Linear Control Systems

enfn
timer Asked: Oct 29th, 2018

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Hello .

I would like you to solve the problems in the attached file . I would like detailed and easy to follow .

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problem #3. Consider the system described by %= AX + Bu h y = cx (with D=0 =) (1) and consider the adjoint equation of (1), given by Ż = - Az + cTv - 12) W = BTz Show that H(s) = - Häls), where H(s) and Hals) are the transfer functions of (i) and (2), respectively. 1 problem #4. For the system X (t) - A X6) with on A = { plot the state - trajectories x, -X₂ plane for the initial condition X(0)= Xo = EEGR. 431 Linear control systems HWH S n Due Date Monday oct. 29/2018 problem #1. Consider the following system [ 83-*N] [%]" y = [1 07:] with D=0 as Determine the transfer function for the above system b) dy(t) + dt Is the system stable? why? problem #2. Consider a system described by the following differential equation + 4 dylt) + 2y Ct) = 4 u(+) dt where y(t) is the output and ult) is the input to the system. Determine the state-space representation for the above system. ence mplifer rror voltage Controller Voltage proportional to shaft speed Throttle actuator Throttle angle Carbu 55 Me 5 Consider the following system with [*]=160][:] + [:]u, す。 input ucto= for tzo otherwise and output h(t)= [1 2] [ x, a) Find the transfer function for the above system. b) plot the solution yt) for an condition o of [ X,10) an initial ]:[:] X10) = X2 (0) Reduce the block diagram shown below Y(s) RCS) 22 Juta S +) S تلا For the system with input rits and output by (t) that is described by the following equation, find the transfer function dez m dy + Ady + 2y = 40 dt Find the closed-loop step response for the following open-coop transfer function, assuming unit feedback . ) stz G(s) = Laplace transform llow the with the 75 :) Find the initial value blo) of the signal Y(s) = s²+45+4
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