State Space Control for the Pendulum-Cart System: A short tutorial on using Matlab® and Simulink®
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- เผยแพร่เมื่อ 6 ก.พ. 2018
- This is a short tutorial on using Matlab® and Simulink® in control engineering. Specifically, it is about designing and testing of a (digital) state feedback controller including a state observer for a simplified model of the so-called pendulum-cart system.
This tutorial can be seen as a supplement to the exercises of the lecture “CAE in der Regelungstechnik” by LRS at TUK.
By: Alen Turnwald
Note that it is presumed that you are already familiar with the concepts of linear control and systems in state space.
For the preliminaries, please refer to the corresponding lectures and literature.
The completeness and correctness of the statements in the video are NOT guaranteed.
-- Edit:
- At 9:43: B has to be changed to C after copying! (This ist done during a cut.)
The simulation is also available at:
github.com/turnwald/CAE_Exercise
Homepage: www.eit.uni-kl.de/liu/
![Linear Quadratic Regulator (LQR) Control for the Inverted Pendulum on a Cart [Control Bootcamp]](http://i.ytimg.com/vi/1_UobILf3cc/mqdefault.jpg)
For Matlab version R2019b, the subsystem of the simulink model needs to be as such:
input gain must be Matrix(K*u) : should read B*u
output gain must be Matrix(u*K) : should read u*B
and feedback gain must be Matrix(K*u) (u vector) : should read A*uvec
I spent hours bashing my head against the wall on this. Despite having taken a systems class, I am mostly clueless when it comes to reading these diagrams, but I kind of understand it. I just need to spend more time with it.
It's really useful. Thank you. And I also made some other adjustments , then the model can run correctly.
Bro.... Thank you!!!
Lmao, a life saver right here
Bro, you literally saved my life lol
Can people actually like and up his comment so everyone could see this update
Thank you for the tutorial.. This is the only video that I could find in youtube that explains a state feedback and observer design construction in a clear and concise manner. Please do keep them coming...
the animation and your LaTeX document look so nice! well done with this project
For new versions of Matlab (2018b), the block of A matrix must be configured like Matrix (K*u) (u vector). Nice Video EIT!
Thank a lot! Could you explain to me the difference between 'Matrix (K*u)' and 'Matrix (K*u) (u vector)'?
thank you sir! your vedio helps me a lot
YOU ARE SO GREAT! PROFESSOR . a student from china
really helpful! thank u so much
Thank you very much. Very usefull
thank you so much !
Love you sir ❤ from India
Could you talk about how to create the animation model?
Peisham has the same question I do. How did you create the inverted pendulum animation in Figure 1? I need to learn how to do that.
Sir how can we consider the exogenous (reference +disturbance ) input in the state-space model in Simulink?
How do you control the pendulum angle to not rotate beyond certain angle (say 5 degree)?
Hello sir, can you please share the link of that document you used for the pendulum analysis. Thank you
thank you
Thank you sir! Can I obtain a procedure for deriving the equations of motion for that system?
Hallo Allen, this is very insightful, thanks. I already sent you a message via Research gate.
sir, I am trying to design a MPC controller for active suspension system by using the MATLAB script and simulink rather than using the in-built MPC block available in the matlab.. can you please make a video to how to do it... or atleast guide me somehow!! PLEASE.. thank you.
Hey can you please tell me where can I read about those dynamic equations
how do you make the animation? thanks for the video !!
Can anyone tell me, how to combine the Matlab control with an Adams subsystem?
How you create the animation model?
how to get A, B C D matrix of linearization formula?
How do you choose the sampling time for the zero-order-hold ? Is it the lowest sampling time of the sensors or some average sampling time of the sensors and I interpolate the sensor values which have a lower sampling time ?
This is the sample time you choose for you controller depending on your requirements and rsources
hello when ever i try to type the observer matrix i get an error that it is not defined i need a solution for that if anyone can you help me please.!!
Hey you have taken in simulink model x0 is a variable but in my Matlab model it was not taking so help me
Hello, at 14.57 min, you said a term 'input of word', what you mean by that?
What is g_q variable in Plant/constant1 block? I get the error for invalid setting in block. I set it to 1 and my simulatiion ran slowly.
A warning i am receiving is "Matching "Goto" for "From" 'Plant/output/From2' not found"
Hi,
g_q is the input matrix. Set it to [1;0]. Aslo, I added a newer version of the simulation to GitHub that does not contain g_q.
DANKE !!
Can u explain the plant ?how can I do it,?
Please 🙏
Do you have a project to furuta pedulum ?
At 27:12, when the observer feedback is created, the author writes "-Ob" into the Gain-Block. But shouldn't it be the transponsed (Ob^T)? At least according to the literature I found...
Thank you!
can u explain more please ??? i have problem with this part
I am wondering, how we can control inverted Pendulum, juts on the knowledge based on position x?.
