prelab2

prelab2 - ECE 194D Prelab 2: Due Thursday, April 7, 2011,...

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Prelab 2: Motor System Identification In Lab 2, we will experiment with several single-input single-output (SISO) control strategies for the Lego motors, to gain hands-on intuition for both transient and steady state behaviors. Before designing any controllers, however, we will first characterize important model elements that capture the dynamics of the plant; ideally, these should capture both linear and nonlinear effects. First, let us hypothesize a model. Each model assumption is presented first in words and then in equation form. You should need only the equations to complete the prelab; the text is included to justify the model. During lab, you may find evidence our assumed model is not quite right, and so understanding and later refining these assumptions could be useful if you wish to improve performance in future labs. We will assume the Power Level command to the motor, p m , (which is a value from -100 to 100 for the Lego NXT system) can be modeled simply as a voltage (of as-yet unknown scaling). In reality, there is a PWM (pulse-width modulated) signal involved, but the inductance of the motor will (we hope) provide enough of a low-pass filtering effect that we can treat the voltage as an average value, proportional (i.e., linear) to the p m . ܸ ൌܭ ݌ We also assume the electrical time constant of the motor is so fast (i.e., ߬ ൌܮ is very small) that the electrical impedance relating voltage and current in the motor can be approximated simply as a resistance, R m : ݅ ൌܸ And that motor torque is linearly proportional to current: ܶ ൌܭ ݅ Also, the back EMF (electromotive force) reduces the net voltage across the motor by an amount linearly proportional to the angular velocity of the motor. Since power is related as ܸ ݅ ൌܶ ߱ , the same motor torque constant relating torque to current also relates back EMF and motor speed: ܸ ௕௔௖௞ ൌെܭ ߱ This linear loss can be lumped with any other linear damping due to the mechanism (gears, etc.) itself, collectively represented as a viscous damping term in the dynamics, b eff , that is proportional to the angular velocity of the output shaft , ω s : ܶ ௩௜௦௖௢௨௦ ൌെܭ
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prelab2 - ECE 194D Prelab 2: Due Thursday, April 7, 2011,...

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