Skip to content Skip to navigation

Connexions

You are here: Home » Content » Collocated / Noncollocated Control of 2DOF Rectilinear System

Navigation

Lenses

What is a lens?

Definition of a lens

Lenses

A lens is a custom view of Connexions content. You can think of it as a fancy kind of list that will let you see Connexions through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to Connexions materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual Connexions member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

This content is ...

Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
  • National Instruments display tagshide tags

    This module is included in aLens by: National InstrumentsAs a part of collection:"Control Systems Laboratory"

    Comments:

    "This course, ASE 170P at the Univ. of Texas at Austin, introduces students to fundamental control systems theory with emphasis on design and implementation. These labs focus on technical […]"

    Click the "National Instruments" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.

Collocated / Noncollocated Control of 2DOF Rectilinear System

Module by: Robert Bishop. E-mail the author

User rating (How does the rating system work?)
Ratings

Ratings allow you to judge the quality of modules. If other users have ranked the module then its average rating is displayed below. Ratings are calculated on a scale from one star (Poor) to five stars (Excellent).

How to rate a module

Hover over the star that corresponds to the rating you wish to assign. Click on the star to add your rating. Your rating should be based on the quality of the content. You must have an account and be logged in to rate content.

:
(0 ratings)

Summary: 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.

Note: Your browser may not currently support MathML. See our browser support page for additional details. You can always view the correct math in the PDF version.

Collocated / Noncollocated Control of 2DOF Rectilinear System

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 for the system.

Pre-Lab

  1. Consider the system shown below. Both mass carriages are loaded with four 0.5 k g 0.5 k g brass weights and the medium stiffness spring is connecting them.
    Figure 1: 2DOF Plant Configuration
    Figure 1 (plant.jpg)
    Derive the equations of motion for this system and rewrite them so that the control effort is u ⁡ t u⁡ t (DAC counts) and the respective positions, velocities, and accelerations are: x 1 e x 1 e , x . 1 e x . 1 e , x .. 1 e x .. 1 e , x 2 e x 2 e , x . 2 e x . 2 e , x .. 2 e x .. 2 e
  2. From your EOM derive the appropriate transfer function numerator and denominator polynomials N 1 s N 1 s , N 2 s N 2 s , and D ⁡ s D⁡ s in the block diagram below:
    Figure 2: PD + Notch Filter Control
    Figure 2 (model.jpg)
  3. Using root locus techniques, find the rate feedback gain k v k v that provides satisfactory damping of the complex roots of the inner loop x 1 s / R * s x 1 s / R * s .
  4. With k v k v determined, you can now design for the system given by G * s G * s in the block diagram. Design a notch filter, G n s = N n s / D n s G n s = N n s / D n s with two poles at 5.0 H z 5.0 H z and two additional higher frequency poles at 8.0 H z 8.0 H z , using ζ = 2 / 2 ζ= 2 /2 for both poles. Place the zeros of G n s G n s such that they cancel the oscillatory poles of G * s G * s . Finally, normalize the notch filter transfer function to have unity DC gain.
  5. Write a LabVIEW VI that simulates this plant configuration with two differentcontrollers. Write your VI so it displays the response of both mass carriages.
    1. 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 the inner feedback loop. With these gains, what do you notice about the behavior of the second mass carriage? Remember to record these gains so you can implement them in the lab. Now iteratively reduce the controller gains until you are able to achieve minimal overshoot for both carriages (try for less than 10 % 10% ) with as fast a response as possible. Again, don't forget to record the gains.
    2. Noncollocated: Simulate the controller you designed in steps 3 and 4 above. Find k p k p and k d k d to meet rise time and overshoot less than 0.5 sec 0.5sec and 10 % 10% , respectively.

Lab Procedure

  1. Configure the Model 210 plant for this experiment. Be sure to check that you are using the medium stiffness spring between the first and second carriages.
  2. 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.
  3. Implement the high-gain controller from step 5.1 of the pre-lab and perform a 3000 count step and save the plot. Notice the behavior of the second mass carriage. Gently displace the carriages and note the relative stiffness of the servo system at the first mass.
  4. Now implement the low-gain controller from step 5.1 and perform a 3000 count step and save the plot. Manually displace the first and second masses and note their relative stiffness. Are they generally more or less stiff than for the controller from the step above? How does the speed compare to the high-gain controller? How about the steady-state error?
  5. Now implement your noncollocated PD + notch filter controller from step 5b of the pre-lab and perform a 3000 count step; save the plot. From the response plot, determine the rise time and overshoot of the second mass carriage.

7.4 Post-Lab

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

Content actions

Give Feedback:

E-mail the module author | Rate module ( How does the rating system work?)

Rating system

Ratings

Ratings allow you to judge the quality of modules. If other users have ranked the module then its average rating is displayed below. Ratings are calculated on a scale from one star (Poor) to five stars (Excellent).

How to rate a module

Hover over the star that corresponds to the rating you wish to assign. Click on the star to add your rating. Your rating should be based on the quality of the content. You must have an account and be logged in to rate content.

(0 ratings)

Download:

Module PDF

Add module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections directly in Connexions. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need a Connexions account to use 'My Favorites'.

| A lens (?)

Definition of a lens

Lenses

A lens is a custom view of Connexions content. You can think of it as a fancy kind of list that will let you see Connexions through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to Connexions materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual Connexions member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks