8 24 In This Chapter We Described The State Space Representation Of Single Input Single Output Systems In General S 1 (36.56 KiB) Viewed 15 times
8 24 In This Chapter We Described The State Space Representation Of Single Input Single Output Systems In General S 2 (32.02 KiB) Viewed 15 times
8 24. In this chapter, we described the state-space representation of single-input, single-output systems. In general, systems can have multiple inputs and multiple outputs. An autopilot is to be designed for a submarine as shown in Figure P3.15 to maintain a constant depth under severe wave distur- bances. We will see that this system has two inputs and two outputs and thus the scaler u becomes a vector, u, and the scaler y becomes a vector, y, in the state equations. z(t) where v: mean sea level X= Z w() FIGURE P3.1512 It has been shown that the system's linearized dynamics under neutral buoyancy and at a given constant speed are given by (Liceaga-Castro, 2009): x = Ax+ Bu y = Cx y = ‚ - ; U= Wo OB
A B= -0.038 0.0017 -0.092 1 0 0 1 -0.0075 -0.023 0.0017 -0.0022 0 0 0.896 0 0.0015 0 -0.0056 0 -3.086 and where 0 0 00 ; C = го 0 1 07 0001 w = the heave velocity q = the pitch rate z = the submarine depth 0 = the pitch angle S8= the bow hydroplane angle 8s = the stern hydroplane angle Since this system has two inputs and two outputs, four transfer functions are possible. z(s) 8B(s)' s(s) a. Use MATLAB to calculate the system's matrix transfer function. MATLAB ML b. Using the results from Part a, write the transfer e(s) function and dB(s)' e(s) ds(s)*
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