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Something is linear if it can be modeled by a linear equation, i.e.
y = Ax + B
Where A and B are constants.
Form example, voltage an current in a resistor are linear:
V = I R
V is y
I is x
A is R
B is 0
Non linear is everything else.
For example, the voltage and current in a diode have an exponential relationship over some range.
There can be more variables also, but for a linear system, only the first power of each variable appears and no other functions;
z = Ax + By + C
if you have N independent variables in a linear system, it takes N equations to describe the system.
Bob
y = Ax + B
Where A and B are constants.
Form example, voltage an current in a resistor are linear:
V = I R
V is y
I is x
A is R
B is 0
Non linear is everything else.
For example, the voltage and current in a diode have an exponential relationship over some range.
There can be more variables also, but for a linear system, only the first power of each variable appears and no other functions;
z = Ax + By + C
if you have N independent variables in a linear system, it takes N equations to describe the system.
Bob
hevans1944
Hop - AC8NS
More particularly, if a control system can be modeled or described by linear differential equations it is linear. Every other control system is non-linear. All real (stuff you can actually build) control systems are non-linear but are often approximated as linear over some operating range so their behavior can be approximately predicted.
Wikipedia provides a broad overview and definitions of linear and non-linear systems. Also visit this Google web page search result for links to other sources of information.
Wikipedia provides a broad overview and definitions of linear and non-linear systems. Also visit this Google web page search result for links to other sources of information.
Last edited:
hevans1944
Hop - AC8NS
It appears, at least to me, that you do not yet have the necessary math skills to analyze or understand control systems. A prerequisite to the study of linear control systems is the ability to set up and solve a system of linear differential equations that describe the control system. For simple linear control systems, the equations can be solved analytically and solutions obtained after specifying initial conditions.
Back in the day, analog computers were used to setup the initial conditions and solve the characteristic equations using linear analog circuits such as linear amplifiers, integrators, and (sometimes) differentiators as necessary to describe a particular control system. Today, numerical solutions are found using digital computers, but you must still understand the math to set up the programming. More important than the math, you must also understand how to model the physical components of a control system and be aware of the limitations of your model. GIGO principle in effect here: Garbage In, Garbage Out.
You can begin to learn about control systems by starting your journey analyzing, building, and measuring simple analog control systems. Many budding engineers start with linear amplifiers, implemented with operational amplifiers using negative feedback. Learn all you can about how to calculate their closed-loop performance in terms of gain, stability, bandwidth, response time, noise performance, and output capability.
It will be many years (if ever) before you will be able to analyze and understand non-linear control systems. Not everyone even gets that far. I know I didn't. After graduating from college with a bachelor of electrical engineering degree, I gave up my formal study of control systems and never did pursue non-linear control systems. Bottom line: no rocket science for me. There are far more capable and smarter people to travel that road than I.
Good luck in your studies and your effort to learn English as a second language. If you do master English, go on to try learning Mandarin and perhaps Japanese and German. Some people do seem to have a knack for learning foreign languages. I studied German in high school and in my first year of college to no avail, but I may try again to learn in retirement. It would be nice to able to speak and read French, too, because it is such a melodic language. The point here is to aim high and put forth your best effort.
Back in the day, analog computers were used to setup the initial conditions and solve the characteristic equations using linear analog circuits such as linear amplifiers, integrators, and (sometimes) differentiators as necessary to describe a particular control system. Today, numerical solutions are found using digital computers, but you must still understand the math to set up the programming. More important than the math, you must also understand how to model the physical components of a control system and be aware of the limitations of your model. GIGO principle in effect here: Garbage In, Garbage Out.
You can begin to learn about control systems by starting your journey analyzing, building, and measuring simple analog control systems. Many budding engineers start with linear amplifiers, implemented with operational amplifiers using negative feedback. Learn all you can about how to calculate their closed-loop performance in terms of gain, stability, bandwidth, response time, noise performance, and output capability.
It will be many years (if ever) before you will be able to analyze and understand non-linear control systems. Not everyone even gets that far. I know I didn't. After graduating from college with a bachelor of electrical engineering degree, I gave up my formal study of control systems and never did pursue non-linear control systems. Bottom line: no rocket science for me. There are far more capable and smarter people to travel that road than I.
Good luck in your studies and your effort to learn English as a second language. If you do master English, go on to try learning Mandarin and perhaps Japanese and German. Some people do seem to have a knack for learning foreign languages. I studied German in high school and in my first year of college to no avail, but I may try again to learn in retirement. It would be nice to able to speak and read French, too, because it is such a melodic language. The point here is to aim high and put forth your best effort.
hevans1944
Hop - AC8NS
You might want to learn it so you can talk to Chinese business people. In case you didn't notice, China is becoming a rather large trading partner with just about everyone in the world. Might help you financially to speak and read at least one dialect of Chinese. But maybe you can just sit in front of your computer and rely on Google Translate. Your choice.
You should Google some of those questions you are asking, and then come back here for clarification. For example, there is no such thing as an "analog pc" unless you want to consider a slide rule as an analog personal computer. I still have my Post slide-rule, just in case there is failure of civilization and all the electricity goes away. I could still do calculations using the slide-rule, by candle light if necessary, but certainly during the day. An abacus (still used in China and other Asian countries) comes in handy for doing additions and subtractions, but mine is packed away somewhere and I have not used it for many years.
