User:DukeEgr93/Lab 7
This page provides guidance for Labs 6 and 7 for Controls in Summer 2020. It assumes knowledge of SISOtool and Root Locus design as given by User:DukeEgr93/RL Example and Chapter 9 of Nise 8e.
Introduction
For this part of the lab, you will end up designing and simulating a PD controller for a marginally stable plant and a lead controller for an inherently unstable plant. The plants themselves will be built using passive elements and operational amplifiers. In your report, you will be discussing how well your designs satisfy the criteria given for the system based on both the mathematically simulated results and the circuit simulations.
Building The Plants
The plants for this lab will be second plants with two poles and no zeros. The first plant will be marginally stable with poles at $$\pm j2$$ and the second will be unstable with poles at $$\pm 2$$/. The gain in each case will be 4, meaning:
These transfer functions are easy enough to simulate in MATLAB, but you will also be building circuits to simulate them. Unstable circuits generally require some kind of amplification and some kind of feedback. For this lab, the plant will consist of two pure integrators cascaded together (creating a double pole at the origin) along with a difference amplifier (to provide a feedback loop and amplification). There will also be a voltage controlled voltage source to adjust the sign on $$K$$.
