Happenings – 24 March (2) Control Theory

My general question in control theory was: should I work thru some ancient classical design problems, as they do, with root-locus, nyquist, Nichols, and bode plots? As a minor issue, I would need to select examples from among a few books. But the design methodology appeared to be: use frequency domain analysis to estimate control system parameter values which would lead to a desirable time-domain response of the system.

It occurred to me that my computer and Mathematica® are powerful enough to show the time-domain response in real time.

I can simulate the system in the time domain. I don’t need to be predicting the time-domain effect of changing a parameter in the frequency domain: I can move a slider and see the effect of varying parameters.

Too much work, you say? On the contrary. It’s way easier than, say, multiple plots of a function at different parameter values. Basically just wrap a “manipulate” command around one plot command.

Now, I’m not talking – yet – about a complicated simulation for modeling nonlinear effects (perhaps most important would be saturation, a maxed-out control effort). What I’m saying is that simulation is cheap and requires almost no coding in Mathematica®l. This will still require that I estimate the range of parameter values, and it will require that I have some idea what I can accomplish by changing a specific parameter, so I’ll still be learning something about design. But I won’t be working in one room (frequency domain) while trying to change something in another room (time domain).

I don’t have a control system example, but in order to make sure I could do this in Mathematica®l, I used the following example from bequette. We have a transfer function with one unknown parameter tn…

I get the time-domain behavior in response to a unit step input…

A typical static presentation of the behavior of the system would look like:

(This was an illustration of “numerator dynamics”: the system eventually tends to the new set point of 1, but for some values of tn, the initial response of the system is in the wrong direction.)

There is a command called Manipulate. Apply it to a plot command, for example, and Mathematica® gives me a slider. The graph changes as I slide the blue ball. Not only an animation, but one I get to control (no pun intended). And, yes, I can have more than one slider.

Here are 3 snapshots of the slider in different positions. For this problem, the response is immediate.

As I said, why should I sit in the frequency domain trying to estimate time-domain behavior? I can watch the time domain as I change parameters.

(It took some time getting that to work; none of the help file examples included the parameter as an argument in the function definition, but the way I did it, it needs to be.)

control theory books

“… fighting your way through this book will not, in itself, make you an expert in process control.” Luyben, “Process Modeling…”, p. 7.

The following books have been added to the bibliography; the entry for carstens has been edited to reflect my now-formal categories.

Carstens, for example, described PID, but used a rate generator to shift his bode plot sideways; the schaum’s outline, by contrast, barely mentions PID, and designs lead-lag controllers instead.

I think I am going to work thru Ellis next, for his treatment of observers, namely the luenberger observer, in a classical setting.

On odd days of the month, Tewari is the book I think I want to work thru for state space properly. On even days of the month, I think I want to start with the state space chapter in Franklin et al. Then, in either case, I’ve got to curl up with Kailath’s linear systems: there’s the mathematics of state-space.

If I’m trying to look at process control, I generally pick up all three of Bequette, Stephanopoulos, and Luyben.

For continuous EE control theory, I had been working thru Franklin et al., a fine general-purpose undergraduate text. They have a second text for digital control.

Bequette, B. Wayne; Process Control: Modeling, Design, and Simulation.

Prentice Hall, 2003. ISBN 0 13 353640 8.

[controls: classical & modern, ChE, continuous; 9 mar 2008]

This is a wonderful overview. Don’t misunderstand: this is a typical “you can’t cover all this in one semester” text, but he mentions a whole lot of things, and I want more on just about everything he does… good intro to IMC (internal model control). 

This is a first course in process control. Matlab.

Carstens, James R.; Automatic Control Systems and Components.

Prentice Hall, 1990. ISBN 0 13 054297 0

[controls: classical EE continuous; 9 mar 2008]

This book caught my eye when I saw that he had transfer functions for specific devices used in control systems; it won my heart when he distinguished between the parameters in his math models and the parameters to be found in catalogs!

This is an introductory and hands-on book. 

DiStefano, Joseph J., Stubberud, Allen R., Williams, Ivan J.; Schaum’s Outlines: Feedback and Control Systems.

McGraw-Hill, 1990 (2nd ed.). ISBN 0 07 017052 5.

[controls: mostly classical, EE, continuous & discrete; 9 mar 2008]

8 of its chapters are analysis / design using nyquist / root-locus / nichols / bode. This is where I find out what mathematica can do, and what it struggles with: “just the facts, ma’am.”

This is a first course in process control; no significant computer software.

Ellis, George; Control System Design Guide.

