Answer Happy

USV Model The objective of pitch control system is to have the pitch angle of the USV, 8, (t), follow the pitch command (pitch input) , (t). the block diagram is shown in Figure 1. Pitch command Pitch gain 0, -K Commanded elevator deflection Ga(s) = de.com H(s) H(s) = Elevator actuator G(s) = Ga(s)Gb (s), where -0.125 s² +0.226s +0.0169/3¹ 8+3 Elevator defliection de K,8 Figure 1. Pitch Control loop The vehicle dynamics are represented by the product of two transfer functions Ga and Gb, which form the transfer function G(s) between the elevator deflection angle set by the elevator actuator (the system input) and the pitch angle, 6, (1),(the system output). Gr(s) Pitch rate sensor Gr(s) = Vehicle dynamics Ga(s) (8 +0.435) (8+1.23) The elevator actuator: The elevator actuator receives the commanded elevator deflection angle decom and positions the elevator surface accordingly, at an angle de. Ideally, one should have de decom, however the actuator is not an ideal device and have a limited bandwidth. Therefore, the relation between Sexcom and de is characterized in terms of a low pass filter, which has the transfer function as equation (3) (3) (1) (2)
The pitch control system: The pitch control system includes the pitch gain compensator (controller) (-K) and the pitch rate sensor. The sensor is essentially a differentiator that produces the pitch rate from pitch measurements; it is represented by a transfer function Kss. In this assignment, we will assume that the pitch rate sensor is disabled, i.e., K₁= 0, and the controller uses only the pitch gain (-K). By selecting the value for K, properties of the system can be changed. Note the sign "_" of the compensator; see Figure 1. This sign is to counter the sign "-" of the vehicle dynamics transfer function; see equation (1) and equation (2). This is necessary to avoid occurrence of positive feedback in the system. Design Requirements: 1. Find the transfer function of the subsystems. 2. Then, find the overall transfer function of the system. 3. Use the given schematic parameters (B=1.00, 1.50, 1.90) for three configurations to model the system. 4. Find the system stability, steady-state response, and time response. 5. Plot the root locus for the system using MATLAB 6. design the USV's Pitch control system without rate feedback (Ks = 0) for the above three configurations.