EET 273 Spring 2017 – HW4

  1. You are designing a basic control system using only an ON/OFF controller. You select an upper setpoint of 1.5, and a lower setpoint of 0.5. Assume that it takes the system roughly 1 second to go from the LSP (lower setpoint) to the USP (upper setpoint), and vice versa. On the graph below, draw the expected output of the system, and the expected output of the controller. (Using a simulator may be helpful here.)

  1. The setpoint for a particular system is shown in the graph below. Draw an output graph that has the following performance characteristics: (note that the step input “steps” at the 1 second mark)

a)Zero steady-state error

b)Overshoot of 20%

c)Rise time (10-90%) of 1 second

d)Settling time (5% of final value) of 9 seconds

  1. In any automated (controlled) system, there is a process variable, a setpoint, and a manipulated variable.There is also something called a load, which influences how well the control system is able to maintain the setpoint. Provide a general description for a “load,” and then identify the load(s) in each of the followingmanually-controlled processes:

Example 1: Temperature control application

Example 2: Level control application

Example 3: Flow control application

Example 4: Temperature control application

  1. For the 4 systems in question #4, imagine you are a manual operator of these systems. In other words, YOU are the controller in an otherwise open-loop system.

In each of these examples, determine which way you should move the valve to counteract an increase in the process variable resulting from someindependent change in the process.

  1. You are installing a new buffer tank in a microchip factory that will be used to provide filtered, de-ionized water to process equipment throughout the factory.It has awater outlet that connects to the process equipment in the factory, and a water inlet that is controlled by a closed loop control system that you will design. When designing the control system, you decide to use a proportional controller, which will use the output from a liquid level meter, and adjust the input flow to the tank based on the current water level. When there is a large difference between the current water level and the setpoint, the flow rate will be high to fill the tank quickly, and when there is a small difference between the current water level and the setpoint, the flow rate will be low.

After the tank is installed, you fill the tank manually, and calibrate the level sensor. You set the setpoint for the tank to be 50%, or half full. You then test the level sensor calibration by slowing filling the tank from empty, and observing that the flow starts high, and then tapers off until the setpoint is reached, exactly what you’d expect from a proportional controller. You also notice that the final water level settles atprecisely the 50% mark, and you are quite pleased with yourself and your calibration skills.

Next, the factory starts running, and water starts exiting your new buffer tank through the outlet. Your proportional controller detects the drop in water level, and water starts flowing through the inlet to replace the water that is being used by the factory. You watch the system run for a while, and you notice that no matter how hard your proportional controller tries to add water back in, it never fully reaches the 50% setpoint that it did when the system was idle, instead there is a significant steady state error. How do you explain this behavior? What is the cause of this steady state error? What could you do to reduce the steady state error? Using this proportional controller, could you ever hope to reduce the error to zero?