about transisent response

Hi, firends:
I am studying automatic control system. Seemsly, only in second system or first system the theory offers the mathmatic equation for settling time and
overshot, for the high order system, we only have to get the diagram of time response to check overshot and settling time, isn't it? Thank you very much!
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yang hong wrote:

More or less. You could, if you were persistent, come up with a mathematical equation for each different type of system. Doing so, however, would take more time out of your life than you'd ever save by diagramming and checking each instance you run into.
Frankly, in my ever so humble opinion the primary value of the various performance calculations is more to give you an idea of the effect of system characteristics on the system performance, rather than to have a firm guide for system design.
--

Tim Wescott
Wescott Design Services
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'...the theory...' to which you refer is actually the mathematics of differential (or possibly difference) equations and their solutions. This topic is not exclusive to automatic control. Because automatic control is primarily concerned with the dynamic response of feedback control systems, it uses that same mathematics that has been developed over hundreds of years (since Newton) to model and understand the dynamic response of any physical system, whether mechanical, electrical, biological, etc. Simple and memorable analytical solutions are readily available for low-order linear differential equations, and because so many real-world systems can be approximated by 1st, 2nd-order dynamic responses, then any engineer concerned with system dynamics in any discipline (not just in control engineering) needs to be familiar with the essential characteristics and the shortcuts and rules-of-thumb that can be used to describe their behaviour. For higher-order equations the analytical solutions can be onerious to resolve, and in any case they do not have a form that is indicative of the time-response: there are no simple equivalents of things like natural frequency and damping ratio that can be picked-out from the analytical solution. So one, turns to numerical solutions and response plots.
Kelvin B. Hales Kelvin Hales Associates Limited Consulting Process Control Engineers E-mail: snipped-for-privacy@khace.com Web: www.khace.com
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Kelvin Hales wrote:
...

...
My hat is off to you, Sir!
That is a cogent summary and statement of purpose that belongs in the introductions to texts on math and engineering. Unfortunately many engineers reach retirement without ever figuring that out.
Jerry
--
Engineering is the art of making what you want from things you can get.

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I thank you! (Now, for my next trick....)
Kelvin B. Hales Kelvin Hales Associates Limited Consulting Process Control Engineers Web: www.khace.com
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I spent many years in Systems Analysis which encompassed the working and understanding of control systems (hydromechanical,analog & digital). Unlike what typically occurs in a plant, system response was very fast; in the .020 to 3 sec time frame--control of the steady state and transient response of a jet engine. I'm not into the conceptual mathematical modeling that defined the dynamics of the complete system but once that was out of the way, got very involved into the block (functional & logic) diagrams. These systems are very complex usually with more than one parameter controlling the engine at the same time (eg. speed, temperature). Add to that the effects of a variable exhaust nozzle and an afterburner system and you end up with a nightmare of interaction between several control loops transitioning (on the fly) from one control mode to another. Then you have the fact that the dynamic response of the engine does not remain the same as the operating conditions change--You have to control this beast from sea level static up to Mach 2.0; from sea level to 60,000 ft. and at inlet temperatures of minus 65 F to 130F. So the control system has to be flexible and robust enough to provide a transient response that meets rigid requirements and at the same time protects against overspeed, overtemperature, flameouts, stall etc. and to transition into any one of a number of failure modes in the event there is a system malfunction. It is next to impossible to analytically and mathematically define transient system behavior under all the operating conditions noted above. So what's the alternative?? What has not been discussed in this thread and what we relied very much on was the use of a transient model. The model allowed us to simulate any operating condition and any transient and gave us a good insight into predicting the behavior of the engine and to observe the time response of any defined parameter, control or engine.. More importantly, however, was the ability to input any operating condition and simulate any transient (throttle push) while in the throes of investigating and troubleshooting a field problem. There was a pretty big separation between those that did the analytical modeling and those of us that had to work with the hardware and diagnose/troubleshoot and fix operating problems. Having said all this, I guess my purpose was to interject and mention that one can only go so far with the mathematics, stability plots and analytical methods. Do those of you involved in plant systems etc. stop with the block diagrams or do you move on into developing the transient models? MLD
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Actually, the process guys build dynamic models for training purposes and for doing gross tests of the controls for the more complex process (not necessarily the more complex loops).
But in the end we build the plant, make all controllers adjustable and then tune the controls live during early operations. If things get seriously out of hand, the automatic shutdowns will cover our ass, save our necks, etc. I understand this procedure is not optimal for aircraft :-) Or is that why test pilots have parachutes?
Walter.
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MLD wrote:

What do you mean by a transient model? Is this a linearized mathematical model at one operating point, or do you measure the response of an engine, or what?
I do a lot of work with small motion controllers for production machines. On those systems I generally start from a mathematical model which I use to inform the process of setting sampling rates, determining required ADC and DAC accuracy, and coming up with the initial controller structure. Once I have real hardware I do sine sweeps to measure responses, then use that to feed back into the loop tuning. I have not so far, however, needed to deal with the range of operating conditions that you do.
--

