advertisement

MODERN CONTROL FINAL EXAM 1. Derive state models for the following system G ( s) 2005/1/12 1 s 3s 5s 1 3 2 and design the full-state feedback gain matrix K to place the closed-loop pole at –2+2j. 2. Consider the linear system described by 1 0 0 X (t ) X (t ) U (t ) 1 2 1 Y (t ) 1 0X (t ) 1 U (t ) If we change the state variables to obey the relationship X 1 X 1 X 2 and X 2 X 1 X 2 what is the state-space representation in the state X ? 3. A dc motor control system has the form shown in Fig(1). The three state variables are available for measurement (X1 is position; X2 is velocity and X3 is field current); the output position is X1(t). Select the feedback gains so that the system has damping ratio 0.8 with 2 second settling time. Furthermore, if we consider designing a compensator that provides asymptotic tracking of a reference input with zero steady-state error, what should we do? 1 1 0 1 X (t ) 1 3 0 X (t ) 0U (t ) 4. Determine and explain this state 0 1 0 4 Y (t ) 1 0 0X (t ) model is uncontrollable or unobservable ? 5. Please explain the observer design procedure as possible as you can. GOOD LUCK AV8D !! , Name : No :