.

This is my solution. I first convert A,B, C in integer through the well-known formula y = A*4+B*2+C*1, where A is the MSB and C is the LSB. Such formula is implemented through 3 Gain Blocks (with gains 4,2 and 1 respectively) blocks and a sum block with three inputs. Then the value of y is used as input of a look-up table which maps y into {1,2,3,4}, depending on which input of the switch I need.

However, I have the problem that the gain blocks "integrate" the boolean values. For instance, as I have a neat step at the input of the gain block (i.e. something like that _| ), but the output looks like a ramp (i.e. something like that _/). This leads to unexpected behavior of the system. I have tried to reduce the fundamental step size (I am using a fixed-step solver), and the situation gets a bit better, but not completely solved. How can I solve this?

Thanks! :)

Answer 1

[Doug Eastman]

The issue with the lines being slanted is due to the fact that Simulink sees these signals as continuous so it will connect the fixed-step discrete points with lines rather than stair-steps. The slopes don't actually matter though since the simulation is not being executed between the two points. If you would like to see the stair-step you could discretize the signals using a Zero-order Hold block with the same sample rate as your base step size.

Alternatively you could use a variable-step solver with zero crossing detection so that you will get a time step at the exact moment of transition for each of the compare to constant blocks. That will also product a clean vertical edge with a continuous signal.