Size of the error at emergence from controller saturation

1 Size of the error at emergence from controller saturation 

With Type I integral desaturation, the integral term is limited when the partially desaturated output, C (r), takes a value outside the controller s output limits (see equations (22.16) and (22.17)). 

Suppose that the error is positive and non-decreasing so that the partially desaturated output, C, will be increasing. Eventually, at time, t , say, the value of c l will reach the upper output limit of the controller. At this point using equation (22.18)  

The integral term, 7o, will now be held, and will retain thereafter the value  

Now suppose that after a further time, the error begins to fall, and that at a later time, t  

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