Tim Wescott
Wescott Design Services
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above. So

what
allowed
good
time
any
between
with
that
analytical
block
To answer your question--Transient model is a mathematical simulation of the engine and control system. The engine is defined via the thermodynamics of the compressor, combustor, turbine, the mechanical components etc. It is not a linear model as there many functional curves that define the thermodynamic behavior and a whole slew of time constants as a function of the inlet conditions (altitude, Mn, pressure recovery, inlet duct losses etc.). The engine operating requirements change dramatically as a function of the flight conditions and these changes have to accounted for in the Model. There are also restraints that must be included in the Model-- such as --stall characteristics, combustor blowout (flameout) boundaries, compressor stability maps to mention a few. The thermodynamics of the afterburner system and so on. Then there is the control system which is designed to provide the steady state and transient operation as well as to protect the engine against itself. Again, the control system dynamics are not linear and are biased by the operating conditions--fuel flow, pressure, servo flow to the various control components, engine (pump) speed and so on. These all have to be built into the Model. And as previously noted, the Model allows us to look at any parameter, engine or control as a function of time or any number of parameters plotted against one another. When making a design change to fix a problem at sea level or altitude for example, the Model is used to evaluate the change over a range of flight conditions through out the flight envelope, altitude and Mn, to insure no surprises when it gets into the air. When I said that things happen very quickly I guess quickly is a relative term based on what you, or others, might define as fast. Let me give an analogy of the time domain that we often deal with. You have a tachometer in your car--when you step on the gas the tach moves, seemingly, almost simultaneously with the change in the gas pedal position. Well, most of my work took place in the time frame between stepping on the gas and the initial movement of the tach. Think about it--a lot of things happen in that time frame. Step on the gas pedal--linkages/cables have to move--throttle position changes increasing the air flow into the engine and increases the demand for fuel --the fuel pump responds increasing fuel flow--the increased fuel mixes with the air and is drawn into the cylinder--at the right time the spark plug fires--the fuel/air mixture ignites powering the piston resulting in a change in engine speed.--All of this takes maybe 20+ millisec or so. When you get into looking at something like a compressor stall, you're dealing with .005-.010 secs in trying to figure out what happened to cause the stall. Don't know if I actually answered your question or not--just seemed to have been carried away <g>. MLD
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So
what
allowed
good
with
analytical
block
I assumed 'transient model' was synonymous with 'dynamic model'; as in, for example, dynamic simulation.
Kelvin B. Hales Kelvin Hales Associates Limited Consulting Process Control Engineers E-mail: snipped-for-privacy@khace.com Web: www.khace.com
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You assume correctly--transient Model>>Dynamic Model.>>Dynamic Simulation. All mean the same to me. MLD
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MLD wrote:

Ah. I was hoping that was the case, because that's what I thought you meant.
--

Tim Wescott
Wescott Design Services
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Although here we do actually maintain a very clear distinction between the activities of 'modelling' and 'simulation' and the results of those activities; i.e. 'models' and 'simulations. Especially since there is more than one way of finding the solution, in simulation, to any given model; e.g. sequential vs. equation-based solvers, choices of numerical integration methods, different simulation software packages & simulation environments, etc.
Kelvin B. Hales Kelvin Hales Associates Limited Consulting Process Control Engineers E-mail: snipped-for-privacy@khace.com Web: www.khace.com
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It is apparent that your definition of "simulation(s)/modeling" as compared to mine most likely comes from where we sit. Obviously, I am much looser in my definitions. I was not into the conceptional design of the analytical/mathematical methods used in describing the dynamics of a system. I have a great respect for the talent it takes to put together a complex model. We have a unit whose sole function is to provide that kind of modeling support (steady state or transient). Basically, I was an end user--- for me, the dynamic model was a tool to be used for many varied purposes----to evaluate/tune-up transient system behavior with respect to meeting system requirements; investigate field/production problems; to define/evaluate fixes; simulate off-design conditions and failure modes; evaluate the introduction of proposed design changes and so on. In many cases, key parameters taken from the infamous aircraft "black box" were used as inputs to the model and used to help understand what was going on at the time of an incident under investigation. Certainly not unlike the things that are done with and used with the systems that you're involved in--just a difference in the end product. MLD
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We typically work with Chemical and Process Engineers to develop rigourous dynamic models of plant (based on physics, chemistry, thermodynamics, etc.) and its controls; then we use both dynamic simulation studies and dynamic analysis of the model to investigate the potential transient behaviour of the plant under various operating and disturbance scenarios. We use various feedback-controller design techniques from Control System Science to determine critical controller tuning settings in advance of plant commissioning - especially for those controls which are not amenable to trial-and-error tuning during commissioning, or for which the closed-loop performance is important in achieving/evaluating good overall system behaviour. Case Studies have included gas compression plant for air and natural gas; liquid-phase and fluidized-bed chemical reactors; boilers, HRSGs and site-wide steam systems; distillation columns; water-treatment plant; calciners; oil-field 1st-stage treatment, especially for slugging production flow, etc. Currently completing simulation on a site-wide steam-system with 7x170t/h-boilers + 510t/h from HRSGs, with around 150 steam-pipes, 20-consumers. The blocks in our block diagrams are therefore rigourous models of system elements, typically with many hundreds of blocks per system. If we need linear models; e.g. for frequency-response analysis, then our simulation software allows us to linearise our rigourous models between any two points. I'll be talking next on what we do in Water Treatment Plant in 'Session3D: Modelling and Data Structures' at this event <http://www.iee.org/events/water.cfm#prog1 .
Kelvin B. Hales Kelvin Hales Associates Limited Consulting Process Control Engineers Web: www.khace.com
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Kelvin Hales wrote:

snip
It never ceases to amaze me how much more performance there can be in a loop after you've tuned it b'guess & b'gosh, and how often that kind of performance isn't necessary.
Kevin hit the nub here: There are times when you have to tune the loop before you ever turn the system on, and there are times when you have to formally tune the loop just to optimize performance.
I would add that there are times when you need to go from models when you are implementing a loop that is going to exhibit a rapidly changing structure due to nonlinearities (e.g. a motor with a current limit, being driven into a stop in which it will jam if it's going too fast when it hits).
But there are also 1000's of loops that don't need much tuning at all; as long as they're stable and there's an integrator in there somewhere keeping the setpoint correct they'll make money all day long.
--

Tim Wescott
Wescott Design Services
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