# EECS 160B Sampled-Data and Digital Control Systems (2012-2013)

#### EECS 160B Sampled-Data and Digital Control Systems

**EECS 160B Sampled-Data and Digital Control Systems (Credit Units: 3)** Sampled-data and digital control systems. Sampling process and theory of digital signals; z-transform and modeling; stability; z-plane, frequency response, state-space techniques of digital control system synthesis. Prerequisite: EECS31; EECS160A, EECS160LA. (Design units: 2)

1. Model sampled-data digital control system using z domain transfer functions. (EAC a, EAC d, EAC j, EAC k)

2. Analyze a digital control system in z domain. (EAC b, EAC c, EAC d, EAC e, EAC g, EAC h, EAC i, EAC j, EAC k)

3. Do stability analysis in the z domain. (EAC b, EAC c, EAC d, EAC e, EAC g, EAC h, EAC i, EAC j, EAC k)

4. Perform root locus design in z domain. (EAC b, EAC c, EAC d, EAC e, EAC g, EAC h, EAC i, EAC j, EAC k)

5. Perform frequency domain design. (EAC b, EAC c, EAC d, EAC e, EAC g, EAC h, EAC i, EAC j, EAC k)

The discrete mathematics of signals and systems, including sampling, difference equations, discrete convolution, z-transforms, and discrete Fourier transforms; the design methods for analog control systems, including root locus, Bode, Nyquist methods for lead networks, lag networks, lead-lag networks, and PID compensators.

- Digital vs. analog control systems; sampling and quantization; discrete-time approximations, PID controllers. (week 1)
- Difference equations and discrete-time transfer functions; state-variable descriptions and canonical forms; pulse response and stability; sampled-data systems. (week 2)
- State-space forms; numerical computation, nonlinear models; dynamic response of a discrete-time system. (week 3)
- Step response, pulse response and related responses for discrete-time systems. Performance specifications, rise time, settling time, overshoot, damping ratio, natural frequency; frequency response, frequency response functions for discrete-time systems, and use of discrete Fourier transform. (week 4)
- Sampled-data systems; sample and hold circuits; sampled signal spectrum, aliasing, and choosing a sampling frequency; block diagrams for sampled-data systems, block diagram algebra; intersample ripple. (week 5)
- Design via discrete equivalents; numerical differentiation and integration, forward, backward and trapezoidal rules; bilinear and prewarping of frequency domain specifications; state space equivalents; zero-pole matching equivalents. Midterm examination. (week 6)
- Design via transformation techniques; error coefficients for discrete-time systems; discretizing analog designs; direct design by root locus; specifications in the z-plane. (week 7)
- Discrete-time root locus, design in the z-plane; constant damping and frequency lines; design by pole-zero placement. (week 8)
- Design in the frequency domain; Bode plots and Nyquist plots; stability; gain and phase margins; sensitivity analysis functions. (week 9)
- Low frequency gains and error coefficients; compensator designs; direct design by characteristic polynomials. (week 10)

Meets for 3 hours of lecture and 1 hour of discussion each week for 10 weeks.

Not required; however, MATLAB is available in several open computer laboratories for the students to use.

None.

Contributes toward the Electrical Engineering Topics Courses and Major Design experience.

Students are taught how to identify a control system design problem; to develop analytical performance specifications from given requirements; to formulate appropriate mathematical models of analog electro-mechanical systems; to develop sampled-data equivalent models from the analog models; and to design digital models of appropriate compensation networks to satisfy the performance specifications.

- Weekly Home work assignments: 10%
- Midterm exam: 40%
- Final exam: 50%
- Total: 100%

Mathematics and Basic Science: 0.0 credit units

Computing: 0.0 credit units

Engineering Topics: 3.0 credit units

Engineering Science: 1.0 credit units

Engineering Design: 2.0 credit units