Designing a control system for a heating system

[Aeroeri25]

Homework Statement

F = Fahrenheit
A particular temperature control system uses electrical heaters, exterior thermal insulation and a thermostat for maintaining the temperature at 170 F +/- 1 F. The thermostat turns the heater on when the temperature drops to 169 F and on at 171 F. Heater consists of a 3 ohm resistor supplied by a 28 volt source (1 watt = 3.4 Btu/hr). The heat capacity of the device is 0.1 But/F. Heat is lost to the environment by conductive heat transfer, the constant of the process being 3.6 But/F/hr.

(1)Prepare a block diagram of the control system.
(2) Sketch the variation of the device temp vs. time through a complete control cycle, for environmental temperature of 70 and -20 F, taking the initial temperature to be that of the environment.
(3) What is the lowest environmental temperature for which the desired temperature can be maintained?

Homework Equations

This is where I am having problems. None are given, maybe they were in the previous week, but i was out. I tried asking the TA but to no avail.

The Attempt at a Solution

I drew a block diagram similar to the attached picture.
Parts two and three aren't that hard if I knew the transfer functions in part 1.
When i solve for T(s) i get this:

T(s) = (Q(s)C(s)T_desired)/(1+Q(s)C(s)T_desired)

but my problem is finding Q(s) and C(s).

Any help on how to get started?

 

[KataKoniK]

Thank you for your post. I am a scientist and I would be happy to assist you with your questions about the temperature control system.

For part 1, the block diagram you have drawn is a good start. To complete it, you will need to include the transfer functions for the heater and the heat loss to the environment. The transfer function for the heater can be calculated using Ohm's law (V=IR) and the given information about the resistor and voltage source. The transfer function for heat loss can be calculated using the given information about the constant of the process and the heat capacity of the device.

For part 2, to sketch the variation of the device temperature vs. time, you will need to use the transfer function you have calculated in part 1. You can use this transfer function to plot the response of the system to different environmental temperatures. This will show you how the temperature of the device changes over time for different starting temperatures.

For part 3, to determine the lowest environmental temperature for which the desired temperature can be maintained, you will need to look at the transfer function again. This time, you will need to set the desired temperature to 170 F and solve for the environmental temperature. This will give you the lowest temperature at which the system can maintain the desired temperature.

I hope this helps you get started on your homework. If you have any further questions, please don't hesitate to ask. Good luck with your studies!

 

[Mene]

it is important to approach this problem with a systematic and analytical mindset. Here are some steps you can take to design a control system for this heating system:

1. Clearly define the problem and understand the requirements: In this case, the problem is to design a control system for a heating system that can maintain a temperature of 170 F +/- 1 F. The system should also be able to turn on the heater when the temperature drops to 169 F and off when it reaches 171 F. It is important to understand these requirements before proceeding with the design.

2. Identify the components and their functions: Based on the given information, the main components of the heating system are the electrical heater, exterior thermal insulation, and the thermostat. The heater is responsible for generating heat, the insulation helps in minimizing heat loss, and the thermostat controls the on/off operation of the heater.

3. Prepare a block diagram: As you have already done, a block diagram is a useful tool to visualize the components and their interactions in a control system. It can also help in identifying the input, output, and feedback signals.

4. Determine the transfer functions: The transfer function is a mathematical representation of how the output of a system responds to the input. In this case, you will need to determine the transfer function for the heater, the insulation, and the thermostat. This can be done by using the fundamental laws of thermodynamics and heat transfer principles.

5. Analyze the system: Once you have the transfer functions, you can analyze the system to understand its behavior. This can include stability analysis, frequency response analysis, and transient response analysis.

6. Design the controller: The controller is the key component that will ensure that the system maintains the desired temperature. Based on the analysis, you can design a suitable controller that will take into account the system dynamics, the desired temperature, and the environmental temperature.

7. Simulate and test the system: Before implementing the control system, it is important to simulate and test it to ensure that it meets the requirements. This can be done using software tools such as MATLAB or Simulink.

8. Implement and monitor the system: Once the control system is designed and tested, it can be implemented in the actual heating system. It is important to continuously monitor the system and make any necessary adjustments to ensure that it is functioning properly.

In summary, designing a control system for a heating system requires a thorough understanding of the problem, the components