# 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**

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

**Lesson 2**

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

**Lesson 3**

- Create transfer functions of translational mechanical systems
- Create transfer functions of rotational mechanical systems
- Define linearly independent motion, degrees of freedom

**Lesson 5**

- Create transfer functions of compartment models
- Create transfer functions of hydraulic systems

**Lesson 6**

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

**Lesson 7**

- Convert a transfer function to state space and vice versa
- Convert a transfer function to a DE and vice versa

**Lesson 8**

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

**Lesson 9**

- Write the DE for a first order system
- 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
- Sketch the response of a first-order system from its equation or LaPlace transform
- Calculate the steady state value of a first-order system, given its DE or LaPlace transform
- Sketch the response of a first-order system to an impulse or step input

**Lesson 10**

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

**Lesson 11**

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

**Lesson 12**

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

**Lesson 13**

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

**Lesson 14**

- Find the equilibrium point of static control systems graphically and with MATLAB
- Implement static control systems in Simulink

**Lesson 15**

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

**Lesson 16**

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

**Lesson 17**

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

**Lesson 18**

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

**Lesson 19–20**

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

**Lesson 21**

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

**Lesson 22**

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

**Lesson 23**

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