( a and K are unknown ) Real System Model Sensitivity Equations + - Required for Feed Forward Model. Numerical Power models typically are non-invertible. Zeros on the right half plane make the system unstable. Excess of poles over zeros of Power distribution is non-monotonic (no 1-1 mapping). Find “equivalent” set of monotonic functions. Automation is the key to high volume, low cost, and high consistency manufacturing ensuring performance, reliability, and quality. No standard for OE packaging and assembly automation. Misalignment is common between optical and geometric axes. Packaging is critical to success or failure of optical microsystems % cost of optical component/system is in packaging. Decompose complex waveform into Piece-Wise Linear (PWL) Segments. Each segment valid in specified region. Find an inverse model for each segment. Noise, an external disturbance, inaccurate modeling could lead to deviation from the actual values. Activated at a lower sampling frequency. Specific and appropriate tasks. Provides opportunities for the system to improve upon its power model. Adjust the accuracy on the basis of “experienced evidence.” It follows thatand Step 1: Assume system to be described as, where y is the output, u is the input and is the vector of all unknown parameters. Step 2: A mathematical model with the same form, with different parameter values is used as a learning model such that Step 3: The output error vector, e, is defined as. Step 4: Manipulate such that the output is equal to zero. Step 5: Sensitivity matrix S is given by The learning model adjustment scheme consists of assuming initial values for, adjoining the sensitivity equations to the model equations and using. Criteria for choosing  If  is too large, the schemes will diverge. is too small, then If  will approach very slowly. Selection of a suitable  and the weighting matrix Q are determined by a trial and error process. Receiver Fiber Encoder X-Y Amplifiers Source (Laser) Break-out 60 Interpolator PID controller Inside the PC Power Meter Power meter Aperture Test fiber Linear Motor 1.Shubham K. Bhat, T.P.Kurzweg, Allon Guez.” Simulation and Experimental Verification of Model Based Opto-Electronic Packaging Automation”, Photonics East Conference, Philadelphia, October 26-28, Shubham K. Bhat, T.P.Kurzweg, Allon Guez, “Advanced Packaging Automation for Opto-Electronic Systems”, IEEE Lightwave Conference, New York, October T.P. Kurzweg, A. Guez, S.K. Bhat, "Model Based Opto-Electronic Packaging Automation," IEEE Journal of Special Topics in Quantum Electronics, Vol.10, No. 3, May/June 2004, pp Shubham K. Bhat, T.P.Kurzweg, Allon Guez, “Improved Performance in Optical Communication System through Advanced Automation”, IEEE Sarnoff Symposium, April ADVANTAGES: Support for Multi-modal functions Technique is fast Cost-efficient Visual Inspect and Manual Alignment Initialization Loop Move to set point (X o ) Measure Power (P o ) Stop motion Fix Alignment Set Point=X o Learning Algorithm Model Parameter Adjustment Optical Power Propagation Model Correction to Model Parameter {X k }, {P k } FEED - FORWARD Off the shelf Motion Control (PID) (Servo Loop) Assembly Alignment Task Parameters Tracking parameter (  is a and K have initial estimates of 0.1 and 4 a and K have actual values of 1.44 and 5.23 Edge Emitting Laser Coupled To a Fiber Near Field CouplingPiecewise Linear segments Aperture = 20um x 20um Fiber Core = 4um Propagation Distance = 10um For the first segment, assuming a unity gain Learning Loop of PWL segmentLearning Identification of two unknown variables KpKp KpKp P d (s) P r (s) R(s) E(s) Desired Power Received Power 4 Piecewise Linear segments Learning Identification Implementation “+” represents the initial guesses of the plant model. “o” represents the final model (obtained using the learning algorithm). “-” represents the actual plant model. “o” represents the actual plant response. Other colored solid lines show how the actual slopes and intercepts are tracked from the initial guess. We present a system with two unknowns exhibiting input-output differential equation The variables u, y, and are to be measured Step 1: and { } Step 2: { Assume estimated model and } The Sensitivity coefficients are contained in Step 3: where, and Accurate Plant and Inverse Model is the key to the success of Model Based Control.