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ECEN 605LINEAR SYSTEMS

Instructor: S. P. Bhattacharyya*(Dr. B.)

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Course information

ContactOffice: 244C, WERCemail: spb@tamu.eduTel: 979-845-7484

Assignments and Tests

I All homeworks are required.

I There will be three tests.

I Homework grade 60%

I Test grade 40%

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Syllabus

1. Single input Single output systems

1.1 Laplace Transform Review1.2 Linear Algebra Review1.3 Static and Dynamic Models1.4 State Variable and Transfer Function Models1.5 Stability and Stabilization1.6 Tracking, disturbance rejection and pole placement1.7 Classical control, Nyquist criterion and stability margins

2. Multivariable Systems

2.1 Realization Theory2.2 Stated Feedback2.3 Observers

3. Linear Quadratic Optimal Control

3.1 H2 optimal control (LQR)3.2 H∞ optimal control

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A Short History of Control

1764Watt’s Governor for speed control of steamlocomotives by negative feedback

James Watt(1736 ∼ 1819)

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1860“On Governors” Maxwell developed a thirdorder dynamic model. The characteristic rootswere functions of (m, l , k) the designparameters. Oscillations corresponded to theprosimity of the characteristic roots to the jωaxis, as in “resonant” systems such asoscillators and bridges.

James ClerkMaxwell(1831∼1879)

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1877Routh criterion developed a method ofcounting root distribution of a polynomial withrespect to the left and right half planes,without calculating the roots. Wins AdamsPrize.

Edward JohnRouth(1831∼1907)

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1892Lyapunov’s Ph.D thesis develops criteria forthe stability analysis of nonlinear systems. Aleksandr

MikhailovichLyapunov(1857∼1918)

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1900∼1910Wright Brother’s flightresearch

Orville Wright(1871∼1948)

Wilbur Wright(1867∼1912)

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1926H. S. Black invents the feedback amplifier toprovide accurate gains using unreliablecomponents. These forms the basis ofoperational amplifiers and integrated circuits,fundamental to modern control,communication and signal ( audio and video )processing systems. Black’s Amplifier.

Harold StephenBlack(April 14, 1898∼ December 11,1983)

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1932H. Nyquist develops a criterion to predictclosed loop system stability based onmeasurements of the open loop frequencyresponse of the system. Nyquist Criterion.

Harry Nyquist(February 7,1889 ∼ April 4,1976)

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1942 ∼ 45H. W. Bode, building on the work of Nyquist,develops frequency response methods fordesigning control and feedback systems usinglogarithmic plots.

Hendrik WadeBode(December 24,1905 ∼ June 21,1982)

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1940 ∼ 50Servomechanism theory is researched anddeveloped to a high level to meed the demandsof World War II. MIT Radiation Labs, NorbertWiener, H.W. Bode, W.R. Evans N. Nicholsand others drive the effort.

Norbert Wiener(November 26,1894 ∼ March18, 1964)

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1950 ∼ 60Richard Bellman inventsdynamic programming. L.S.Pontryagin develops theMaximum Principle.

Richard E.Bellman(August 26,1920 ∼ March19, 1984)

Lev Pontryagin(September 3,1908 ∼ May 3,1988 )

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1957 ∼Soviet Union launches the Sputnik.

1960 ∼Kalman introduces quadratic optimization andstate space methods. Space race is on. U.S.decides to send a man to the moon. Design ofautomatic pilots (autopilots.) Man lands onMoon July 24th 1969.

Rudolf EmilKalman(May 19, 1930∼ )

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1960’sTremendous progress in computer technology drives control andcommunication.

1970’sResearchers find that the Linear Quadratic Optimal Systems canhave very small stability margins.

1980’sResearch on Robust Control intensifies. H∞ optimal control isintroduced. Proofs of the stability of Adaptive Control Systems arepresented. Kharitonov’s Theorem and its extensions are developed.

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1990’sUAV’s, disk drives, GPS, Machine Learning Control, Robotics.Fragility of Optimal, High Order Systems.

2000’sGenomic Signal Processing, Cancer treatment as a ControlProblem, Gene manipulation and control, Nano systems andcontrol, Atomic Force Microscopy. Developments in PID Control.

2010’sControl of UAV’s, drones and driverless cars. Control of SmartGrids. Robotic surgery. Systems Biology. Flocking, Formation,Consensus Control of Multi Agent Systems.