EE4612 Control System Design Assignment 3

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 (N-m-sec²/rad) is the moment of inertia of the load, B (N-m-sec/rad) is the load friction, K_t (N-m/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:

1. The first page should show the name of the work, course code, instructors name, the team number and the participants.
2. Keep separated each section of this report by means of one introductory page. Remember that this report has three different sections.  Please number all pages of the report.
3. Divide each section by steps. Write the text of what each step requests.  Then place the required information as an answer to that request.
4. Use only one language for your report, either English or Spanish. If your selection is Spanish, you have to know that you have to translate all technical terms.  Use the MS Word speller if you notice your sentences do not sound properly.  Avoid repeating the same term many times.  Use the MS Word Thesaurus to find synonymous terms.
5. Use only one font stile. Keep the same size and space among sentences through the entire document, including formulas.  Use letter sizes like 10, 11 or 12.  Consider using single space among lines to reduce the number of pages of the report to a minimum.
6. Try to keep information related to a specific section in only one page. Avoid splitting this information in two pages.
7. If you write paragraphs, use MS Word to align the text to left and right margins. This alignment creates a clean look along the left and right side of the page.  Text for formulas should be placed at the center.
8. Remember to use a simple and direct language. You may want to facilitate as much as possible the understanding of what you are doing to an audience not necessarily expert in the topic, but which would appreciate a lot your effort in doing so.

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 closed-loop 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:

1. Table showing the iteration process to achieve the M_p specifications (3 to 10 iterations).
2. Include the s - domain open-loop transfer function of the P controller & system plant.
3. Root locus plot for the open loop system. Show the position of the closed loop poles, damping ratio

? and the frequency ?_n.

1. Include the s - domain closed-loop transfer function of the P controller & system plant.
2. Time plot of the output due to a step input applied to the closed-loop system. Show the values of t_r, t_p, M_p, and t_s.
3. Time plot of the error due to a unit ramp input applied to the closed-loop system. Show the value of the steady state error.

 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 P-I-D gains.

Step # 3: Include:

1. Include the s - domain transfer function of your designed controller in filter and industrial formats.
2. Include the s - domain open-loop transfer function of the PD controller & system plant.
3. Root locus plot for your open-loop system. Show the position of the closed loop poles, damping ratio ? and the frequency ?_n.
4. Include the s - domain closed-loop transfer function of the PD controller & system plant.
5. Time plot of the output due to a step input applied to your closed-loop system. Show the values of t_r, t_p, M_p, and t_s.  You must include a time simulation of 2 times the required settling time (t_s).
6. Time plot of the error due to a ramp input applied to your closed-loop system. Show the value of steady state error.  For the PID controller design you must include a ramp input time simulation of 2 times the integral time (t_i). 

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 closed-loop 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

Table B: Plant Parameters

Table C: Controller Parameters in Filter Format

Table D: Controller Parameters in Industrial Format

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:

A tolerance of ± 5% will be accepted for the t_s specification, and a ± 0.005 (0.5%) for M_p