How to build a hodograph

Construction of hodographs Mikhailov with the software package "Mathcad" is necessary in order to obtain a simple and intuitive tool for solving problems on the stability of automatic control systems. The Mikhailov criterion of stability – a characteristic that is a prerequisite for the functionality of any industrial robot or manipulator.

Instruction

1. Having a data set of complex frequency domain functions, go directly to the construction of a hodograph using the mathematical package "MathCad". Select real and imaginary part. Substitute numerical values in the complex frequency function.
2. In the top menu select: "New..." – "Blank document". Here you'll shape the program to build the Mikhailov hodograph.
3. Set the resolution of the hodograph range of numbers of index i.
4. Define the studied range, indicate the frequency step. Take action based on the value of the index i. As a rule, in practical calculations, the highest value of frequency does not exceed the number 1000.
5. Specify the numerical values of real and imaginary parts of the original characteristic equation that you calculated previously.
6. Computationally, get the array of values of the frequency, as well as the data of the real and imaginary parts.
7. Now, having obtained arrays of values, start building Mikhailov hodograph. Select in the package "MathCad" the built-in function "Tools charts". Then click the option "Decerto graph. Here you must define the identifiers of the axes. Corresponds to the x-axis of the real part? Meets the y-axis the imaginary part or not?
8. In the submenu of the "Format...", make the chart options. As a result, you will get the hodograph of a complex frequency function.
9. Use the "Trace..." So you determine in the corresponding trace window, absolutely accurate values of the hodograph, choosing any point in the calculated arrays.