Process Dynamics, Instrumentation & Control - Fundamentals Quiz (50%)

Explanation
Controlling the temperature of a bathing shower using hot and cold stream knobs is an example of feedback control because it involves continuously monitoring the temperature of the water and making adjustments to the hot and cold knobs based on the desired temperature. The feedback comes from the user's perception of the water temperature and the adjustments made to achieve the desired temperature.

Explanation
The P controller introduces offset because it only considers the current error between the desired and actual values, without taking into account the past error or the future trend. This means that even if the system reaches the desired value, there will still be a steady-state error or offset.

Explanation
A derivative controller does not eliminate offset but rather reduces it. It helps in reducing the time taken to reach the setpoint and improves the stability of the system. However, it can lead to oscillations if not properly tuned or if the system has inherent instability. Therefore, the statement that a derivative controller eliminates offset but introduces oscillations is false.

Explanation
The inverse Laplace transform is used to find the original function from its Laplace transform. In this case, the Laplace transform is 100/(s+5). To find the inverse Laplace transform, we need to determine the function that when transformed using Laplace transform, gives us 100/(s+5). The correct answer is 100 exp (-5t) because when we take the Laplace transform of this function, we get 100/(s+5), which matches the given Laplace transform.

Explanation
A second order system can be modeled as two first order systems in series because a second order system can be broken down into two first order systems by considering the transfer function. By doing so, the overall system can be analyzed and understood better. This decomposition helps in simplifying the analysis of complex systems and allows for easier control and design. Therefore, it is true that a second order system can be modeled as two first order systems in series.

Explanation
Bode plots are graphical representations of the frequency response of a system. They show the magnitude and phase shift of the system's output in response to different frequencies of sinusoidal inputs. Therefore, Bode plots can be used specifically for sinusoidal inputs to analyze the behavior and characteristics of a system at different frequencies.

Explanation
Inverse response refers to a situation where the output of a system initially moves in the opposite direction to a change in input before eventually settling down to the expected response. This behavior is typically associated with negative poles in the process transfer function, not positive poles. Therefore, the statement that inverse response has positive poles is incorrect.

Explanation
Inverse response is not characterized by negative roots in the process transfer function. Inverse response refers to a phenomenon where the output of a system initially moves in the opposite direction to a change in the input. It is typically observed in systems with significant dead time. The presence of negative roots in the process transfer function may indicate other characteristics or behaviors of the system, but it is not directly related to inverse response.

Explanation
In a second order underdamped system, the damping coefficient (ζ) is always less than 1. This coefficient determines the rate at which the system returns to equilibrium after being disturbed. If the damping coefficient is equal to 1, the system is critically damped, and if it is greater than 1, the system is overdamped. Therefore, the correct answer is ">1".

Explanation
The Routh-Hurwitz criteria is a mathematical method used to determine the stability of a system by analyzing the coefficients of its characteristic polynomial. By applying this criteria, one can determine if the system is stable or unstable based on the signs of the coefficients. Therefore, the statement that Routh-Hurwitz criteria can be used to determine the stability of a system using its closed loop characteristic polynomial is true.

Explanation
A feed forward controller requires extensive and accurate knowledge of the process model because it uses this information to anticipate disturbances and adjust the control signal accordingly. By understanding the process model, the feed forward controller can calculate the necessary corrective action without relying solely on feedback from the system. This allows for faster and more accurate control, as the controller can proactively compensate for disturbances before they affect the system's output.