The state space model to describe the dynamics of a hot air balloon is given as:...

 

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The state space model to describe the dynamics of a hot air balloon is given as: B-08-8--8- h(t) [T(t)] i(t) = h(t) +0u(t) + w(t) (1) where the state variable T(t) is the temperature change of air in the balloon, u(t) is the manipulated variable and is proportional to change in heat added to air balloon, v(t) is the vertical velocity of the balloon, h(t) is the change in altitude from steady-state altitude, w(t) is the vertical wind velocity, which is the disturbance for the control problem. The normalized constants in the model are T₁ = 1, T2 = 10, a = 1 and 3 = 0.01. 1. Can we measure velocity v(t) and temperature T(t) and construct an observer to estimate the altitude h(t)? why? (5 marks) 2. Assume that T(t), v(t) and h(t) are measured. Design a state feed- back control for the air balloon, where the closed-loop poles are posi- tioned at -2. Simulate the closed-loop response with initial conditions T(0) = v(0)h(0) = 1 without the wind disturbance. In the simula- tion, simulation time Tsim = 20 and At = 0.001. Present closed-loop responses of the three state variables and the control signal (10 marks). The state space model to describe the dynamics of a hot air balloon is given as: B-08-8--8- h(t) [T(t)] i(t) = h(t) +0u(t) + w(t) (1) where the state variable T(t) is the temperature change of air in the balloon, u(t) is the manipulated variable and is proportional to change in heat added to air balloon, v(t) is the vertical velocity of the balloon, h(t) is the change in altitude from steady-state altitude, w(t) is the vertical wind velocity, which is the disturbance for the control problem. The normalized constants in the model are T₁ = 1, T2 = 10, a = 1 and 3 = 0.01. 1. Can we measure velocity v(t) and temperature T(t) and construct an observer to estimate the altitude h(t)? why? (5 marks) 2. Assume that T(t), v(t) and h(t) are measured. Design a state feed- back control for the air balloon, where the closed-loop poles are posi- tioned at -2. Simulate the closed-loop response with initial conditions T(0) = v(0)h(0) = 1 without the wind disturbance. In the simula- tion, simulation time Tsim = 20 and At = 0.001. Present closed-loop responses of the three state variables and the control signal (10 marks).

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BE4908 J9 VH 21 001 V4 6 4 T V bilt 0 TH du dt f ... View the full answer