110年 - 110 國立臺灣科技大學_碩士班招生試題_自動化及控制研究所：自動控制系統#103772

1. Given the system represented in state space as follows:
  
Convert the system to one where the new state vector, z, is
  (10%)

2. For the system shown in Fig. Problem 2, a step torque is applied at θ₁(t). Find the transfer function, G(s) = θ₂(s)/T(s), and the peak time forθ₂(t) (15%) 

3. For the circuit shown in Fig. Problem 3, find the values of R₂ and C to yield 8% overshoot with a settling time of I ms for the voltage across the capacitor, with vi(t) as a step input. (25%)

4. The block diagram of a control system with tachometer feedback is shown in Fig. Problem 4. Construct the root loci of the characteristic equation for K≥0 when K_t ≥0. (13%)
  

6. Determine the conditions on b₁, b₂, c₁, and c₂ so that the following system is completely controllable and observable. (12%)