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Embedded Systems October 2000 Vol13_11

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PID stands for "proportional, integral, derivative." These three terms describe the basic elements of a PID controller. Figure 1 shows a block diagram of a basic PID controller. In this case the de rivative element is being dri ve n only from plant feedback. The plant feedback is subtracted from the com- mand signal to gene rate an e rror. This e rro r ignal drives the pro por- tio nal and il1legral eleme nts. T he resulting signals are added togethe r and used to drive the plant. I haven 't descl-ibed what these eleme nts do yet- we' ll get to that later. I've includ- ed an alternate placement fo r th e pro- portio nal element (dotted lin es)- thi s can be a better location fo r the proportio nal element, depending on how you wa nt the system to re pond to commands. Sample plants In orde r to discuss this subject with any sense of reality we need some example systems. I'll use th ree exam- ple plants througho ut this article, and show the effects of applyi ng the vari- ous controllers to them: • A motor driving a gear train • A precision positioning system • A thermal system Each of these systems has different characteristics and each o ne requires a diffe rent control strategy to get the bes t pe rfo rmance. Motor and gear The fi rst example pla nt is a motor driving a gear tra in , with th e o u tput positio n of th e gear train be ing mo ni to red by a pote n tiometer o r some o the r posi tio n readi ng devi ce. You might see this kind of mecha- ni sm driving a carr iage o n a printe r, o r a thrott le mechanism in an auto- mo bil e crui se control sys tem, o r almost any oth e r mode rate ly prec ise position controlle r. Figure 2 shows a diagram of such a sys tem. T h e mo tor is driven by a vol tage th at is commanded by software. The motor o utput is geared down to drive the actua l mecha n ism. The positio n o r this tin al drive is measured by th e pote n tiome te r. A DC motor driven by a voltage wan ts to go at a constant -peed that is pro portional to the applied voltage. Usually the motor armature has some resistance that limits its abili ty to accel- erate, so the motor will have some delay between the change in input volt- age and the resulting change in speed. The gear train takes the movement of the motor and multiplies it by a con- stant. Finally, dle potentiometer mea- sures the position of the output shaft. Figure 3 shows the step I the motor and gear combination. I'm using a time constant value of <0 = 0.2s. The step respo nse of a sys tem is just the behavio r of the o utput in respo nse to an input lhat goes from zero to some constant value at time t = O. Since we' re dealing with fa irly generic examples here I've shown dle step response as a fraction of fu ll scale, so it goes to 1. Figure 3 shows the step input and the motor response. The -espo nse of FIGURE 1 A basic PID controlle~ Proportional r,~ -- command error~' Integral Derivative feedback Software Hardware Embedded Systems Programming OOOBER 2000 87

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