Design Project Ece382

Design Project ECE382/ME482

DP7.8

8/8/05

OBJECTIVE:

The first objective of the project was to obtain a steady state error that was equal to zero. With this objective achieved, we then compared the percent overshoot and rise time. The main objective aimed to have an overshoot of fewer than 6% and having the smallest rise time possible.

INTRODUCTION

The overall system consisted of a closed-loop feedback system. The system represents a robotic arm actuated at the elbow joint. The overall system is represented as a block diagram below.

Procedure

To begin, we assumed that Gp(s) was equal to 1 and our gain, K, was also equal to 1. With this assumption, we found the transfer function to be:

OVERALL TRANSFER FUNCTION WHEN Gp(s)=1:

T = GpG1G2/[1+G1G2H]

0.3009 s^3 + 2.708 s^2 + 8.424 s + 6.017

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s^4 + 12 s^3 + 52 s^2 + 86 s + 6

With the aid of Matlab, we then created a Root-locus plot to find the values of gain, K.

PLOT OF ROOT LOCUS FOR K>=0;

STEADY STATE ERROR:

We needed to select the input controller Gp so we could get a steady state error equal to zero for a step input so this required T(0) = 1.

ess = Lim as s->0 of s(E) where E = R - Y = R[1 - T] where T is the system transfer function. Therefore our calculations showed that we needed to set Gp = 0.1504 to get a zero steady state error.

TRANSIENT RESPONSE:

The project required us to plot y(t) for K = 1, 1.5 and 2.85. These are shown on the next three pages.

TRANSIENT RESPONSE WITH K = 1:

TRANSIENT RESPONSE WITH K = 1.5: