Question

Given the following block diagram, with G_{f}=10, G_{c}=20, G_{p 1}=\frac{2.0}{1.0 s^{2}+10.0 s+20.0}, G_{p 2}=\frac{5.0}{1.0 s^{2}+5.0 s+25.0}, H=1.0 s+6.0 а.(50%) Convert this system into state-space form, accounting for the multiple inputs and out-puts. There are several ways to transfer the block diagram into state-space, but let's try to remodelthe state-space from the beginning. \text { - The plant transfer functions give us the plant dynamics } \dot{x}=A x+B u \text { and } u=[u d]^{\wedge} T^{\prime \prime} The sensor H(s) relates the state to the output: y = Cx- - The feedback defines the control law: U(s) = G.(Gf * R(s) - Y(s)), which can be substituted intothe plant dynamics to find the closed-loop form. С.(50%) Simulate the response of the system using basic numerical integration. To a- Reference: r(t) = 5 - Random Noise, normally distributed, zero mean with o = 2: d(t) = 2 * rand() Note you already have the model of the system from the state-space, and this is a linear system.You can calculate the derivative and propagate the system directly.

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