On-off control use higher limit and lower limit to bound output signal. the output signal will be oscillation around the given set-point. this phenomena is usually a simple hysteresis loop.
My question is why we use error signal for on-off control as show you in Figure ,I'm thinking it is not use for this algorithm .
well.. actually, the root of bang-bang control is discontinous control, which is the simplest one and based on pratical knowledge.. Why do we use switching function?? Loosely speaking, you don't have to know the model of plant precisely and you can ignore the uncertainty in your system. It's quite different if you implement continous control signal (like PID, LQR, and so on). Switching means that, there are only two conditions, whether the 1st value or 2nd value (upper and lower bound), that's why error signal is the input for this controller, since we can obtain the value of upper or lower bounds according to how much error signal that you've obtained. For example, if the error is above 5, but the upper bounds is only 2, the the control signal will fed "2" to the plant.. I think, it's just all about practical way, how you can determine well your upper and lower bound of bang -bang control itself.
Thank Ramadhani Subroto First, I'm think upper and lower bound have same unit as output . For example , if I'm want to control temperature of heater system I'm set upper bound at 40 C and lower bound at 35 C , then i'm fix set point temp at 37 C , so the out put of heater system will be oscillation around the given set-point.
After your information, it mean upper and lower bound in on-off control algorithm are maximum control effort and minimum control effort to the plant . it not mean maximum Temp (40 C) and minimum Temp (35 C). Therefore, we use two condition of control effort to determine the bounds of real unit (Temp) of this system and I'm don't know how to convert control effort condition to my design bounds ?
indeed.. the bound is used to limit control signal.. so that such control signal will osillate around this value..
you have to know first the characteristic of your actuator.. how much control signal that is needed to make certain output, that's why identification and system modelling is needed before you implement such controller. for example, if I give step input with value 5 Volt, how much steady state output.. then you can try another value of input
Bang bang controller is very simple to implement and belongs to the wide class of discontinuous controllers.
The main drawback is the chattering phenomenon it will induce, that is the oscillating around a mean value. Oscillations will be limited by using hysteretic functions or atan like functions. If you are interested in such systems, have a look on sliding mode control, which is the theoritical approach for such systems.
The problem is best solved by the theory of optimal control considering the input constraints. The Pontryagon principle of maximum and the theory of n-interval, by A. A. Feldbaum, could be used. Furthermore, the switching function can be derived in terms of the system states and not only by the error signal.
Mr. Frederic : Have you conducted the research with sliding mode control theory? All my researches are about sliding mode control :)
Error signal is used for switching between minimum control effort and maximum control effort. Detailed theory of relay control systems is pretty complex. I can recommend you the book I. Boiko "Discontinuous Control Systems" Birkhauser, Boston, 2009.
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