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Embedded Systems October 2000 Vol13_11

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II caLcuLate the integraL term operation pre Lly close to the limit of the speed attainable using PI control with this plant. Before we leave the d iscussion of Integral control by itself usually decreases stability, or destroys it alLO- g ther. Figure 11 shows the motOI - and gear with pure integral control (pGa in = 0). The system doesn 't settl e. Like the precision actuator with propor- tional contro l, the motor and gea r sys- tem with integral control alone will oscillate with bigge r and bigger swi ngs until something hiL5 a limit. (Hopefully the limit i n't breakable.) Figure 12 shows the temperature control system with pure integral con- trol. This sys tem takes a lot longer to settle out than the same plant with proportional control (see Figllre 10), but notice th at when it does senle out, it settles out to the target value- even with th e disturbance added in. If your problem at hand doesn 't reqllire fa t settlin g, this might be a workable system. Figure 12 hows why we use an inte- gral term. The integrator state "remembers" all that has gone on before, which is what allows the con- troller to can el o ut any long teml errol-s in the output. This same mem- ory also contribut e to instability-the controller is always respo nding too late, after the plant has gotten up speed. To stabilize the two previous systems, you need a little bit of their present value, which you get from a proportional term. Figure 13 shows the motor and gear with proportional and in tegTal (Pl ) control. Compare thi s with Figllre. 8 and II. The position takes long(,r to s(,ttle out than the system with pure proportional control, but it wi ll not eule LO the wrong spot. Figure J 4 shows what happens when you use PI control o n the heater system. The healer srill se ttles Ollt to the exact target tempel-ature, as with pure integral control (see Figur(' 12), bllt with PI control, it settl es Olll two to three times fast(,r. This figure shows integrators, there are two more things I need to point out. First, since you arc adding up the error over time, the sampling time th at you are running becomes important. Second, you need to pay attention to the range of your integrator to avoid windup. The rate that the integrator state changes is equal to the average error multip lied by the integrator gain multip lied by the sampling rate. Because the integrator tends to A MORE POWERFUL ALTERNATIVE TO OllERS Design your custom micro- processor-based board around the Rabbit 2000™ (ore Module. The core module is based on the new Rabbit 2000 microprocessor, and can handle programs of up $29 • • • • • • • • • • qtY100 $39qtyone to 50,000 ( statements. Benefit from easy and rapid development with this low-cost solution! RABBIT 2000™ CORE MODULE FEATURES 40110 pins 4 serial ports 7 timers Battery-backed timeldate clock 128K-512K SRAM 256K flash Clock up to 25.8MHz Slave port Remote cold boot Excellent math processing Development Kit only 5169 Includes core module, prototyping board, complete Dynamic C~ software development system (not a trial version), PC serial cable for real·time debugging, and documentation on CD·ROM Order the Rabbit 2000™ Core Module Kit ontine at www.rabbitsemicondudor.com or call 530.757.8400 2932 Spafford Street, Davis, CA 95616 • Fax 530.757.8402 Make t he Rabbit 2000T" Core Module t he heart of your custom board design. A low-cost manufacturing license is a lso avai lable. Embedded Systems Programming oaOBER 2000 95

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