Elsevier, 2004, 3rd ed. ISBN 0 12 237461 4.

[controls: classical, EE, mostly continuous; 9 mar 2008]

From an introduction, to motion and position control. I call it EE but he uses primarily PID. He was recommended for his treatment of “observers” in an otherwise classical EE treatment of control systems.

This is a second course in controls; proprietary software, only for PCs.

Franklin, Gene F., Powell, J. David, Emami-Naeni, Abbas; Feedback Control of Dynamic Systems.

Pearson Prentice Hall, 2006 (5th ed). ISBN 0 13 149930 0

[controls: mostly classical, EE, mostly continuous; 9 mar 2008]

This is a well-respected senior year text, and I enjoy it. It has one long state space chapter.

This is a first course. Matlab.

Kailath, Thomas; Linear Systems.

Prentice Hall, 1980. ISBN 0 13 536961 4

[linear algebra; controls: modern, EE, continuous & discrete; 9 mar 2008]

For my experience, there isn’t a lot of linear algebra here, but what there is being used thoroughly. I think it’s a great look at modern applied linear algebra, which is what it was recommended to me as.

Not a first book on the subject (neither linear algebra nor state space).

Luyben, William L.; Process Modeling, Simulation, and Control for Chemical Engineers.

McGraw-Hill, 1990 (2nd ed.). ISBN 0 07 039159 9.

[controls: classical, ChE, mostly continuous; 9 mar 2008]

I like luyben’s style. In content, I can’t see a whole lot of difference between this and Stephanopoulos; except this is a little more modern.

Multiple chapters about multivariate and about digital.

This is a first course in process control; uses Fortran rather than Matlab.

Stephanopoulos, George; Chemical Process Control.

Prentice Hall 1984. ISBN 0 13 128629 3.

[controls, classical ChE, mostly continuous; 9 mar 2008]

I think this is the classic text. It’s well written and has lots of examples and problems. One of the two books I reach for practical process control; Bequette seems a little more academic.

This is a first course in process control; no significant computer software.

Schaum’s Outlines: Feedback and Control Systems; DiStefano, Joseph J., Stubberud, Allen R., Williams, Ivan J.

McGraw-Hill, 1990 (2nd ed.). ISBN 0 07 017052 5.

[controls: mostly classical, EE, continuous & discrete; 9 mar 2008]

8 of its chapters are analysis / design using nyquist / root-locus / nichols / bode. This is where I find out what mathematica can do, and what it struggles with: “just the facts, ma’am.”

This is a first course in process control; no significant computer software.

Tewari, Ashish; Modern Control Design with Matlab & Simulink.

Wiley, 2002. ISBN 0 471 49679 0.

[controls: modern, EE, mostly continuous; 9 mar 2008]

“This book aims at introducing the reader to the basic concepts… while covering in detail what may normally be considered advanced topics, such as multivariable state-space design… optimal control, Kalman filters, robust control, and digital control.”

ch 2 is a summary of classical control theory. 

A first course in state space. Matlab.

more books

The following books have been added to the bibliography page. They were mentioned in today’s “Happenings”. One is control theory, two are upper division physics books, and one is a popular book about physics.

Carstens, James R.; Automatic Control Systems and Components.

Prentice Hall, 1990. ISBN 0 13 054297 0

[classical controls; 25 feb 2008]

this book caught my eye when i saw that he had transfer functions for specific devices used in control systems; it won my heart when he distinquished between the parameters in his math models and the parameters to be found in catalogs!

This is an introductory and hands-on book. 

Zwiebach, Barton; A First Course in String Theory.

Cambridge University Press, 2004. ISBN 0 521 83143 1.

[string theory; 25 feb 2008]

This is the text for an upper-division couse at M.I.T.

Lederman, Leon, with Teresi, Dick; The God Particle.

Bantam Doubleday Dell, 1993. ISBN 0 385 31211 3.

[popular physics, particle physics; 25 feb 2008]

This is a popular book, and I had forgotten just how much fun it was to read. Even if you’ve seen The Standard Model of particles, you may enjoy this book; and if you don’t know the standard model, this is a fine place to start. (The title refers to the Higgs boson; it was that or the god-damned particle, he said.)

Griffiths, David; Introduction to Elementary Particles.

Wiley-VCH, 1987. ISBN 0 471 60386 3.

[elementary particle physics; 25 feb 2008]

An upper-division text. I really like his style, as well as his apparent precision. For an example of style: “In general, when you hear a physicist invoke the uncertainty principle, keep a hand on your wallet.”