ASEN 3200 Orbital Mechanics and Attitude Dynamics Spring 2004 Axelrad ASEN3200_Controls.doc 1 ASEN 3200 Attitude Control Review 1. Passive Stabilization Questions • In what sense does spin stabilize a spacecraft? Is spin about any axis “stable”? • What is the principle behind dual spin satellites? In what direction does the angular momentum point (r, v, h?) • What is gravity gradient stabilization? Does a gravity gradient satellite remain nadir pointing? What does a gg stabilized satellite look like? Calculations • Compute torque required to reorient a spinning satellite. Compute thrust and location of thruster to accomplish this. 2. Laplace Transforms Questions • What is a transfer function? • What is “s”? Calculations • Conversion from time domain to/from Laplace for constant (step), sinusoid, exponential, damped sinusoid. • Laplace transforms of integrals, derivatives • Laplace transform of differential equation and computation of transfer functions. • Partial fraction expansion • Compute poles of a transfer function 3. Second Order Linear ODE’s Questions • What is a 2nd order linear ODE? • What types of motion can it describe? • If a 2nd order linear ODE has no forcing input, what motions are possible? • What does a stable 2nd order ODE look like? What makes it stable? • What is the significance of the transfer function pole locations? Calculations • Given an ODE compute transfer function, find poles • Characteristics of response to a step input (matching ODE, or poles, or TF to/from a step response) • Step response characteristics as a function of ζ, ωn, - overshoot, rise time, peak time, settling time • Use of final value theorem to compute accuracy of tracking a step input or disturbance • Characteristics of response to a harmonic input (matching ODE, or poles, or TF to/from a frequency response) • Amplification factor 4. Control of a 2nd order system Questions • Block diagrams of a feedback control system • Desired (or reference) input, disturbance input Calculations • Write equation of motion for single axis attitude control. • Select proportional and derivative gains to achieve specified step response. • Limitations on control authority • Use of final value theorem to compute accuracy of tracking a step input or disturbanceASEN 3200 Orbital Mechanics and Attitude Dynamics Spring 2004 Axelrad ASEN3200_Controls.doc 2 ASEN 3200 Quiz A-3 NAME PRACTICE April 24, 2003 Open book, Open notes, Please show your work clearly. 1. Derive the closed loop transfer function ()()dssθθ. 2. For Kd=0 and Kp=2, find the transfer function poles and determine if the system is stable or unstable, oscillatory or non-oscillatory 3. Compute values for Kp and Kd such that the poles of the transfer function are located as shown in the figure to the right 4. For the system specified in part 3 carefully sketch the response to a unit step input. Compute and label the settling time, overshoot, and period of oscillations for this system. Make sure to label your axes. 5. What changes, if any, to Kp and/or Kd are required to decrease the maximum overshoot? 6. List 2 passive methods for attitude stabilization and 2 types of actuators that can be used for active attitude control of a satellite in low earth orbit. -3 -2 -1 0 1 2 3-3-2-10123x x imaginary realdθθ 13s−Kp Kd _ +