# BME 444 - Exam 2 Instructional Objectives

# Exam Date: Tuesday, May 7, 12:00-3:20

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

**Nise 1**

- Define control system
- Define characteristics of a system response
- Define open loop and closed loop control systems
- Define input/reference, controller, summing juction, process/plant, output/controlled variable, output sensor/transducer
- Draw a block diagram of a control system given a description
- Describe the design process for feedback control systems
- Classify differential equations

**Nise 2**

- Explain how to use Matlab to perform a Laplace transform, inverse Laplace transform, and partial fraction expansion
- Convert a differential equation into Laplace notation
- Create a transfer function of a system given a differential equation
- Create a transfer function of an electrical circuit
- Solve differential equations of systems
- Create a transfer function of a translational mechanical system
- Create a transfer function of a rotational mechanical system
- Create an electric circuit analog of a mechanical system
- Derive the transfer function of systems with gears

**Nise 3**

- Create a state-space representation of linear, time-invariant systems
- Model systems in state space
- Convert a transfer function to state space and vice versa

**Milhorn 8**

- Define differences between physiological and technological control systems
- Draw control system representations of physiological systems given a description
- Find the equilibrium point between two graphs in a physiological control system
- Linearize a non-linear function

**Milhorn 3**

- Model physiological systems using mechanical (translational and rotational) and electrical elements
- Use a mass balance to model a physiological system
- Use Fick’s law to model a physiological system
- Write differential equations for 0, 1st, and 2nd order chemical reactions

**Nise 4**

- Use poles and zeroes of a transfer function to determine system time response
- Qualitatively describe the transient response of 1st order systems
- Calculate time constant, rise time, and settling time of 1st order systems
- Identify the four types of responses for 2nd order systems given pole location, and vice versa
- Write the general response equation of 2nd order systems given the pole locations
- Find the damping ratio and natural frequency of a 2nd order system
- Calculate the settling time, peak time, percent overshoot, and rise time for an underdamped 2nd order system
- Determine if a higher-order system can be approximated as a 2nd order system
- Determine the effect of adding poles and zeros to a 2nd order system

**Nise 5**

- Draw basic elements of block diagrams
- Simplify cascaded and parallel blocks
- Simplify a control system with feedback into a single block
~~Rearrange blocks before and after summing junctions and pickoff points~~- Adjust the design of a feedback system to achieve desired outputs
~~Convert a block diagram to a signal-flow graph and vice versa~~~~Use Masonâ€™s rule to simplify a signal-flow graph~~~~Convert a state-space representation to a signal-flow graph and vice versa~~

**Nise 6**

- Define stable, unstable, and marginally stable in terms of natural response and bounded-input/bounded-output (BIBO)
- Generate a Routh Table given an equivalent closed loop transfer function

**Nise 7**

- List the types of test inputs
- Calculate SS error for unity feedback systems in terms of \(T(s)\) for step, ramp, and parabolic inputs
- Calculate SS error for unity feedback systems in terms of \(G(s)\) for step, ramp, and parabolic inputs
- Calculate static error constants, \(K_p\), \(K_v\), \(K_a\)
- Determine system type and characteristics based on static error constants and vice versa
- Calculate the steady state error in a unity feedback system due to an input and a disturbance
- Calculate the steady state error in a non-unity feedback system due to an input and a disturbance
- Calculate the actuating signal in a non-unity feedback system
- Calculate the sensitivity of a function to a parameter

**Nise 8**

- Calculate magnitude of \(F(s)\) given \(s\)
- Determine number of poles from a root locus plot
- Determine if a point is on the root locus plot
~~Sketch a root locus plot given G(s) and vice versa~~

**Nise 9**

- Convert magnitude to decibels and vice versa
- Calculate the magnitude and phase of a transfer function
- Given a frequency, find a magnitude/phase from a Bode plot (or vice versa)
- Determine the stability, gain margin, and phase margin of a system given a Bode plot
- Determine the range of stability of a system from a Bode plot
- Calculate the transfer function of a system with a time delay
- Define the changes that a time delay causes in a Bode plot
- Define closed loop gain, open loop gain, and loop gain
- Given the poles of \(G(s)H(s)\) and a Nyquist plot, determine if a system is stable
- Determine the range of stability of a system from a Nyquist plot
- Determine the gain margin and phase margin from a Nyquist plot