# 0.6 Collocated / noncollocated control of 2dof rectilinear system

 Page 1 / 1
The objective of this lab is to implement a PD controller for a 2DOF system with an oscillatory mode. Students will gain a better understanding of the limitations of PD/PID control for higher order systems. Students will design, simulate, and implement a non-collocated controller with multiple feedback loops to acquire an acceptable response for the system. The controller will be designed and implemented in LabVIEW using the Simulation Module and Control Design Toolkit.

## Objectives

• Implement a PD controller for a 2DOF system with a oscillatory mode.
• Understand the limitations of PD/PID control for higher order systems.
• Design, simulate, and implement a noncollocated controller with multiple feedback loops to acquire an acceptable response forthe system.

## Pre-lab

• Consider the system shown below. Both mass carriages are loaded with four $0.5kg$ brass weights and the medium stiffness spring is connecting them. Derive the equations of motion for this system and rewrite them so that the control effort is $u\left(t\right)$ (DAC counts) and the respective positions, velocities, and accelerations are: ${x}_{1e}$ , ${\stackrel{.}{x}}_{1e}$ , ${\stackrel{..}{x}}_{1e}$ , ${x}_{2e}$ , ${\stackrel{.}{x}}_{2e}$ , ${\stackrel{..}{x}}_{2e}$
• From your EOM derive the appropriate transfer function numerator and denominator polynomials ${N}_{1}\left(s\right)$ , ${N}_{2}\left(s\right)$ , and $D\left(s\right)$ in the block diagram below:
• Using root locus techniques, find the rate feedback gain ${k}_{v}$ that provides satisfactory damping of the complex roots of the inner loop ${x}_{1}\left(s\right)/{R}^{*}\left(s\right)$ .
• With ${k}_{v}$ determined, you can now design for the system given by ${G}^{*}\left(s\right)$ in the block diagram. Design a notch filter, ${G}_{n}\left(s\right)={N}_{n}\left(s\right)/{D}_{n}\left(s\right)$ with two poles at $5.0Hz$ and two additional higher frequency poles at $8.0Hz$ , using $\zeta =\sqrt{2}/2$ for both poles. Place the zeros of ${G}_{n}\left(s\right)$ such that they cancel the oscillatory poles of ${G}^{*}\left(s\right)$ . Finally, normalize the notch filter transfer function to have unity DC gain.
• Write a LabVIEW VI that simulates this plant configuration with two differentcontrollers. Write your VI so it displays theresponse of both mass carriages.
• Collocated: Simulate your critically damped PD controller from Lab #3 where you are feeding back the position of the first carriage. Use the PD controller with the differentiator in theinner feedback loop. With these gains, what do you notice about the behavior of the second mass carriage? Remember to record thesegains so you can implement them in the lab. Now iteratively reduce the controller gains until you are able to achieve minimalovershoot for both carriages (try for less than $10%$ ) with as fast a response as possible. Again, don't forget to record thegains.
• Noncollocated: Simulate the controller you designed in steps 3 and 4 above. Find ${k}_{p}$ and ${k}_{d}$ to meet rise time and overshoot less than $0.5\mathrm{sec}$ and $10%$ , respectively.

## Lab procedure

• Configure the Model 210 plant for this experiment. Be sure to check that you are using the medium stiffness spring between thefirst and second carriages.
• Code the two controller structures (collocated PD and noncollocated PD + notch filter) into the LabVIEW control loop.Again, you can use a case selector to easily switch between the two algorithms.
• Implement the high-gain controller from step 5.1 of the pre-lab and perform a 3000 count step and save the plot. Notice thebehavior of the second mass carriage. Gently displace the carriages and note the relative stiffness of the servo system at the firstmass.
• Now implement the low-gain controller from step 5.1 and perform a 3000 count step and save the plot. Manually displace thefirst and second masses and note their relative stiffness. Are they generally more or less stiff than for the controller from the stepabove? How does the speed compare to the high-gain controller? How about the steady-state error?
• Now implement your noncollocated PD + notch filter controller from step 5b of the pre-lab and perform a 3000 count step; save theplot. From the response plot, determine the rise time and overshoot of the second mass carriage.

## 7.4 post-lab

• What was the predominant behavior of the second mass carriage with the highgain collocated PD controller? Can you give anexplanation for the difference in the responses of the two masses in terms of their closed-loop transfer functions?
• What differences did you observe in the responses between the low-gain and high-gain collocated PD controllers?
• What was the rise time and overshoot for your noncollocated PD + notch filter controller. Was this better or worse than youwere able to achieve with the collocated controllers? How did the steady-state error of the system for this controller compare tothat of the low-gain collocated PD controller?

anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Got questions? Join the online conversation and get instant answers!