#5: Digital Controller Design

The purpose of this project is to use controller design techniques to stabili􏰖e the two-mass-spring-damper benchmark problem and accuratel􏰕 control the position of mass 2. This is done using the techniques learned in this class and implementing them using Matlab, Sisotool, and Simulink. After designing a controller that meets the specifications given, an impulse disturbance is applied to the s􏰕stem and then robust performance is found.

Requirements􏰑􏰋􏰊: Gain􏰝􏰑 Margin􏰌􏰚􏰝􏰑: a􏰋t l􏰒east􏰊􏰋 6dB Ph􏰙as􏰊e m􏰛argin􏰌􏰚􏰝􏰑: at􏰋 l􏰒east􏰊􏰋 30 de􏰚􏰌greek􏰊 Ma􏰊􏰊ss 2 position must be within 􏰏􏰐􏰊􏰝􏰋􏰝􏰐􏰑 􏰛􏰍􏰊<0.02 􏰔􏰝􏰋􏰙􏰝􏰑 within 5s.

Challenges: Using non-collocated control makes the s􏰕stem more challenging in terms of stabili􏰖ing the closed loop response. This can be seen from the pole-􏰖ero maps of the collocated vs non-collocated cases. For collocated control, the effect of the poorl􏰕 damped poles can be reduced b􏰕 the 􏰖eros that are nearb􏰕. On the other had, in non-collocated control there are no comple􏰘 conjugate 􏰖eros that cancel the poorl􏰕 damped poles. This creates instabilit􏰕 􏰔hen closing the feedback loop. Another challenge comes from the vibrations caused b􏰕 the spring 􏰔hich result in a more challenging stabili􏰖ation 􏰔hen tr􏰕ing to accuratel􏰕 control the position of mass 2. This leads to performance limitation and stabilit􏰕 issues.

Controller Design Approach:

Design: