Feedback Control theory for PC automation in the home




	Feedback Control Feedback (or closed loop) control is where control theory really starts to get interesting. ? What do we mean by feedback? Feedback is information fed back into the control system providing information about the current status of what it is trying to control. Let's clarify with an example. You are driving a car along a straight and level road. You press the accelerator until the speed reaches 30mph. You then ease off on the accelerator a touch to maintain that constant speed. You are now participating in a closed loop control system. The objective, or target, of control here is the desired speed of the car. The input to the control loop is the reading of speed seen by you on the speedometer and the output is the control of the accelerator pedal. The intelligence at work here (I use the phrase in the most general sense !) is you, the driver. As you drive along the road there is a dynamic interaction between the speedometer reading and the position of the pedal. As you detect an error in the target speed of 30mph you apply a correcting action using the pedal. In terms of feedback, you are feeding back the detected error in the target speed and applying it to the pedal. (For the moment we will ignore the mathematics that would dictate constants of proportionality etc… and focus on the fundamental characteristics).










	So, all is well. We have the car under control, with our personal feedback loop and are wondering what all the fuss is about… feedback control is easy. Before we get too confident let's make some changes to this control system, and see where it takes us. Some of the changes may seem a little strange but stay with me, because they will lead to a better understanding further down the line. Let's replace the accelerator pedal with a switch. "On" gives maximum acceleration and "off" gives none at all. Crazy?, of course it is but imagine your attempts at trying to maintain a steady speed. You would probably find that your speed would oscillate above and below your target of 30mph, probably quite significantly. You could perhaps achieve a better control with higher speed shorter pulses of the switch but you would then be facing the problem of speed of response of the engine. The engine will not deliver power instantly (well at least not the cars I drive). Without a significant duration of switch-on time you may not see any change in speed.

	This scenario is called "Bang-Bang" control and the oscillations about the target speed are called "Hunting". Bang-bang control is the most basic form of feedback control. In its favour we have to say that it is normally the least expensive to implement but against it is the quality and accuracy of achieving the target. Generally we can say that it is more suitable for control systems with slow changing targets. Choosing the switching points more carefully can make some improvements. In the case of the car, the accelerator could be switched on when the speed drops to 28 mph and switched off when 32mph. This allows time for the engine to respond and reduces the amount of switching but sacrifices the accuracy of control. i.e. the range of hunting is, at best, 28 - 32 mph. Another common example of bang-bang control is the central heating thermostat. If you set 20 degrees on the dial, it will normally switch on when the temperature falls to 18 and off when at 22. This gap between on and off is called "Hysterisis". Now ask yourself this question; why was it easier to control the speed using the accelerator pedal rather than the switch ? (read on).




		Next: Proportional Control

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© Copyright PC-Control.co.uk 2004
© Copyright PC-Control.co.uk 2004