Automatic Control Systems 2017 Spring Semester Assignment Set 1 Dr. Kalyana C. Veluvolu Deadline: 11-APR - 16:00 hours @ IT1-815 1) Find the transfer function / for the following system using block diagram reduction technique. 2) Determine the transfer function / for the following system shown below. Both masses slide on a frictionless surface, and 1,1 /. Find when is an unit impulse function. 3) Consider the mechanical system shown below. Determine the transfer functions 1 and.
4) In large disk drive systems containing linear actuators, the motion is control by a voice-coil motor (VCM), as shown in Figure 3. The force F produced is proportional to the current i in the coil. The link between the head ( and the servo body ( ) is flexible with spring constant K. Draw a block diagram of the system and obtain the transfer function from input to output y. The relevant equations are given below. Mechanical system: F = and 0 = Current flowing in magnetic field produces the force: F = Motion in magnetic field produces the force: Electrical circuit: L 5) A simple but practical feedback control system is shown below. It is a positioning system or position servo for a large video satellite antenna modeled as a mass having a large moment of inertia, J. An output potentiometer measures the output shaft position, converting the position to a proportional voltage according to. Where, is the output shaft angle in radians and is the output potentiometer voltage; is the constant of proportionality between shaft position and potentiometer voltage, is the total voltage V divided by the maximum rotation of the potentiometer: /. The input potentiometer slider position r is converted to a voltage with a potentiometer identical to the potentiometer,. The difference between the two potentiometer signals is then amplified with gain, where is the error voltage output of the difference amplifier. This voltage is then further amplified with gain and is applied to the motor terminals, where is the motor voltage. The second amplifier is the power amplifier, which is capable of supplying the electrical power necessary to drive the motor. The motor is coupled to the antenna with a gear train, of ratio, /., where is the motor shaft angle and is the angular position of the antenna with moment of inertia J. is much smaller than since the high-speed shaft of the motor must drive the antenna at low speed but with a much higher torque. The control motor has negligible armature inductance and negligible internal damping.
/ ; where / / and 1/ A Position servo Draw the block diagram and find the transfer function of R(s) to the. 6) A system and its response curve are given below. Determine the values of,, and.
7) Not all second-order systems are designed to give a standard 2 order response. Consider the power steering for an automobile. The feedback system can be modeled as the block diagram shown in the figure below. For a unit step input A(s), find values of and for which the response w(t) is critically damped and has a steady-state gain of 0.4 unit. Repeat for a damping ratio of 0.7 and a steady-state gain of 0.2 unit.. 8) The open loop transfer function of a unity feedback system is given by 1 where T and K are positive constants. By what factor should the gain K be reduced such that (a) The peak overshoot of the system to unit step input is reduced from 75% to 25%, and (b) The damping ratio increases from 0.1 to 0.6? 9) A second-order under-damped system has the overall transfer function as follows: 2 It is possible to achieve a response that does not exhibit any overshoot and undershoot by an appropriate choice of the input function r(t) to give the desired output as shown in below figure. Determine the value of, A and B when ζ = 0.7, 5 rad/sec.
10) Consider the closed-loop feedback system shown below. Determine the range of K for which the system is stable using Routh array stability criterion. 11) Construct Routh array and determine the stability of the system whose characteristic equation is 2 8 12 20 16 16 0. Also, determine the number of roots lying on right half of s-plane, left half of s-plane and on imaginary axis. 12) Consider the block diagram of a disk storage data-head positioning system as shown in figure below. Derive the relationship between and for which the closed-loop system is stable. Construct a parameter plane of versus and show the following regions in the plane (a) Stable and unstable regions. (b) Trajectory on which the system will have sustained oscillation. (c) The point in which the sustained oscillation frequency is 6 rad/s.