Module9 Rous criterion

1 Stability judgment

Method1:

Step1:

Solve the characteristic equation and solve for all poles

Step2:

A is stable if no pole is to the right of the S-plane;

One of B is unstable on the right side of the S plane;

If c has poles on the imaginary axis (with pure imaginary roots), the response tends to be constant (real poles) or oscillating (conjugate complex poles), which is also unstable

★★★Method2: Rouse criterion

Rouse, table:

Write the characteristic equation coefficients in the first two lines, the even numbers are just right, and the odd numbers are not enough to complement 0 at the end

Example:

Step1: The coefficients are all positive and there are no items

Step2: Leraus table

Note: do not write decimals, fractions can be positive or negative

Special case:

① Common factors can be determined by row:

② The first column appears 0: use ε to replace the rous table, and finally take the limit ε approaches the infinitesimal integer (0.0001).

③ Integral behavior 0:

Step1: add a line of coefficients to construct an auxiliary equation, and the derivative is the coefficients of all 0 lines

Step2: judge the first column, if there is a change sign, it will be unstable

Step3: if there is no change sign, solve the auxiliary equation and work out the pole position, judge whether it is stable or not by the pole position (the teacher said it is unstable in the virtual axis)(technique: the auxiliary equation uses rouse criterion to judge whether it is stable or not, if the term is not stable)

The last element in the first column of the Rous table is equal to the constant term of the equation without subtracting.

About time brings simple calculation, but verification needs to be multiplied back. In the case of calculators in the exam, it cannot reflect the convenience of about points. I think not about points is conducive to checking

All 0 lines appear, indicating that the poles are on the imaginary axis

The notes