# Exam Date: Tuesday, May 9, 12:00–3:20 PM.

These instructional objectives provide you with a guide for learning the course material. During the examination you should be able to:

Lesson 1

1. Define control system, system law, transfer function, system properties
2. Explain how engineers and scientists approach systems
3. Define open loop and closed loop control system
4. Define input/reference, controller, summing junction, process/plant, output/controlled variable
5. Draw a block diagram of a system given a description

Lesson 2

1. Convert a differential equation into LaPlace notation, and vice versa
2. List the four standard types of inputs to systems
3. Classify differential equations
4. Create transfer functions of electrical circuits

Lesson 3

1. Create transfer functions of translational mechanical systems
2. Create transfer functions of rotational mechanical systems
3. Define linearly independent motion, degrees of freedom

Lesson 5

1. Create transfer functions of compartment models
2. Create transfer functions of hydraulic systems

Lesson 6

1. Create a state-space representation of linear, time-invariant systems

Lesson 7

1. Convert a transfer function to state space and vice versa
2. Convert a transfer function to a DE and vice versa

Lesson 8

1. Use MATLAB commands or Simulink to simulate the response of a system to inputs
2. Simulate systems using transfer functions, state-space representations, or integrator-blocks

Lesson 9

1. Write the DE for a first order system
2. Determine the time constant, rise time, and settling time of a first-order system from its differential equation, sketch, or LaPlace transform, or vice versa
3. Sketch the response of a first-order system from its equation or LaPlace transform
4. Calculate the steady state value of a first-order system, given its DE or LaPlace transform
5. Sketch the response of a first-order system to an impulse or step input

Lesson 10

1. Write the DE of a second order system
2. Determine the roots of a second order system
3. Classify the output of a second order system as undamped, underdamped, critically damped, or overdamped
4. Write the equation form of the step response of a second order system
5. Calculate the damped frequency of an underdamped second-order system
6. Calculate $\zeta$, $\omega_n$, $\omega_d$, $T_r$, $T_p$, $%OS$, and $T_s$ of a system
7. Determine values for components of a system required to meet design specifications

Lesson 11

1. Calculate the magnitude and phase of a transfer function given a frequency
2. Convert phase angle to time shift and vice versa
3. Use magnitude and phase to predict the relative shape of input and output waveforms
4. Convert magnitude to dB and vice versa
5. Read values from a phase and magnitude plot

Lesson 12

1. Calculate the cutoff frequency, time constant, and DC gain of a first-order system
2. Calculate bandwidth of first and second-order systems
3. Explain effect of $\zeta$ on the frequency response of second-order systems
4. Design filters with specific cutoff frequencies
5. Explain what a filter does
6. Calculate the location of the peak in the frequency response of a second-order system

Lesson 13

1. Manipulate block diagrams
2. Define and calculate open-loop gain, loop gain, open-loop transfer function, and closed-loop transfer function
3. Draw control system diagrams from a description of a system

Lesson 14

1. Find the equilibrium point of static control systems graphically and with MATLAB
2. Implement static control systems in Simulink

Lesson 15

1. Explain the difference between first- and second-order transient system responses with and without feedback
2. Explain the effect controller gain has on system output for first- and second-order systems
3. Calculate the output and/or transfer function of a system with feedback and a disturbance
4. Calculate $\tau$ for first-order systems with feedback
5. Calculate the steady state value for first- and second-order systems with feedback and a disturbance, given a step input

Lesson 16

1. Calculate $\zeta$ and $\omega_n$ for 2nd order systems with feedback and disturbances if the controller is P, PD, or PID
2. Calculate the steady-state output of a system given a step input and a P, PD, or PID controller
3. Describe the effect a P, PD, or PID controller has on the system response

Lesson 17

1. Calculate steady-state error for a system with or without a disturbance for any input
2. Determine system type and use this information to infer characteristics of the system
3. Calculate the error constant of a system

Lesson 18

1. Define stability in terms of BIBO
2. Describe how gain, and the controller, can make a system unstable
3. Determine if a system is stable
4. Generate a root locus plot for a system
5. Determine the pole location on a root locus plot for a specific $K$ (gain) value
6. Determine a maximum $K$ (gain) value for a system before it becomes unstable
7. Determine system response given gain, or vice versa
8. Calculate the gain and phase margin of a system

Lesson 19–20

1. Explain the causes of Type I and Type II diabetes
2. Explain how Type I and Type II diabetes affect the glucose and insulin response compared to a non-diabetic
3. Sketch a closed-loop feedback system that could be used to regulate glucose levels
4. Write the linear differential equations that model glucose homeostasis within the body

Lesson 21

1. Summarize the effect of changing $K_P$, $K_I$, and $K_D$ gains on PID controllers
2. Tune PID controllers using the reaction-curve method
3. Tune PID controllers using the ultimate gain method

Lesson 22

1. Determine the effect of zeros on system response
2. Explain how poles can move without changing system response ($\zeta$ or $\omega_n$)
3. Use root locus to design a controller
4. Use frequency response to design a controller

Lesson 23

1. Explain the purpose of the PID Tuner
2. Describe how adjusting Response Time and Transient Behavior in the PID Tuner affect $K_P$, $K_I$, and $K_D$
3. Describe what Save as Baseline does in PID Tuner