Kalman filter unstable in closed loop application

[RubelCa]

I have implemented the closed-loop motor control system as above in a Matlab simulation (pic Kalman.png). Here, the Kalman filter estimates the torque disturbance and angular speed of the motor and those are feed to the RLS algorithm for parameter identification, here it estimates the combined inertia of the rotor and the load. I have successfully simulated it with a constant J feed to the Kalman filter (0.089 for example) instead of feeding estimated J back to the Kalman filter in pic (Kalman1.png), and the RLS parameter identification correctly estimates the inertia which is close to 0.089 (within 0~3% error band).But, when I feed the RLS estimated J to back to the Kalman filter after running for few seconds when the J estimate reaches close to 0.089, using an analog switch, the system becomes unstable and RLS outputs become 'nan'. I tried using an average block (avg of 100 samples) between the RLS and Kalman filter in the J feedback line and it seems to stabilize the system a bit but not for a long time. I guess there is a better way to achieve the following:1) Removing the average block

2) The J (estimated) connection between the RLS and the Kalman filter should be there from the beginning without the need of an analog switch.My control engineering knowledge is not advanced level so any suggestion of an idea, document or a book (application oriented) will be highly appreciated.

 

[Achy47]

It is great to hear that you have successfully implemented a closed-loop motor control system using a combination of Kalman filter and RLS algorithm for parameter identification. However, it seems that you are facing some stability issues when feeding the RLS estimated inertia back to the Kalman filter.

Firstly, I would suggest checking the dynamics of your system and see if there are any inherent instabilities that may be causing the system to become unstable. It is important to ensure that your system is stable before implementing any control techniques.

Secondly, it is important to consider the sampling rate of your system and make sure that it is sufficient for the control algorithms to work effectively. If the sampling rate is too low, it may result in inaccurate estimates and unstable behavior.

In terms of your specific questions, I would suggest exploring other methods for filtering the estimated inertia before feeding it back to the Kalman filter. One suggestion could be using a low-pass filter with a cutoff frequency that is appropriate for your system. This could help to smooth out any sudden changes in the estimated inertia and improve stability.

Additionally, I would recommend looking into adaptive control techniques, which can handle parameter changes in real-time without the need for explicit parameter identification. This could potentially eliminate the need for feeding the estimated inertia back to the Kalman filter.

In terms of resources, I would suggest looking into textbooks on adaptive control, such as "Adaptive Control" by Karl J. Astrom and Bjorn Wittenmark, or "Adaptive Control: Algorithms, Analysis and Applications" by Ioan Doré Landau, Rogelio Lozano, and Mohammed M'Saad. These books provide a comprehensive overview of adaptive control techniques and their applications.

I hope this helps and wish you all the best in your research.