Thank you Walter! But, are you referring to a physical system. I am sorry if, my earlier creates the impression that I am involved in experiments.

I want to solve the problem in matlab/simulink...nothing more.

Regards,

Shashikant

|> What I mean by a single input is that we have one actuator connected to |> the cart. While all of the following can be sensed for feedback: |> position, velocity of cart; and angle and angular velocity of the inverted |> pendulum. |>

|> I approached the problem following way: |>

|> 1) Linearized the non-linear equations of motion. Assumed cart position |> and angle of the pendulum to be available for feedback. |>

|> 2) Got transfer function x/f and a/f where, f is force, x is cart displ |> and a is angle. |>

|> 3) Because of linearization we have got pole-zero cancellation by the |> system. Below are the TFs: |> 1.6 s^2 - 40 |> x/f= ----------------------------- zeros at -5 and 5 |> s^4 + 0.16 s^3 - 40 s^2 - 4 s |>

|> 4 s^2 |> a/f= ------------------------- zeros at 0, 0 |> s^4 + 0.16 s^3 - 40 s^2 - 4 s |>

|> poles at 0 -0.1 -6.3 6.3 |>

|> 4) Please observe that the system has non-minium phase zeros and has |> unstable poles. |>

|> 5) I am using cascaded controller with inner loop for pendulum and outer |> loop for cart position. |>

|> 6) I can stabilize the inner loop (i.e. pendulum angle) using lead and lag |> compensator with angle as feedback. |>

|> 7) I am also able to get stable open loop (for complete system) with |> feedback from both, angle and position. However, position feedback is |> making inner loop unstable (Note: inner loop is initially designed with |> feedback from angle only) |>

|> 8) I am using rltool/SISO tool in matlab for design purpose. |>

|> I am trying hard to get solution to the problem. This is my first exposure |> to control. Any input for any of the steps above would be of great help. |>

|> I checked controllability and observability in matlab. The system is |> controllable and observable (matlab returns rank=4 for both). I looked |> into the IEEE paper, most part of it is Greek and Latin for me. |>

|> Regards, |>

|> Shashikant |> (sarada at tamu.edu) |>

|>

|> On Fri, 14 Nov 2003, dave y. wrote: |>

|> |Tell you what, why don't you assume just a tiny bit of noise in the |> |system and then tell me you can do this. In the meantime, just to |> |experiment with the concept of open loop a bit, the next time you're |> |driving down the x-way, why don't you point the car straight down |> |the road, then take your hands off the wheel and close your eyes. |> |You can use the time remaining to contemplate the merits of your |> |position (at least in theory). |> | |> | |> |On 14 Nov 2003 10:08:12 +0100, Lars Imsland |> |wrote: |> | |> |>dave y. writes: |> |>

|> |>> Are you sure you've got the assignment described correctly? You have |> |>> to measure both cart position and pendulum angle to make this work, |> |>> and that represents a two input system. If, for example, you only |> |>> measure cart position and don't know what the pendulum angle is, you |> |>> don't have a chance of keeping it balanced. |> |>

|> |>It is definitely possible (at least in theory...) to control both cart |> |>position and stabilize upright position of the pendulumm using force |> |>on cart as (single) input. This is done in numerous published |> |>articles. One that springs to mind, is |> |>

|> |>@article {Ata99, |> |> AUTHOR = {Atassi, Ahmad N. and Khalil, Hassan K.}, |> |> TITLE = {A separation principle for the stabilization of a class of |> |> nonlinear systems}, |> |> JOURNAL = {IEEE Trans. Aut. Control}, |> |> FJOURNAL = {Institute of Electrical and Electronics Engineers. |> |> Transactions on Automatic Control}, |> |> VOLUME = {44}, |> |> YEAR = {1999}, |> |> NUMBER = {9}, |> |> PAGES = {1672--1687}, |> |> ISSN = {0018-9286}, |> |>} |> |>

|> |>> On Mon, 10 Nov 2003 23:53:47 -0600, Shashikant N Sarada |> |>> wrote: |> |>>

|> |>> >Hi |> |>> >I am working on a project on inverted pendulum. I have to control |pendulum |> |>> >rotation as well as cart position within given specifications. I am |using |> |>> >Matlab/Simulink and am designing as a single input-multiple output |system. |> |>> >I am able to control pendulum angle but not the cart position. Has |> |>> >anybody worked on similar problem? |> |>> >

|> |>> >Any input will be of great help! |> |>> >

|> |>> >Regards, |> |>> >

|> |>> >Shashikant |> | |> | |> | |>

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