2. (3 points) Describe what a well-designed closed-loop control system would do to system output variable x(t)
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To simplify the problem now approximate the open-loop system with a lower order system as follows: G_{OL}(s) = frac{0.6(s+4)}{s(s+3.5)(s+1+8.5j)(s+1-8.5j)}. Part 1 has shown us that tuning parameters A and w for input v = Asin(wt) to achieve a desired behaviour of y(t) is not efficient, so we turn again to closed-loop control. A position sensor is purchased to measure y(t) accurately. First, use a controller C(s) = K such that the voltage supplied to the motor is v = K(r - y), where r is a reference signal. Q8-13. Produce the Bode Diagram for the closed-loop system with K = 70. On the Canvas quiz, you will be given different values of w. (Q8-10) Find the values of gain [dB] for the given values of w. [Canvas Input: two signed numbers - 5% tolerance allowed] (Q11-13) Find the values of phase [deg] for the given values of w. (The answer should be in degrees and in the range [0°, 360°)) [Canvas Input: two signed numbers - 5% tolerance allowed] Q14-16. For K = 50, plot r(t) = 10 sin (wt) and the corresponding y(t) for w = 0.75 [rad/sec], w = 7.5 [rad/sec], w = 75.0 [rad/sec] (two graphs on the same axes for each frequency). Capture enough time to show the steady-state response of y(t). Find the value of y(t) - r(t) when t is 100 s for w = 0.75, 7.5, 75.0 [rad/sec]. [Canvas Input: Three signed numbers - 5% tolerance allowed]
Sri K.
Adi S.
Consider a mechatronic system described by: y(t) = 1.5y(t−1) − 0.865y(t−2) + u(t−1) + 0.9u(t−2) + e(t) − 0.4e(t−1) where u(t) and y(t) are the input and output of the plant at the discrete-time instant, t, respectively. e(t) is a zero mean white noise sequence. (i) Express the above equation into a general form and give the polynomial A, B, and C. (ii) Obtain the desired closed-loop characteristic equation when poles at z = −0.6 ± j0.4. (iii) Design and describe a self-tuning control algorithm based on this system.
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