Simulink Control Design™ - MathWorks

How the Software Treats Loop Openings

Simulink Control Design software linearizes models using a block-by-block approach. The

software individually linearizes each block in your Simulink model and produces the

linearization of the overall system by combining the individual block linearizations. For

more information, see “Exact Linearization Algorithm” on page 2-218.

To obtain an open-loop transfer function from a model, you specify a loop opening. Loop

openings affect only how the software recombines the individual linearized blocks. In

other words, the software ignores loop openings when determining the input signal levels

for each block, which affects how nonlinear blocks are linearized.

For example, in the following model, to compute the response from e 2 to y 2 without the

effects of the outer loop, you open the outer loop by placing a loop opening analysis point

at y 1.

k 2

e (^2) u 2 y 2
g 2 g 1

r e^1

k 1

y 1

Here, k 1 , k 2 , g 1 , and g 2 are nonlinear blocks.

The software linearizes each individual block at the specified operating point, creating the

linearized blocks K 1 , K 2 , G 1 , and G 2. At this stage, the software does not break the signal

flow at y 1. Therefore, the block linearizations include the effects of the inner-loop and

outer-loop feedback signals.

To compute the transfer function from e 2 to y 2 , the software enforces the loop opening at

y 1 , injects an input signal at e 2 , and measures the output at y 2.

2 Linearization