1st Order Nonlinear equation - Control

In summary, the conversation is about a first order nonlinear equation that describes the speed of an electrical motor during start-up. The equation includes constants and variables such as time and motor speed. The speaker is looking for a way to solve the equation analytically and has tried various methods with no success. Another person mentions that there is a closed form solution using Maple, but it involves complicated Airy functions.
  • #1
danielgdls
1
0
Hello everybody,


I've come cross the following first order nonlinear equation when trying to solve
for the speed of an electrical motor at any given time t during motor start.

y'=-(ay^2)+bx+c ; y(0)=0 ; a, b and c are constants; y=motor speed; x= time

The Motor Starter uses a linear Torque control and the load exhibits a quadratic
dependence of the motor speed. I am sure there is a possibility of solving this analitically.
I've tried changing variables, reduction and using substitution with no success. Maybe I
am missing something or haven't found the right substitution...Any ideas? I'll appreciate
any help on this.

Daniel.
 
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  • #2
I plugged it into Maple, and there is indeed a closed form solution. But it's a complicated mess of Airy functions, so I don't think there's a "silver bullet" substitution that's going to make this nice for you.
 

FAQ: 1st Order Nonlinear equation - Control

What is a 1st order nonlinear equation in control?

A 1st order nonlinear equation in control refers to a type of mathematical model that describes the behavior of a system or process in which the output is dependent on the input, but the relationship between the two is nonlinear. This means that the output does not change in a proportional manner to the input and there may be complex relationships between the two variables.

How is a 1st order nonlinear equation different from a 1st order linear equation?

A 1st order linear equation describes a system or process in which the output changes in a proportional manner to the input. This means that the relationship between the two variables is linear and can be represented by a straight line on a graph. In contrast, a 1st order nonlinear equation does not have a linear relationship between the input and output, and may require more complex mathematical models to accurately describe the system.

What are some real-world applications of 1st order nonlinear equations in control?

1st order nonlinear equations are commonly used in control systems to model and regulate the behavior of complex systems such as chemical processes, biological systems, and electrical circuits. They can also be used in fields such as economics, ecology, and engineering to describe and predict the behavior of various systems.

How are 1st order nonlinear equations solved?

Solving 1st order nonlinear equations can be a complex process and often requires the use of numerical methods or computer simulations. In some cases, it may be possible to find an analytical solution using techniques such as integration or substitution. However, in most cases, the equations are solved using numerical methods such as Newton's method or the Runge-Kutta method.

What are the limitations of using 1st order nonlinear equations in control?

While 1st order nonlinear equations can accurately describe the behavior of many systems, they have some limitations. For example, they may not accurately represent systems with time-varying inputs or those that exhibit chaotic behavior. In addition, the complexity of solving these equations can make it challenging to use them in real-time control systems.

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