FIG 5.12. Adding a two-mode controller can eliminate offset. in .NET

Generate QR Code in .NET FIG 5.12. Adding a two-mode controller can eliminate offset.

FIG 5.12. Adding a two-mode controller can eliminate offset.
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Selecting the Feedback Controller
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It might be mentioned at this point that proportional time control of a constant-speed motor is a practical and inexpensive system. Two outputs must again ,be provided, with a dead zone between. Both outputs are modulated with time proportioning, one for a positive error, the other for a negative. Offset is encountered in the two-state loop, but the motor now overcomes it. Proportional time control with a constant-speed motor is essentially integral control, with a reset time of (5.6) The time constant of the valve motor, T,, is the time required to drive it full stroke.
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THE DUAL-MODE CONCEPT
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What would you like a controller to do, forgetting for the moment what it is reasonable to expect The most severe demand would certainly be to follow a step change in set point perfectly. This could be demanded of the controller, but not of the process, because it requires infinite process gain. The speed at which a variable may change is limited by the maximum rate at which energy may be delivered to the process. A valve may only open fully, not infinitely. Therefore it can only be asked that the controller not interfere with the maximum speed of the process. To duplicate the remainder of the step input, the control loop must be stable to the point that no overshoot or oscillation is observable. Nor should there be any offset. Finally, the controller ought to be insensitive to input noise, which is usually present in some form. TO summarize, the ultimate controller should be capable of achieving the following loop-response characteristics: 1. 2. 3. 4. Maximum speed Critical damping No offset Insensitivity to noise
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Any control system that can satisfy the above demands will also satisfy any minimum integral error criterion, regardless of what function of the error may be used, and regardless also of the nature of the input signals. The character of the process determines the complexity of t#he controller which is to accomplish the goals listed above. If the process is a pure single capacity, an on-off controller will provide maximum speed, critical damping, and no offset. An on-off controller is sensitive to noise, however. Significantly, this simplest control device is capable of achieving
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Nonlinear Control Elements
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the ideal closed-loop response on the simplest process. As the process complexity increases, on-off control is no longer optimum, and combinations of less severe linear or nonlinear elements must be used to provide stability. Obviously the nature of the process determines the design of the controller which will elicit the best loop performance. With regard to difficult processes, control functions which approach the demands of the four points of performance listed above need to be set forth: 1. ;\Iaximum speed implies that the controller be sat,urated for any measurable deviation. Such a demand limits the selection to an on-off controller. But if the tolerance may be widened somewhat, then the controller need only sat,urate in response to a large signal. (How large the signal must be will vary with the difficulty of the process.) 2. Critical damping can be achieved by both low gain and derivative action, but the latter amplifies noise. Critical damping implies an asymptotic approach to the set point. To accommodate maximum speed, the zone of critical damping must be restricted to a narrow band about the set point. Therefore this criterion and its solution apply specifically to small-signal response. 3. Zero offset requires a controller with infinite gain, in the steady state. An integrator supplying reset action is sufficient to satisfy this criterion. 4. Low noise response can be obtained through low gain or low-pass filt ering, but low-pass filtering degrades the speed of response of the loop. The only condition, then, which tends t o reconcile this requirement with the others, is the application of low gain to small signals. Of particular significance is the combination of high gain to large signals and low gain to small signals. The exact combination of parameters that will be most effective for a specific applicat ion may not be obtainable in a single controller. It may then be necessary to use two controllers, intelligently programmed to the best advantage of t heir individual features. The combination of two controllers operating sequentially in the same loop has been called a dual-mode system.
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