None

This notebook contains material from cbe30338-2021; content is available on Github.

< 3.5 Practical Proportional (P) and Proportional-Integral (PI) Control | Contents | Tag Index | 3.7 Integral Windup and Bumpless Transfer >

3.6 Lab Assignment 3: Relay and PI Control

This lab assignment introduces the use of relay, proportional (P), and proportional-integral (PI) control for the Temperature Control Laboratory. In this assignment you will

1. implement and test a relay control for the dual heater/sensor system
2. implement and test a proportional-integral (PI) control algorithm for a single heater/sensor

3.6.1 Exercise 1. Relay (or On-Off) control

Create a notebook to implement a relay control for the Temperature Control Lab subject the following requirements:

• Simultaneous control of sensor temperatures T1 and T2.
• Use a tolerance value $d$ of 0.5 deg C.
• Set the minimum and maximum values of the heater to 0 and 100%, respectively. lab.P1 and lab.P2 should be left at their default values.
• Show the results of an experiment in which the setpoints are adjusted as follows:
  • SP1 is initially ambient temperature. SP1 increases to 35 deg at time t=20 and remains constant.
  • SP2 is initially ambient temperature. SP2 increases linearly to 45 deg C beginning at t=120 with the transition complete at time t=220.
  • Run the experiment until you reach a steady oscillation about the final operating point, and for no shorter than 600 sec.

Questions:

1. After the system has settled to a steady oscillation about the final operating point, what is the maximum deviation from the setpoints?
2. What is the approximate switching frequency of the manipulated variables?

%matplotlib inline
from tclab import TCLab, clock, Historian, Plotter

# insert code below

3.6.2 Exercise 2. Implementing a PI Controller

Create a notebook to implement PI for the Temperature Control Lab.

• Using the simulation mode, create an implementaton of PI control and, by trail and error, find values for Kp and Ki, that provide a fast and accurate acquisitioni of the desired setpoint.

• Show the results of an experiment in which the setpoints are adjusted as follows:

  • SP1 is initially ambient temperature. SP1 increases linearly to 45 deg C beginning at t=20 with the transition complete at time t=120.
  • Run the experiment until you reach a steady oscillation about the final operating point, and for no shorter than 600 sec.

Questions:

1. After the system has settled to a steady oscillation about the final operating point, what is the maximum deviation from the setpoints?

< 3.5 Practical Proportional (P) and Proportional-Integral (PI) Control | Contents | Tag Index | 3.7 Integral Windup and Bumpless Transfer >