Partially desaturated output

Thus we will be able to evaluate the desaturated integrator output provided we are able to evaluate R(tn)- We shall now show how this may be done. First consider the behaviour of R in the three possible different circumstances for the partially desaturated output. Cl, namely ... 

Condition I. The partially desaturated output falls below the lower controller limit, i.e. Ci(rn) < Cmin... 

Condition 2. The partially desaturated output lies between the controller limits, i.e. c,i,in < C (r ) < Cmax... 

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) ... 

Considering the case of the controller emerging from high saturation, when the partially desaturated output, C (f), has come back down to the controller output saturation level, Cma,. It is clear that the controller can come out of saturation now, but only if C (/) is falling, i.e. if ... 

The partially desaturated output, C (r), will be little different from because of the resetting of the desaturated integrator specified by equations (22.20) and (22.21), repeated below ... 

Here C is the partially desaturated controller output, given by... 

Inspection of equations (22.21) to (22.23) shows that the fully desaturated controller output, c, is equal to the partially desaturated controller output, C, whenever the latter falls within the allowable controller output range, Cmin to Cm,. But if C moves outside this range, then the controller output will remain at the closest limit, Cmin or Cm,. 

The modified proportional term now replaces the normal proportional term in equation (22.22), so that the partially desaturated controller output, C, is now given by... 

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