Practicum 5A

The goal of this practicum is to design a proportional control system that will provide your robot with the ability to track desired depths and meet transient response specifications.

You will use the simulator that you used in LabVIEW in practicum 1B to validate your control system.  Instead of controlling the simulated robot motor with a PWM signal (like you did in P1B), you will control the motor with a P control system. As you will find out below, this will all be integrated into the block diagram of your LabVIEW simulator.

Additionally, we will be making some final preparations for putting your robot in the WATER!

You will need your LabVIEW simulator (VDSim_PWM.vi) from the library you modified in Practicum 1C. If you do not have your VDSim_PWM.vi, you can use the library on Sakai located under “Resources/Practicums/LabView Code” and called "E79_F19_PostP1C.llb". Recall that the simulator allows a user to input the robot’s mass, buoyancy force, and drag coefficient as model parameters (see Figure 4.1). The simulator also allows a user to set the motor thrust PWM signal in real time to drive the robot up and down. 

REMINDER: When closing a VI, a window may pop up prompting you to save the VI and any lower level VI’s used within it, even if you didn’t make any changes. This will happen with any VI from a library that was just downloaded onto the computer, such as from Sakai or Google Drive. When that window pops up, just click the “save all” option, then it shouldn’t pop up again for that VI as long as it stays on the computer. If you need to re-download a library, then this window will pop up when closing the VI’s from that library, and you will need to save them once again so the window won't pop up anymore. 

In your block diagram, use a Subtract Function block, Multiply Function block, and Feedback Node to create a proportional (P) feedback control system that will allow you to track a desired position (i.e. depth). Recall that the key to P control is to set the control signal f(t) (i.e. throttle in this case) to be proportional to error:

See Fig. 5.2 below for an example of a LabVIEW block diagram of the P control system.  This is the same figure as the one shown in Figure 4.2.

Determine the natural frequency ωn and damping ratio ζ as functions of KP for the new closed loop system. To do this, you will need to start with your governing equation that you derived based on lumped element mechanical modeling.

In this case, fB is the buoyancy force that should cancel out the mg term. One way to determine the natural frequency and damping ratio is to substitute your control law into the governing equation, take the Laplace transform, and find the transfer function relating Z(s) to Zdes(s). The result should be a second order transfer function from which you can extract the natural frequency and damping ratio.

Predict the step response of the system for three different values of KP and fill in the “predicted” columns of the Table 5.1 on the next page. Calculate the percent overshoot and rise time as functions of natural frequency and damping ratio. Recall (from Module 2 videos 10 & 11) that the maximum percent overshoot MP can be calculated from as:

and the rise time tr as:

The arctangent can be calculated with Excel using the atan2 function, rather than the atan function. 

NOTE:  atan2 takes two arguments (atan2(x,y) where atan2(x,y) = atan(y/x)). Also the denominator (x) should be the negative term to get positive results. A negative numerator (y) goes clockwise on the radian circle.  

If you are using other software, be sure to use a version of the arctangent function that produces an output like that of atan2 so that the calculations will be correct.

Design a system, i.e. select a proportional control gain KP, that minimizes the rise time of the system while ensuring MP is less than 20%. Have an instructor check your gain and simulated step response.

Write your gain on your submission sheet. Plot the response and add it to your submission sheet.

In the final practicum of the semester, you will need your PCB to be fully functional: your thruster, pressure sensor and temperature sensor need to work simultaneously.

To make sure that all of these systems operate at the same time, dry test your robot at one of the dry test stations (using the instructions on Reference Page).  In addition to the previous dry test, be sure that the temperature curve on the VI changes when you heat up your thermistor.  If you have not yet added your thermistor to your umbilical, do so now using the umbilical assembly instructions.

If any part of your dry test doesn't work, then test the failing subsystem independently:

• To test your thruster, repeat the steps in Section 5 of Practicum 4B manual.  

• To test your pressure sensor, repeat Section 7 of Practicum 2D manual. 

• To test your thermistor, repeat Section 4.2 of Practicum 4A .  

If you find that your board is not operational and you aren't able to debug it, then notify a proctor or professor.  It is important to debug your PCB before deployments in the next few weeks.  Demonstrate to a proctor or professor that your thruster, pressure sensor, and temperature sensor are all operational at a dry test rig, including the ability to get the motor to flip directions in P control mode.