Please answer all the remain part continue from Part A
Posted: Thu May 26, 2022 10:57 am
Please answer all the remain part continue from Part A
The block diagram of a two-area power system is shown in Fig-1. R₁ APD1(s) Steam Turbine Governer Kg1 Ket Kpt AXE1(s) AF1(8) 1+sT 1+T₂1 1+T₂ 2xT12 Governer K₂2 Steam Turbine K₁2 AXE2(s) Kpz U₂ AF2(S) 1+T₂2 1+Tg 1+8T₂2 APD2(s) R₂ Figure 1: Two area power system (a) (7 points) Represent this system in state space form considering the state vector z as: x = =[Af₁ APm₁ AXE₁ Af₂ AP₂ AXE₂ APties] (b) (3 points) The values of various parameters are: R₁ = R₂ = 2.4, Kp₁ = Kp₂ = 120, Tp₁ = Tp2 = 20,Tt₁ = Tt₂ = 0.5, Kg₁ = Kg = 1,K₁₁ = Kt₂ = 1 Tg₁ = Tg2 = 0.08,712 = 0.0342,012-1. Find the eigenvalues of the open-loop system and plot the open-loop response i.e. the frequency deviations Afi and Af2 for AP₁ = 0.01 and APd₂ = 0.05. 2. A high performance helicopter has a model shown in Fig-2. The goal is to control the pitch angle of the helicopter by adjusting the rotor thrust angle 6. The equation of motion of helicopter are Ö= -0₁0- - aut+nó Ï=g0 - α₂0 - 0₂1 + gỗ 1. U₁ APm1(s). APm2(s) + 312 APH1e1(s)
where x is the translation in the horizontal direction. For a military performance heli- copter, we find that 0₁ = 0.415, 0₂ = 0.0918, a₁ = 0.0111, 0₂=1.43, n= 6.27 & g = 9.8 All the parameters are in appropriate SI units. Body fixed axis 18(1) x(t) Figure 2: Helicopter Pitch Angle 0,Control (a) (5 points) Find the state variable model of this system considering the pitch angle 0, pitch velocity and horizontal velocity i as state variables. Thus, select the state variables as ₁ = 0, ₂ = 0,and ₂ = (b) (5 points) Compute the transfer function between the pitch angle and the rotor thrust angle & and find the poles and zeros of the system. (c) (5 points) Design a state feedback controller u=-Kx+r such that the maximum percentage overshoot M, < 20% and the setting time T, = 10sec. Obtain the closed loop response for step command. Hint: It is better to place the third pole at the zero of the open-loop system. (d) (5 points) Compute the feedforward gain and obtain the closed loop response of the system with state feedback controller with feedforward control. (e) (5 points) Design a state feedback controller with integral controller for this system and obtain the closed-loop response for step command. (f) (5 points) Design an observer based state feedback controller with integral action and compare the performance with that obtained without an observer.
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where x is the translation in the horizontal direction. For a military performance heli- copter, we find that 0₁ = 0.415, 0₂ = 0.0918, a₁ = 0.0111, 0₂=1.43, n= 6.27 & g = 9.8 All the parameters are in appropriate SI units. Body fixed axis 18(1) x(t) Figure 2: Helicopter Pitch Angle 0,Control (a) (5 points) Find the state variable model of this system considering the pitch angle 0, pitch velocity and horizontal velocity i as state variables. Thus, select the state variables as ₁ = 0, ₂ = 0,and ₂ = (b) (5 points) Compute the transfer function between the pitch angle and the rotor thrust angle & and find the poles and zeros of the system. (c) (5 points) Design a state feedback controller u=-Kx+r such that the maximum percentage overshoot M, < 20% and the setting time T, = 10sec. Obtain the closed loop response for step command. Hint: It is better to place the third pole at the zero of the open-loop system. (d) (5 points) Compute the feedforward gain and obtain the closed loop response of the system with state feedback controller with feedforward control. (e) (5 points) Design a state feedback controller with integral controller for this system and obtain the closed-loop response for step command. (f) (5 points) Design an observer based state feedback controller with integral action and compare the performance with that obtained without an observer.