A radio telescope must be accurately positioned to be effective. Once positioned any errors due to disturbances from aerodynamics loadings (from gusts of wind) must be corrected quickly. A control system capable of achieving this is shown in Figure Q5, where R(s) is the desired angular position whilst C(s) is the actual position, T«(s) is the disturbance produced by the wind, G1(s) the controller transfer function and G(s) is the transfer function of the telescope and drive motor. The transfer functions and system parameters are given as Ka G|(s) = 5 = 0.6, T = 0.2 s G(s) = Wn = 10 rad/s, s2 + 2(wn$ + w;" TS + 1' a) Derive the transfer function relating the actual position C to the torque disturbance Ta for a zero reference input. b) If a gust provides a sudden torque disturbance which is equivalent to a unit step input in T4, what value of K. gives a steady state eorof 0.4°. Qutput position c) What range of values of K will ensure a stable system? Ta(s) Telescope & Controller drive motor R(s) C(s) G|(s) G(s) Figure Q5.

A radio telescope must be accurately positioned to be effective. Once positioned any errors due to disturbances from aerodynamics loadings (from gusts of wind) must be corrected quickly. A control system capable of achieving this is shown in Figure Q5, where R(s) is the desired angular position whilst C(s) is the actual position, T«(s) is the disturbance produced by the wind, G1(s) the controller transfer function and G(s) is the transfer function of the telescope and drive motor. The transfer functions and system parameters are given as Ka G|(s) = 5 = 0.6, T = 0.2 s G(s) = Wn = 10 rad/s, s2 + 2(wn$ + w;" TS + 1' a) Derive the transfer function relating the actual position C to the torque disturbance Ta for a zero reference input. b) If a gust provides a sudden torque disturbance which is equivalent to a unit step input in T4, what value of K. gives a steady state eorof 0.4°. Qutput position c) What range of values of K will ensure a stable system? Ta(s) Telescope & Controller drive motor R(s) C(s) G|(s) G(s) Figure Q5.

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

See similar textbooks

Similar questions

Find and sketch the region of allowable s-plane locations such that a canonical second order system has a settling time less than 4 seconds and an overshoot (for a unit step response) of less than 10 percent.
What are the pros/cons of a second-order dynamic system? What dynamic property is the preferred in general, underdamped, critically damped or overdamped and why?
Find: Static position, velocity, acceleration error coefficients, and corresponding steady state errors. G(s)= K(2s+1)(4s+1)/s2(s2+2s+10) Note: This is a open loop function, input signal are unit step, unit ramp and parabolic. I need answer ASAP. Thank you!
Find out following:i. Sketch the root locus.ii. The number of branches of the root locus.iii. The value of ? and gain ? where the locus crosses the ??-axis.iv. The breakaway and break-in point on the real axis.
Find the range of K using Routh criterion such that all the roots of the characteristic equation lie between -1 and -2 s^3+8s^2+15s+K Also find the value of K for which system is limitedly stable?
Hi can you help me about this question? The figure shows a vehicle crash test simulation. Since the simplified model of the bumper of this vehicle is as follows, a- Find the transfer function of the system. X (s) / F (s) =? b- Assuming that the force F (t) is 1000 δ (t) N, find the displacement x (t). k=5000 N/m b=6000 N*s/m m= 1000 kg δ(t)=Dirac Delta
Find the solution to the difference equation given below?[?] − 0.25?[? − 2] = ?[?]when the unit-step function ?[?] = ?[?] is applied to this system assuming the initial conditions of ?[−1] = 1 and?[−2] = 0.
By plotting the root locus of the system given as the open loop function : G(s)= K/(s*(s+2)); a) When K=4, show the locations of the closed loop poles on the root locus. Determine the Damping Ratio and Natural Frequency values in this gain value. b) Calculate the unit step response of this closed-loop system by calculating the Percent Overshoot, Peak, and Settlement Time values and plot them to scale. c) Scan the region on the root locus where the pairs of conjugate poles must be in order for this inspected system to work at least in the success criteria (greater than the calculated damping rate and natural frequency) in (a).
Consider the circuit is shown in the figure below. The circuit comprises a voltage supply, ?(?), resistor (?), inductor (?) and capacitor (?). Let ?1 = ? and ?2 = ?? be the state variables for this system, where ? and ?? are the circuit current and capacitor voltage, respectively. For this system,a) Derive the loop equation, involving integro-differential equations, from first principles b) Write the state differential equationsc) Write the state-space equation in matrix-vector formd) sketch the signal flow graph
control systems In the electromechanical system given below, it can be seen that the coil can be represented by the series R-L circuit and also the coil It is known that the electromagnetic pulling force (F) is also proportional to the coil current, that is, F = βi. The input of the system is the voltage v applied to the coil and the output is the x path taken by the core. Accordingly, the system find the differential equations and transfer function
The position versus time plots of two oscillators are shown in the figure.a) What is the phase difference between the two oscillators at t = 1.0 s?b) At what times, closest to t = 0 s, do the two oscillators have zero velocities?c) At what times, closest to t = 0 s, are the two oscillators moving with maximumvelocity toward the negative x-axis?
A forced excited m–k–c system is under a harmonic force F: F=5000sinωt If the mass m = 50 kg; k=80E3 N/m; damping ratio=0.3 and dynamic deflection is to be less than 0.08 m. Determine the range of operating excitation frequency. Also the show the operating range of frequency on a graph.