CLASS: 4th 1st Term Exam (2014-2015) Q1 The following block diagram represents the drying oven control system. The dynamic behavior of the oven can be represented by following differential equation: 100.(1) dt +0₁(t) = v(t) Calculate the following: a-Natural frequency on and damping ratio b-The response of the system to step change in 0,(t) of 20 C° E(s) On (s) 0:(s) V(s) 30 Oven 2 + S+4.

The arm angle, e (t), is controlled by a closed-loop system. The input (reference) to the system is the desired angle, and the output is the actual angle. A controller uses the difference between the desired angle and the actual angle to drive the motor, resulting in a motor torque applied to the system. motor torque(t) houlder joint damping(B) The customer wants to make a system to have 1) O steady-state error 2) Less than 10% overshoot 3) Less than 1- For a step inp **ling time Arm length (/) Mass(m) g design a controller to meet the design spec above. 1) Design a controller to meet the design spec. 2) Evaluate your controller using step response (time response) 3) Evaluate your closed-loop system using frequency response (e.g., Bandwidth, Gain margin. Phase margin).

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1. Verify Eqs. 1 through 5. Figure 1: mass spring damper In class, we have studied mechanical systems of this type. Here, the main results of our in-class analysis are reviewed. The dynamic behavior of this system is deter- mined from the linear second-order ordinary differential equation: where (1) where r(t) is the displacement of the mass, m is the mass, b is the damping coefficient, and k is the spring stiffness. Equations like Eq. 1 are often written in the "standard form" ď²x dt2 r(t) = = tan-1 d²r dt2 m. M +25wn +wn²x = 0 (2) The variable wn is the natural frequency of the system and is the damping ratio. If the system is underdamped, i.e. < < 1, and it has initial conditions (0) = zot-o = 0, then the solution to Eq. 2 is given by: IO √1 x(1) T₁ = +b+kr = 0 dt 2π dr. dt ل لها -(wat sin (wat +) and is the damped natural frequency. In Figure 2, the normalized plot of the response of this system reveals some useful information. Note that the amount of time Ta between peaks is…

Can you please show the complete solution of the image below. Thanks! Subject: Mechanical Vibration

6. The figure below represents a time response of a control system. y(r) 0.63 What is it? a) Unit-step response of a Prototype First-Order System; b) Unit-Impulse Response of a Prototype First-Order System; c) Unit-Step Response of a Prototype Second-Order System; d) Unit-Impulse Response of a Prototype Second-Order System.

Solve the following question by hand and without the use of AI. Use detailed mathematical expressions to solve the problem and please do not use AI. Thank You!

A thermocouple is connected to a data acquisition system which is used to measure temperature of air in a duct. For a step-input, the system measures the temperature accurately at steady state. Assume the dynamics of the sensor(thermocouple) limit the system's speed of response. The sensor has a time constant of 0.5 sec. In a given situation, the duct's air temperature varies with time as a sinusoid of frequency 2 rad/s with amplitude of 10°C. In this case, the measured temperature by the system is a sinusoid as wellI, as a function of time. The amplitude of this (measured) sinusoid, at steady-state, is closest to: Select one: а. 10°C b. 5°C С. 3°C O d. 7°C

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