EE 4612  Control System Design
Assignment 3: Design 2  75 points
Situation
Two robots shown are cooperating with each other to manipulate a log shaft prior to inserting it into the hole in the block resting on the table. Long part insertion is a good example of a task that can benefit from cooperative control. The control system of one robot joint is described by the equation:
J?’’ + B?’ = K_{t }e
where J (Nmsec²/rad) is the moment of inertia of the load, B (Nmsec/rad) is the load friction, K_{t }(Nm/volt) is the motor constant, ? is the load angular position (rads), and e is the input voltage of the motor (volts). The feedback gain can be assumed to have a value of 1.
Two Cooperating Robots Inserting a Shaft
Requirements
You are required to improve the performance of the system you are given. There are two cases:
Case #1: Improve the system performance based on a new maximum overshoot (M_{p}) and settling time (t_{s}) specifications. Implement this change using both an analog and a digital controller.
Case #2: Improve the system performance based on a new maximum overshoot (M_{p}), settling time (t_{s}) and steady state error specifications to a ramp test input (e_{ss}?_{ramp}). Implement this change using both an analog and a digital controller.
(You must place the information of your design specifications, as well as the constraints in this section as part of this report)
The numerical information about the parameters (B, J and K_{t}) and performance specifications (M_{p}, t_{s}, and e_{ss}?_{ramp}) for each design team is included in a table two pages ahead. Other design criteria are based on the size of the controller you choose. An Interim Report is required by May 13, 2021.
DESIGN REPORT FORMAT for Design Assignment # 2
Before starting to write your report, read these instructions. They will help you show your work in a professional manner:
Follow these indications:
Section # 1: Statement of the Problem
Step # 1: Explain the situation and requirements as included in the first page of this report. Then explain how to go from the differential equation that describes the process dynamics, to s  domain plant model.
Step # 2: Attempt closedloop compensation by using a P controller with unity feedback (after doing this you will have sufficient information to justify any change in your control strategy). Use the s  domain plant model. Include:
? and the frequency ?_{n}.
Section # 2: Analog PD Controller Design
Step # 1: Display the controller formulas in both filter and industrial formats, and the equations that relate them.
Step # 2: Display a table showing the iteration process to achieve the M_{p} and t_{s} results. After this show the corresponding final values of the PID gains.
Step # 3: Include:
Step # 4: Implement the controller. Use only filter format for the analog controllers.
Section # 3: Analog PID Controller Design
Repeat all steps of Section # 2, but now taking in consideration the improvement of the steady state error specifications. For the time plot of the error due to a ramp input applied to your closedloop system, use a time scale as least twice the value of the integral time (ti).
Section # 4: Data Tables
Step # 1: Fill the tables with all your designs information:
Table A: Design Parameters
Design Parameter 
s  Domain 

P Control 
PD Control 
PID Control 

t_{r} 

tp 

M_{p} 

ts 

ess?ramp 
Table B: Plant Parameters
Parameter 
s  Domain 
Gain 

Poles 

Zeroes 
Table C: Controller Parameters in Filter Format
Controller Parameter 
s  Domain 

P Control 
PD Control 
PID Control 

Gain 

Poles 

Zeroes 
Table D: Controller Parameters in Industrial Format
Controller Parameter 
s  Domain 

P Control 
PD Control 
PID Control 

K_{p} 

K_{d} 

K_{i} 
Section # 5: Conclusions
Develop your conclusions comparing advantages and weaknesses in achieving the desired specifications in your designs as a result of the use of the P, PD and PID compensation.
Section # 6: References
Include a list of references that have served you in the preparation of this report.
Section # 7: Interim Report
Include the final Interim Report with all approved controllers in this section.
Section # 8: Evaluation Sheet
Include the Evaluation Sheet for the Design Assignment # 3 here.
DESIGN TEAMS
Design Team 1: Edwin Rodriguez & Oskar Thurin
Design Team 1a: Natalia Álvarez
Design Team 2: Joel Aquiles & Sheilly Torres
Design Team 2a: Stacey Defillo
Design Team 3: Josué Figueroa & Jose Rodriguez Design Team 4: Christian Gutiérrez & Raul Zayas
DESIGN TEAMS VALUES
Each Design Team will have different plant parameters and design specifications as described below:
Team 
B (Nms/rad) 
J (Nms²/rad) 
K (Nm/volts) 
t_{s} 
M_{p} 
ess?ramp 
1 
50 
10 
20 
0.8 sec 
10% 
0% 
1a 
50 
10 
20 
0.8 sec 
15% 
0% 
2 
20 
5 
5 
1.0 sec 
10% 
0% 
2a 
20 
5 
5 
1.0 sec 
15% 
0% 
3 
40 
5 
10 
0.5 sec 
15% 
0% 
4 
40 
5 
20 
0.5 sec 
10% 
0% 
A tolerance of ± 5% will be accepted for the t_{s} specification, and a ± 0.005 (0.5%) for M_{p}
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