Today small metal parts are mass-produced as for example rollers in cylinder bearings. At high velocity cutting the metal is cut with a great force in a scissor-like device. Both precision and repeatability is important to be able to guarantee good quality, but from an economical point of view it is also important to keep a great manufacturing capacity. The part of the process that is most time consuming is when the metal bar, that is about to be cut, is fed to the right position. Therefore it is interesting to examine if the time used for positioning can be reduced. This thesis examines if more advanced automatic control can be used to speed up the process while maintaining the precision. In order to test and evaluate different theories, two different mathematical models have been developed. The models where implemented in the simulation program SIMULINK in MATLAB and they where compared to and adapted to data measured on the physical machine. One model is developed from physical relationships and mostly used for simulations while the other one, a condition state model, has been used for regulator design. The first question to answer was if it is at all possible to control the process any faster. When a theoretical limit was found the next step was to design a regulator to show that the theory of automatic control does not imply too great limitations. The design that was chosen was condition state feedback where the states were appraised with an observer. A faster system will raise the demands on cycle times and precision. To make sure that the hardware isn’t the limiting factor, design requirements have been set up. A small list of what hardware is available has also been put together (and shows that it is possible to implement such a system). The conclusion is that it is, theoretically, possible to radically increase the manufacturing capacity. The assumptions for this to be accomplished is especially that the uncertainty of the model is minimizedand that hardware with enough capacity can be found.

<p>Today small metal parts are mass-produced as for example rollers in cylinder bearings. At high velocity cutting the metal is cut with a great force in a scissor-like device. Both precision and repeatability is important to be able to guarantee good quality, but from an economical point of view it is also important to keep a great manufacturing capacity. The part of the process that is most time consuming is when the metal bar, that is about to be cut, is fed to the right position. Therefore it is interesting to examine if the time used for positioning can be reduced. This thesis examines if more advanced automatic control can be used to speed up the process while maintaining the precision. In order to test and evaluate different theories, two different mathematical models have been developed. The models where implemented in the simulation program SIMULINK in MATLAB and they where compared to and adapted to data measured on the physical machine. One model is developed from physical relationships and mostly used for simulations while the other one, a condition state model, has been used for regulator design. The first question to answer was if it is at all possible to control the process any faster. When a theoretical limit was found the next step was to design a regulator to show that the theory of automatic control does not imply too great limitations. The design that was chosen was condition state feedback where the states were appraised with an observer. </p><p>A faster system will raise the demands on cycle times and precision. To make sure that the hardware isn’t the limiting factor, design requirements have been set up. A small list of what hardware is available has also been put together (and shows that it is possible to implement such a system). </p><p>The conclusion is that it is, theoretically, possible to radically increase the manufacturing capacity. The assumptions for this to be accomplished is especially that the uncertainty of the model is minimizedand that hardware with enough capacity can be found.</p>

In the thesis, a calibration method for positions of each accelerometer in an Inertial Sensor Array (IMU) sensor array is designed and implemented. In order to model the motion of the sensor array in the real world, we build up a state space model. Based on the model we use, the problem is to estimate the parameters within the state space model. In this thesis, this problem is solved using Maximum Likelihood (ML) framework and two methods are implemented and analyzed. One is based on Expectation Maximization (EM) and the other is to optimize the cost function directly using Gradient Descent (GD). In the EM algorithm, an ill-conditioned problem exists in the M step, which degrades the performance of the algorithm especially when the initial error is small, and the final Mean Square Error (MSE) curve will diverge in this case. The EM algorithm with enough data samples works well when the initial error is large. In the Gradient Descent method, a reformulation of the problem avoids the ill-conditioned problem. After the parameter estimation part, we analyze the MSE curve of these parameters through the Monte Carlo Simulation. The final MSE curves show that the Gradient Descent based method is more robust in handling the numerical issues of the parameter estimation. The Gradient Descent method is also robust to noise level based on the simulation result. / I denna rapport utvecklas och implementeras en kalibreringsmethod för att skatta positionen för en grupp av accelerometrar placerade i en så kallad IMU sensor array. För att beskriva rörelsen för hela sensorgruppen, härleds en dynamisk tillståndsmodell. Problemställningen är då att skatta parametrarna i tillståndsmodellen. Detta löses med hjälp av Maximum Likelihood-metoden (ML) där två stycken algoritmer implementeras och analyseras. En baseras på Expectation Maximization (EM) och i den andra optimeras kostnadsfunktionen direkt med gradientsökning. I EM-algoritmen uppstår ett illa konditionerat delproblem i M-steget, vilket försämrar algoritmens prestanda, speciellt när det initiala felet är litet. Den resulterande MSE-kurvan kommer att avvika i detta fall. Däremot fungerar EM-algoritmen väl när antalet datasampel är tillräckligt och det initiala felet är större. I gradientsökningsmetoden undviks konditioneringsproblemen med hjälp av en omformulering. Slutligen analyseras medelkvadratfelet (MSE) för parameterskattningarna med hjälp av Monte Carlo-simulering. De resulterande MSE-kurvorna visar att gradientsökningsmetoden är mer robust mot numeriska problem, speciellt när det initiala felet är litet. Simuleringarna visar även att gradientsökning är robust mot brus.