Root Locus - More General Approach
Topics
Root Locus and Characteristic Equation
Root Locus on Real Axis
Asymptotes for Infinite Zeros
What You Need to Know (and Don't Need to Know) about Root Locus
In the last class we saw a way to generate the root locus for any system. The roots of the characteristic equation of a system are the system's closed-loop poles. They determine the system response. If we let a parameter in the characteristic equation vary (usually K), we can make a table of closed-loop root locations as a function of K. If we let K vary from 0 to infinity, the root locations trace out the root locus. The path these roots take is called the root locus.
Any system's root locus can be generated by this brute-force method. There is a better, faster way that gives you a rough idea of the shape of the root locus with only a few, easy calculations. That method is described here.
Root Locus and Characteristic Equation
A generic control loop with a P-only controller:
The closed-loop transfer function is
So the characteristic equation is
Recall that the roots of this equation are the closed-loop poles, which determine the nature of the system response. As K varies, the roots of the equation vary. So for different values of K, the system response will be different.