H.w 2: The open loop response, that is, the speed of the motor to a voltage input of 20V, assuming a system without damping is 20=(0.02) dw -+ (0.06)w. dt If the initial speed is zero (w(0) = 0),and using the Runge-Kutta 4th order method, what is the speed at t = 0.8s? Assume a step size of h = 0.4s.
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- Please refer to the instruction below. As7 A42 A76 x, Aer A43 A54 A65 A32 X, A45 A s0 A23 A34 A72 Fig. 8-34 Identify the (a) input node, (b) output node, (c) forward paths, (d) feedback paths, (e) self-loop. Determine the (f) loop gains of the feedback loops, (g) path gains of the forward paths.öalg äbäi The closed-loop system transfer function of a control system is given by the following figure, for unit step input what is the * ?output 2(s – 2) R(s) (s +2)(s + 1) c(s) | %D a- -1+e-2t – e-t b- -1 – e-2t + e-t c- -1 + 4e-2t – 3e-t d- -1 – 4e-2t + 3e¬t a dMatch the transfer function with correct Bode phase plots. s+10 G(s)=(s+100) s+ 100 G(s)= s(s+10) G(s) = (s+10) (s+100) s(s+10) G(s) = (s+100) s(s+100) G(s)= (s+10) G(s) = (+10) (+500) S A. 180 deg- 90 deg 0 deg 90 deg 180 deg- 90 deg 00 00 0 deg C. 90 deg+ 90 deg+ 0 deg -90 deg D. 180 deg F. 90 deg 0 deg 90 deg -180 deg 90 deg 0 deg 90 deg -180 deg 90 deg 0 deg -90dex+ -180 deg 00
- Weight Ple Figure 4: Schematic of a pile driver f(t) m+bv=f(1) m by 3 X pile Figure 5: First-order model of the pile in soil 5. Figure 4 shows a pile driver that is used to drive piles into soil to provide foundation support for buildings. Two major components of a pile driver are a pile and a weight. The pile is in the form of a long rod going into the soil. The weight is to impact the pile at the top with an impulsive force, thus driving the pile into the soil. Figure 5 shows a first-order model of the pile in the soil. The impulsive force produced by the weight is f(t). The resistance of the soil is modeled via a viscous damping coefficient. b. The weight of the pile is balanced by the normal forces in the soil, so it does not need to be considered. In addition, the elasticity of the soil is ignored. Let z(t) and v(t) be the downward displacement and velocity of the pile, respectively. The equation of motion governing the pile velocity v(t) is dv (5) where m is the mass of the pile.…Q.4- A model for feedback control system employing both angular position and velocity feedback is shown in figure bellow .The equation describing d²0 do di the system is J di² - = • K.[V₁-K₁0. K₂0-Ka ((1) Summing V,(r) Motor 白口食 amplifier Velocity sensor K₂8 Position sensor Where J is the rotary inertia KandK are the position and velocity feedback gains, and K, is the gain between the input voltages to the motor torque produced. Derive expression for the closed loop system undamped natural frequency and damping ratio.18- A)Define the following(i) Sensitivity (ii) Transfer function of closed loop control system
- You are tasked to enhance the performance of an analog plant using a digital controller PID. The controller is in connected in series with the plant in a closed-loop configuration. The pulse transfer K(z+a) function is given as GzohGp(s) =- Use sampling time Ts=0.6 second, K=8, a=0.78, b=-0.602 (0+z)(q+z) and c=-0.705. Do the following: i. Obtain the design point in z-coordinates to achieve the requirement of having a system settling time of 3 second, and damping ratio of zeta (z=0.705).Match the transfer function with correct Bode phase plots. G(s) = 5 $+7 G(s)=s+5 G(s) = s+10 S S G(s) = S+ 10 QUESTION 10 90 deg 00 0 deg -90 deg 180 deg B. D 90 deg @ 0 deg -90 deg 180 deg 90 deg @ 0 deg -90 deg 180 deg 90 deg @ 0 deg -90 deg 180 deg1) Determine the steady-state (forced) response and the time constant (or dominant time constant) for each of these systems: a. x+ 2x = 0 with x(0) = 10 b. 4x + 8x + 40x = 20 with x(0) = 0 and x(0) = 0 10x + 4x = 24 with x(0) = 0 C. d. *+ 34x + 64x = 8 with x(0) = 0 and x(0) = 0