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Process Control: Modeling, Design, and Simulation by B. Wayne Bequette

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5.8. Open-Loop Unstable Systems

The examples presented thus far in this chapter have assumed that the process is open-loop (that is, without control) stable. For these systems we can always “detune” a controller enough so that the closed-loop system is stable. Indeed, if we simply let kc = 0, then we have stability because the closed-loop transfer function is equal to the open-loop transfer function. Open-loop unstable systems are much tougher to control, because the control must be tuned “tightly” enough to stabilize the system, yet not so tightly that the closed-loop system will be unstable. Some exothermic chemical reactors and biochemical reactors are operated at open-loop unstable steady states (that is, at least one eigenvalue of the

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