We can build a control system that will automatically adj ust a motorcycle” s radio volume as the noise generated by the motorcycle changes. The noise generated by the motorcycle increases with speed. As the noise increases, the system increases the volume of the radio. Assume that the amount of noise can be represented by a voltage generated by the speedometer cable, and the volume of the radio is controlled by a dc voltage (Hogan I988). If the dc voltage represents the desired volume disturbed by the motorcycle noise, draw the functional block, diagram of the automatic volume control system, showing the input transducer, the volume control circuit, and the speed transducer as blocks. Also, show the following signals: the desired volume as an input, the actual volume as an output, and voltages representing speed, desired volume, and actual volume. An animation PowerPoint presentation (PPT) demonstrating this system is available for instructors. See Motorcycle. [Section 1.4: Introduction to a Case Studyl
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CONTROL SYSTEMS ENGINEERING
- The following is the equation of motion for forced damped vibration of a mass-damper system: mx + cx + kx Fo sin wt The magnification factor variation with respect to the frequency ratio is given in Figure Q5 for various damping ratio values. If it is known that for the system examined the damping ratio is 0.3 and the magnification factor takes the value 0.8, then how the vibration amplitude can be further reduced by only altering the mass, damping coefficient and stiffness coefficient? 4/1055 Amplitude ratio: M = 2.8 2.4 2.0 1.6 1.2 1.0 0.8 0.4 0 = 5.0 0.4 = 0.1 = 0.3 X = 0.4 -=0.5.-- = 1.5 = 2.0 0.8 1.2 1.6 2.0 1.0 Frequency ratio: r = = 3.0 2.4 2.8 3.2 W Wnarrow_forwardA particle vibrates through space. It took 3ms to complete one cycle. What is its frequency in Hz?arrow_forwardA particle vibrates through space. It took 3ms to complete one cycle. What is its frequency in rad/sec?arrow_forward
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- An object was dropped off the top of a building. The function f(x) = -16x2 + 144 represents the height of the object above the ground, in feet, x seconds after being dropped. Find and interpret the given function values and determine an appropriate domain for the function. f(-3) =___ meaning that___ seconds after the object was dropped, the object was___ feet above the ground. This interpretation___in the context of the problem. f(0.5)=___ meaning that___ seconds after the object was dropped, the object was___ feet above the ground. This interpretation____in the context of the problem. f(8)=___ meaning that___ seconds after the object was dropped, the object was___ feet above the ground. This interpretation___in the context of the problem. Based on the observations above, it is clear that an appropriate domain for the function is___arrow_forwardContext The needle of a sewing machine makes a repetitive up and down motion which is described by the equation y(t)=Acos(wt) To choose the settings of the device that will ensure that the needle successfully pierces the textile, you are asked to model the speed in ? of the needle as a function of time. Constraints and information The parameter A represents the range of motion (in m);The parameter w represents the angular frequency. It tells us about the number of back and forth movements that the needle makes per second;The parameter w is given in rad/s, so your calculator absolutely must be in radians mode to do the calculations in this problem;Modelization Establish the model for the y velocity of the needle as a function of time and the parameters A and w. Then test your model by calculating the speed in y of the needle at the moment and with the given parameters: Moment: 4.1 s Amplitude: 0.012 m Angular frequency: 17.9 rad/sarrow_forwardThe following EOMS describe the behavior of an electric motor attached to a torsional spring and damper: [Li + Rz + vb = Vin(t) IÖ= k0b0 + T Importantly, the equations are coupled by the fact that 7 = k₁z and v₂ = k₂0. Here, L, R, kv, I, k, b, and kt are constants. z is the current in the motor, and is the angular displacement of the motor (clearly then, is the motor's angular velocity). Finally, the input to the system is vin (t). Your tasks: A Substituting in the coupling terms (7 = ktz and v k0) into the EOMs, write the state space form of the system x = Ax + Bu, assuming your states are x₁ = z, x₂ = 0, and x3 = 0. Clearly identify your matrices. B Assume that the desired outputs of the system (to be measured) are the current z, the angle and the input Vin all as separate elements in the vector y. Write the output equation y = Cx + Du. Hint: D will NOT be zero in this case. Clearly identify your matrices C Assume there is no stiffness to the spring (k = 0). Using w(t) to represent…arrow_forward
- A kid is plating on a swing and it takes approximately 2.5 seconds to reach on side coming from the other. What is her frequency in Hz?arrow_forwardHow many “accelerators” do you have in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do they produce?arrow_forwardThe ratio of output to input of a system is known as Transfer function. Select one: O True O False Coloct the cinmple cuctom fcom the fellouuingarrow_forward
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