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u tank 1 (((c tank 2 3. Consider the two-tank system depicted in the figure on the next page. Use the physical law q=av2gh to describe the flow coming out of the orifice of a tank, where a[m] is the section area of the orifice, h[m] is the height of the fluid in the tank, and g is the standard gravity acceleration. Use the physical law Ah = qin Yout to describe the evolution of the level inside a tank, where A[m] is the section area of the tank, Lin, Yout[m/s] are the flows in and out the tank. a) Using the notation 21 : height in tank 1 22 : height in tank 2 u : flow rate to tank 1 (input) y : height in tank 2 (output) Q1: section area of orifice in tank 1 02 : section area of orifice in tank 2 Al : section area of tank 1 A2 : section area of tank 2 derive the nonlinear state-space system that describes the two-tank system b) Obtain the expressions of the generic equilibrium point (, 11, 12) Hint: let , be chosen at will, and obtain the corresponding expressions of u and 72 c) Obtain the expressions of the A,B,C,D matrices of the linearised system around (, 71, 12) d) Comment on the structural properties observability, detectability, controllability and stabil- isability) of the linearised system. u tank 1 (((c tank 2 3. Consider the two-tank system depicted in the figure on the next page. Use the physical law q=av2gh to describe the flow coming out of the orifice of a tank, where a[m] is the section area of the orifice, h[m] is the height of the fluid in the tank, and g is the standard gravity acceleration. Use the physical law Ah = qin Yout to describe the evolution of the level inside a tank, where A[m] is the section area of the tank, Lin, Yout[m/s] are the flows in and out the tank. a) Using the notation 21 : height in tank 1 22 : height in tank 2 u : flow rate to tank 1 (input) y : height in tank 2 (output) Q1: section area of orifice in tank 1 02 : section area of orifice in tank 2 Al : section area of tank 1 A2 : section area of tank 2 derive the nonlinear state-space system that describes the two-tank system b) Obtain the expressions of the generic equilibrium point (, 11, 12) Hint: let , be chosen at will, and obtain the corresponding expressions of u and 72 c) Obtain the expressions of the A,B,C,D matrices of the linearised system around (, 71, 12) d) Comment on the structural properties observability, detectability, controllability and stabil- isability) of the linearised system