One of the treatments for Parkinson’s disease in some patients is Deep Brain Stimulation (DBS) (Davidson, 2012). In DBS a set of electrodes is surgically implanted and a vibrating current is applied to the subthalamic nucleus, also known as a brain pacemaker. Root locus has been used on a linearized model of the system to help explain the dynamics of DBS. The DBS model can be obtained by substituting

in the unity-feedback diagram of Figure P8.3.

a. Make a sketch of the resulting root locus as a function of k and find the break-in point and its corresponding value of gain.

b. Find the range of k for closed-loop stability in terms of b.

c. Find the frequency of oscillation when the system has closed-loop poles on the jω axis.

Transcribed Image Text:

ks G(s) = (s – b) 6> 0) %3D