As output of plant is just position, which Is used in observer, to estimate states.
This implies that there is no need of angle measurement for balancing, but we know that for balancing robots and pendulums, it is necessary to have potentiometer or MEMS to measure angle of pendulum..
I believe, if we have just theta in output, means C=[ 0 0 1 0], then self balancing can be achieved, knowledge of position is not a must have thing in balancing, but theta is must..
Thank you very much.
may I ask about this simulation? via email or etc, thank you
@@abeltamikasetiarini2469 Of course
@@leonardorocabejar7307 what your email? Thank you
Great
Hey I'm getting ports or dimensions error in subsystem while I run the x0 for integrator
What should I do?
Watch Chipset's comment and like it so people can see
How do replace it with a plant at 29:49
Hi I just start learning about state space and staff so I tried to follow your video and I have a problem in the signal that come out of the observer, it's doesn't look like the one that come from the original system at all and i don't know why, I tried to change the des_pole accurse from *1 to 0.1 to change the simple time if I remember right but it's barely did some thing
can you help me?
Hi, the problem is that Cd is a Row vector, not like C as a column vector, thus in observor bolck, the output should be Cd * uvec, and also the ob feedback gain should be u*-Ob and puls a transpose bolck. This is because x_dot should be a 4 row vector.
why he is using the gain matrix before the output 9:40
Hi, why does the cart move in opposite direction first then in the correct direction?
This effect is called non-minimal phase behaviour
@@rptulrs2023 Thanks, this behaviour is also visible in some Boston Dynamics robots as well. I tried to figure out and found that such systems are indeed non - minimal phase systems
Thanks sir it was so practical 😍
may I ask about this simulation? via email or etc, thank you
How can i add a PID instead of an LQR
Hello did u find a way to add a pid ?
news??
why does he multiple by B for output instead of C?
i also have the same doubt
👌👌👌👌👌
Error in port widths or dimensions. Output port 1 of 'untitled/System/Integrator' has 4 elements. This port does not accept the dimensions (or orientation) specified by the output signal.
Component:Simulink | Category:Model error
Error in port widths or dimensions. Input port 1 of 'untitled/System/Gain2' is a [1x4] matrix.
this error comes when I run the system. How do I fix it?
I'm not sure which integrator this is, but a very common mistake is that the gains do not have the right multiplication type. In this case, double-click on the gain block and change "Multiplication" from "Element-wise" to "Matrix". Other reasons could be the initial values of the integrators or the orientation of the controller vector which shall be, then, transposed.
I have the same question about that. The integrator is the one at 8.20 in the video. I do change the 'Multiplication' and the initial values is what you input in the video. I do not understand what you mean orientation of the controller cause at that time there is no controller@@rptulrs2023
I think the gain in the right side is wrong. it should be B' not B
@@zhaobingkun4950 You saved me so much time, thanks mate.
@@zhaobingkun4950 thanks I had same error with you but I solve it like you thanks!
Hallo kann man noch mehr Erklärungen haben??
Was für eine Erklärung?
At 29.25 --> Invalid dimensions specified for input port 1 in 'MyModel/Observer/Gain3'. The gain specified has dimensions [1x4], while the input is being set to have the dimensions [1]. These dimensions are not suitable for generating the matrix product of the gain with the input signal
Component:Simulink | Category:Model error
Error in port widths or dimensions. Output port 1 of 'MyModel/Observer/Sum1' is a one dimensional vector with 1 elements.
Component:Simulink | Category:Model error
I using matlab R2017b
try to ad apostrophe transpose the matrix if for example the gain is Cd make it Cd'
have you tried to derive the state space representation
@@abdelkader6347 I just tried the simulation and am trying to understand it. does this video fit in the journal?
@@abdelkader6347 Do you know or have literature similar to this video?
at 31:06 ,I replaced “[K_d ,~ ,~] = dlqr(Ad,Bd,Q,R,N);” with “[K_d ,s ,e] = dlqr(Ad,Bd,Q,R,N);” ,and the result of e is [0.98929,
0.97981,0.968874,0.33317]，，The values in e are all greater than 0, is it because this is calculated in the discretization?
🇵🇸🇵🇸🇵🇸
Let us slow down the experiment a bit. According to the description the idea is to use a proprietary software which is Matlab which runs only in Windows. Secondly, the idea is not to run the controller in a simulator but to execute it on a real robot. And third, instead of running a physics engine like Box2d the idea is to program the forward model from scratch with differential equations.
Provide the code
Could you talk about how to create the animation model?
Hi, it is basically a "series of figures" that are plotted in a triggered Matlab functoin in Simulink. Take a look into the plot-file to follow that. I will try to make a short video on creating such animations as soon as I have some free time.
@@rptulrs2023 "I will try to make a short video on creating such animations" ohh yes
@@rptulrs2023 thank you for this work!
is it possible to control this system with pid controller