**EEE 686
Adaptive Control**

Spring
2012, MW
7:30-10:15, GWC 379

**Instructor: Kostas Tsakalis, GWC
358, 965-1467, **

**Office Hours:** See Schedule on personal web page

**Textbook:** Class notes and selected publications

**Other References:**

S. Sastry and M. Bodson, Adaptive Control:
Stability, Convergence and Robustness. Prentice Hall, 1989;

P. Ioannou and J. Sun, Robust Adaptive
Control. Prentice Hall, 1996.

R.R. Bitmead, M. Gevers and V. Wertz, Adaptive
Optimal Control: The Thinking Man's GPC. Prentice Hall International
Series in Systems and Control Engineering, Ed. M.J. Grimble, Sydney, 1990.

G.C. Goodwin and K.S. Sin, Adaptive
Filtering Prediction and Control. Prentice Hall, Englewood Cliffs, NJ,
1984.

K.J. Astrom and B. Wittenmark, Adaptive
Control. Addison-Wesley, 1989.

K. Narendra and A. Annaswamy, Stable Adaptive
Systems. Prentice Hall, 1989.

**Course Description**

Linear systems are often used to approximate complex systems in control applications. In such cases the parameters of the linear model may be partially unknown and/or time-varying. Adaptive controllers have been developed to counteract such forms of parametric uncertainty and improve the closed loop performance. This is typically achieved by using on-line identification techniques to adjust the parameters of a linear control law. The course addresses the fundamental theoretical principles and practical issues arising in the analysis and design of adaptive controllers. Homework projects, consisting primarily of computer simulations, are designed to expose the basic properties and limitations of adaptive systems and consitute an integral component of the instruction.

**Main Topics:**

Parametric Models, Adaptive
Identification, Persistence of Excitation, Adaptive Control, Stability and
Convergence Properties, Robustness of Adaptive Controllers, Performance
Considerations.

**Prerequisites:**

Linear Systems (EEE 582) or equivalent;
Nonlinear Systems (EEE 586) or equivalent; or instructor's approval.

MATLAB/SIMULINK programming skills.

Some knowledge of applied (numerical)
optimization techniques is desired, but not necessary.

**Grading:**

Design /Simulation projects and other homework.

Typically: A > 85 > B > 75 > C >
60 > ...

**Important Dates:**

**Final Exam: Last day of class, 4/23**

*HW Assignments,
Handouts*

**Reading material:**

Old Lecture Notes (c.1993)

Notes on adaptive algorithms

Notes on applied optimization

Other notes (K. Tsakalis and P. Ioannou,
Linear Time-Varying Systems: Control and Adaptation, Prentice Hall, 1993.
Note: the book was reprocessed to letter size; original table of contents is
not consistent.)

HW#1

**Problem:**

Consider the system G(s) = [4s+25]/[s^{2} + 6s +25]. Write a linear
parametrization and estimate its parameters

from input-output data. Use:

1. PE input signals
(e.g., input = random binary sequence (RBS), summation of several sinusoids,
etc.)

2. Non-PE input signals
(e.g., step, one sinusoid).

Try different estimation algorithms and plot the estimation error and the
parameter error. Discuss your findings.

(In the interest of expediency, you may use reasonable discretization approximations)

Next, design and simulate a bursting scenario with a bounded disturbance of
amplitude 0.1 entering

at the summation node between the two coprime factors.

(For an LS estimator implemented in SIMULINK blocks, see here.)

HW#2

**Problem:**

For the system of HW #1, design various controllers and analyze their
properties.

Consider controllers designed to achieve Pole-Placement (PPC), LQ (LQG), and
Model-Reference (MRC) objectives.

Tune the controllers such that the closed-loop bandwidth is roughly 2x the
open-loop bandwidth. For the MRC,

choose the reference model as a 1st order transfer function with the indicated
bandwidth and unity DC gain.

For all controllers, study the magnitude of sensitivity and complementary
sensitivity transfer functions.

(Notice that in the MRC case there is significant freedom in the selection of
the auxiliary filter.)

1. Consider controllers with and without integral action.

2. For each control law (PPC, LQG, MRC) select one design and develop a
realization that is suitable

for adaptive control implementation. In particular, for the MRC consider a
direct adaptive control implementation.

HW#3

**Problem:**

For the system of HW #1, design and implement indirect adaptive controllers
(LQG, PPC) and analyze their properties.

Use the control objectives from HW#2 and controllers with integral action.
Employ any suitable parameter estimator.

(You may try a few before selecting one.) Test the adaptive controllers with a
low-frequency, pulse-train reference input.

Use initial conditions for the parameter estimates that are 10-20% different
from the target parameters.

Consider cases with and without "random" disturbances, step
disturbances, and the burst-inducing disturbance

of HW#1. In the latter case you should include a low-amplitude PE component at
the plant input so that parameter

drift occurs during the zero-reference input intervals.

Compare the results against the response of a well-tuned, fixed controller.

HW#4

**Problem:**

For the system of HW #1, design and implement direct MRAC's and analyze
their properties.

Use the control objectives from HW#2 and MRC controllers with and without
integral action. Employ any suitable

parameter estimation scheme to perform direct adaptation.

Test the adaptive controllers with a low-frequency, pulse-train reference
input.

Use initial conditions for the parameter estimates that are 10-20% different
from the target parameters.

Consider cases with and without "random" disturbances, step
disturbances, and the burst-inducing disturbance

of HW#1. In the latter case you should include a low-amplitude PE component at
the plant input so that parameter

drift occurs during the zero-reference input intervals.

Compare the results against the response of a well-tuned, fixed model-reference controller.