Subashish
Home
Research
Software
Courses
Students
Workshop
Reading Materials

Control Engineering (ELL225) (Semester-II, 2022-23)

  • Lectures timing and venue: (11:00 AM – 12:00 Noon, On Tuesday, Thursday and Friday, LH111)

  • Tutorials timing and venue: (1:00 PM – 2:00 PM, On Mnday-T2, Tuesday-T3, Thursday-T4 and Friday-T1, LH517)

TAs:

  • Bhargavi Chaudhary (eez208419@ee.iitd.ac.in),

  • Anchita Dey (eez207552@ee.iitd.ac.in)

  • Rudra Sen (eez218218@ee.iitd.ac.in)

  • Poulomee Ghosh (eez208436@ee.iitd.ac.in)

  • Nitish Bishnoi (eea222005@ee.iitd.ac.in)

  • Ashwin K M (eea222010@ee.iitd.ac.in)

  • Sabyasachi Kundu (eea222698@ee.iitd.ac.in)

  • Ananya Mohit (Ananya.Mohit.ee119@ee.iitd.ac.in)

Syllabus

Mathematical Modeling

System Analysis

  • Phase margin (PM) and gain margin (GM) (Lecture 25),

  • Controllablity, observability

Controller Design

Tutorial Problems

Evaluation

  • Minor 1: 15%

  • Minor 2: 20%

  • Major: 40%

  • Course project: 25%

Reference books

  • Control System Engineering, by N. S. Nise (Wiley)

  • Modern Control Engineering, by K. Ogata (Prentice Hall)

  • Modern Control Systems, by R. C. Dorf and R. H. Bishop (Prentice Hall)

Course Project

Riderless bicycle control

The objective of this course project is to develop an autopilot for a rider-less bicycle, as shown in below figure (image taken from Ref. 1), to keep it in upright position with respect to some specified speeds. The details on bicycle dynamics can be found in Ref. 1. Considering following quantities as: i) states: roll angle, roll rate, steer angle and steer rate, ii) input: steering torque and iii) output: roll angle, the dynamics of the bicycle can be expressed as a fourth order linear model as in Ref. 1. The linear model is velocity dependent (often referred to as linear parameter varying model), where one can obtain linear time-invariant state space models corresponding to the different fixed velocities. For this project, consider following three fixed velocities: v1 = 0 meter per second (mps), v2= 3.5 mps and v3 = 5 mps.

Following tasks need to be performed in this project. You may use MATLAB, Scilab or any other computing softwares.

  • Obtain state space models and transfer functions of the bicycle at velocities: v1, v2 and v3. Compute poles and zeros, and the eigenvalues of system matrix A, for the obtained three state space models and transfer functions.

  • Show the time response of system, for: i) zero input with (any) non-zero initial states and ii) unit step input.

  • Analyze stability (asymptotic stable, marginally stable, BIBO stable) of bicycle corresponding to the velocities: v1, v2 and v3.

  • Draw Nyquist plots, Bode plots and Root-locus, considering the open loop transfer functions that are obtained for the velocities: v1, v2 and v3. Describe in your report, which plots are for closed loop system and which are for open loop systems. Give some explainations/concluding remarks (stability, phase and gain margins) that you observe for different plots.

  • A control system (autopilot) needs to be designed to keep the bicycle in vertical upright position. Is it possible to stabilize the bicycle (keep the bicycle in vertical upright position), with the help of appropriate automatic control action (steering torque provided by the actuator), at velocities: v1, v2 and v3. If yes, then design such feedback controllers. Take your own design specifications in terms steady state error, damping ratio and settling time, and then, design controllres to achive these objectives. Three different controllers may be proposed for velocities: v1, v2 and v3. Implement the designed controllers, and show the step input response of the closed loop system. You may use “sisotool” available in MATLAB (or similar simulation software) for designing controllers.

subashish