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One method of controlling a nonlinear system is linearizing the model in an operating point and gain scheduling the controller. The operating point includes a state and an input (the trim input) so when you design a controller for the linear system, you are designing \delta u and you should add the trim input to it. But in most examples of linear control design and gain scheduling, we see that what is produced in the feedback control design of the linear system is considered the control input and the trim input is not added. What us the reason for that?

user45799
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  • can you draw a system diagram to clarify what you're asking? – Pete W Jan 31 '24 at 20:42
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    It is not clear to me what you are asking. Could you perhaps be confusing the control input and the plant input? I assume by "control input for the operating point" that you mean the setpoint input? Maybe you are asking why the error signal $\Delta u$ is a direct input for the control but not the setpoint input? – DKNguyen Jan 31 '24 at 21:00
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    "But in most examples of linear control design..." please edit your question to cite your sources. Probably, the authors feel that the trim input is a trivial detail, or the controller is integrating and they feel that it'll find the trim input without needing one to be explicitly included. – TimWescott Feb 01 '24 at 00:52

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But in most examples of linear control design and gain scheduling, we see that what is produced in the feedback control design of the linear system is considered the control input and the trim input is not added. What us the reason for that?

If by example, you meant examples from text books, that may be because the performance and stability depends on the linear model and the feedback scheme rather than the (fixed) trim component of the input. So the existence of the trim component of the control input would be mentioned a few times in the beginning of a text book and left out in the design and analysis part that appears in the subsequent chapters.

If you checked actual implementations (digital or other wise), you would be able to notice that the actual input to the system is the sum of the trim value and the feedback signal.

AJN
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