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Until now, I have come this far:

The differential equation equals the particular part, and the homogene part:

[tex]x = x_p + x_h[/tex]

The homogene part equals the differential equation when set to zero

[tex]

\frac{d^2x}{dt^2} + \frac{K_p}{A} \times \frac{dx}{dt} + \frac{K_p}{A \times T_i} \times x(t) = 0

[/tex]

Converting the derviates into lambda, and inserting values for constants it turns into this:

[tex]A = 1, K_p = 0,02, T_i = 200[/tex]

[tex]

\lambda^2 + \frac{K_p}{A} \times \lambda + \frac{K_p}{A \times T_i} = 0

[/tex]

Solving the equation with regard to lambda, I get:

[tex]Lambda_1 = Lambda_2 = -0.01[/tex]

It is now time to assume the form of the solution of the homogene part, which should be like this:

[tex]C_1 \times e^{\lambda t} + C_2 \times t \times e^{\lambda t}[/tex]

According to what I have learned, I have to set the whole original equation = starting condition when time = 0 to find them.

Starting condition: [itex]x(0) = 1[/itex]

Consequently:

[tex]x(0) = 1 = x_p + x_h[/tex]

Inserting values for particular and homogene part

(particular part = 1) (t = 0)

[tex]x(0) = 1 = 1 + C_1 \times e^{\lambda 0} + C_2 \times 0 \times e^{\lambda 0}[/tex]

When trying to solve this equation with regards to C1 and C2, I get that C2 is canceled out when multiplying with T = 0.

The real values of C1 and C2 is found when solving the derivate of the start condition with regards to C1 and C2. The first one is to find the relation between them (example: c1 = -c2 or similar)

Can someone help me out here?

The differential equation equals the particular part, and the homogene part:

[tex]x = x_p + x_h[/tex]

The homogene part equals the differential equation when set to zero

[tex]

\frac{d^2x}{dt^2} + \frac{K_p}{A} \times \frac{dx}{dt} + \frac{K_p}{A \times T_i} \times x(t) = 0

[/tex]

Converting the derviates into lambda, and inserting values for constants it turns into this:

[tex]A = 1, K_p = 0,02, T_i = 200[/tex]

[tex]

\lambda^2 + \frac{K_p}{A} \times \lambda + \frac{K_p}{A \times T_i} = 0

[/tex]

Solving the equation with regard to lambda, I get:

[tex]Lambda_1 = Lambda_2 = -0.01[/tex]

It is now time to assume the form of the solution of the homogene part, which should be like this:

[tex]C_1 \times e^{\lambda t} + C_2 \times t \times e^{\lambda t}[/tex]

**C1 and C2 are the constants I have trouble finding**According to what I have learned, I have to set the whole original equation = starting condition when time = 0 to find them.

Starting condition: [itex]x(0) = 1[/itex]

Consequently:

[tex]x(0) = 1 = x_p + x_h[/tex]

Inserting values for particular and homogene part

(particular part = 1) (t = 0)

[tex]x(0) = 1 = 1 + C_1 \times e^{\lambda 0} + C_2 \times 0 \times e^{\lambda 0}[/tex]

When trying to solve this equation with regards to C1 and C2, I get that C2 is canceled out when multiplying with T = 0.

The real values of C1 and C2 is found when solving the derivate of the start condition with regards to C1 and C2. The first one is to find the relation between them (example: c1 = -c2 or similar)

Can someone help me out here?

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