LQR study notes for Christopher Lum lecture, youtube

 

IISC open day contacts:

 IISC Bangalore open day on Saturday 24 February 2024. 
Photos and contact details from the visit:

Funding opportunities for start ups under stem cell fund:

Magnetic levitation stage for precision positioning in the nanometer scale: 

Diamagnetic levitation, PCB coils, graphite middle layer, magnet floats, use closed loop positioning

Constant in the differential equation itself is being changed 

(m,c,k in (ma+cv+kx=f)) with electromagnets to actuate the system instead of using 

force to actuate. Classic example: Vibrating inverted pendulumn on a speaker.

Electro static discharge testing facility at IISc embedded system development:

Voltage interference testing at IIsc for embedded system development:

Compliance testing for embedded system development:

Contact details for compliance testing in embedded system development at IISc

Hydraulic piston and cylinder arrangement with syringes:

Base excitation of multi storeyed building, earthquake simulation for studying the resonance frequency of buildings

Manufacturer of horizontal excitation table:

Switched reluctance motor (SRM) development by Prof G Narayanan

BH curve characterization for electromagnetic core materials

Plotting the BH curve of small transformer cores, showing the hysteresis region with xy plots

Power amplifier for BH curve characterization 

TMS 320 based embedded controller (DSP) with thrust bearing in the background

Schematic of AMB testing rig at IISc

Controller and power amplifier for AMB

Paper by Dr Kamisetty on power amplifiers for AMB (1)

Paper by Dr Kamisetty on power amplifiers for AMB (2)

SRM motor torque control

Close up of radial AMB

Homopolar type AMB for thrust bearing using pot core. I did this in 2017.

H bridge driver for homopolar bearing and core of the homopolar thrust bearing (grey coil , 3d printed)

Demonstration model of radial AMB setup

Dr Kamisetty and his friend at AMB lab. Dr Ashutosh not present for 

exhibition. Dr Shahjahan, who made this last year during PhD has settled in UK

Kamisetty (2)

Kamisetty (3)

Radial AMB and homopolar thrust AMB

Closeup of thrust AMB (1)

Closeup of thrust AMB (2)

Closeup of thrust AMB (3)

SRM motor design tool

Thank you.

DynCont#12: Eigen value and eigen vector 3Blue1Brown

• A vector will span a line passing through it. All points along the span, the line, can be reached by the vector using scalar multiplication.
  
•  A matrix multiplication rotates and scales a vector
• A matrix multiplication will only scale a Eigen vector , without changing its span direction.
• A rotation matrix has no eigen vector. All vectors are rotated.
• A shear matrix has one eigen vector.
• There are matrices with one eigen value and many eigen vectors, like scaling all vectors on a plane.
• See these 3 matrices and one normal eigen vector eigen value matrix in 2GBAB.
  

DynCont#10 Linearising closed loop in simulink, Equilibrium point, trim point.

1.  When linearising a non linear plant, about a trim point, always open the feed back loop
2. Do not place input perturbation and output pickup in simulink in the closed loop
3. Linearising is applicable for unstable systems, so open the feedback loop and linearise the plant alone.
4. Important : Trim point is not Equilibrium point
5. At equilibrium point, all state vector derivatives are zero
6. At trim point, only the constrained state vector derivatives are zero. Example, linearising the aircraft model at a constant forward speed.. 

 

From Analyzing Models (Getting Started) (urv.es)

DynCont#4: SVD, 3Blue1Brown

1.  If determinant is zero, the transformation matrix collapses the input vector to a point in the output vector space
2. A span of the vector is a line , infinite passing through the vector in both the directions. A vector can be multiplied by a constant number and the head of the vector will be somewhere along the line for different constants 
3. Matrix multiplication:
1. Row wise picture, conventional computational approach
2. Column wise picture
3. Transformation from one vector space to another vector space approach
4. Will be edited after listening to the lec again.
   

DynCont#3: SVD, MIT 18.065 Strang you tube lecture video 6

1.  We are looking for a bunch of orthogonal vectors u, which when multiplied by A, give another set of orthogonal vectors v, scaled by sigma
2. Curse of Dimensionality =   A matrix is basically scaling and rotation. For a 2x2 matrix, there are 4 terms . it has 2 scaling values and 2 rotations. The rotations increase the time taken. not the scaling. For 3x3 matrix, there are 9 independent terms with 6 rotations and 3 scaling terms. Similarly, 4x4 matrix has 4 scaling terms and 12 rotations.
3. Rank= If A has rank r, there are r orthogonal vectors , which when multiplied by A give another r orthogonal vectors.
4. If U vectors are orthogonal in AU=sigma V, it can be proven that V vectors are orthogonal by simply substituting VV' = (AU/Sigma1)* (AU/Sigma1)'

DynCont#2: SVD, MIT 18.065 Strang you tube lecture video

1.  A * v = u * Sigma
2. Matrix A times an orthogonal vector matrix = another orthogonal vector matrix scaled by sigma
3. Sigma is diagonal matrix
4. Sigma is the square of eigen values of A A'
5. AA' is symmetric and positive semi definite 
6. If A is mxn, AA' = m x m . Then, it will have m eigen values.
7. If A is mxn, A'A = n x n . Then, it will have n eigen values. If m is greater than n, then m-n eigen values of AA' will be zero.
8. Use of SVD:?
9. SVD from lecture 29 in 18:06?
10. Use of SVD from Knuth?
    

 

DynCont#1: SVD, Knuth you tube lecture video

1.  Singular value decomposition exists for all rectangular matrices
2. A square is a rectangle
3. LR , LQR, LU may not exist for some matrices
4. All matrices are basically rotation and stretching.
5. A = ULV'
6. U and V are rotations
7. L is the scaling 
8. L square will have the eigen values of AA'
9. U and V are orthonormal matrices, so their inverse and transpose are same
   
10.