Term
| how to deal with NL system if NL system is static? |
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Definition
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Term
| when can perfect cancellation happen? |
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Definition
1. NL element appears at control input
2. NL element is globally invertible |
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Term
| can every non linear function be inverted? |
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Definition
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Term
| if perfect cancellation doesn't happen, what are three techniques used to do cancellation? |
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Definition
| 1. invert in restricted range 2. subtract nonliniarity 3. move NL to input by inverting linear dynamics |
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Term
| What are 3 ways to deal with non-linearity? |
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Definition
1. cancel out
2. approximate by linearizing
3. use limit cycles |
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Term
| What are 4 steps for canceling non-linearities out? |
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Definition
1. write desired transfer function with out NL elem
2. write plant
3. expand plant to cancel out NL elems, they will be part of controller
4. design real controller |
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Term
| What is rule of thumb for cancelling out? |
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Definition
| subtraction is outside of inversion |
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Term
| Is non-linear elements commutable? |
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Definition
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Term
| Can you invert the non-linearity if plant is unstable? |
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Definition
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Term
| What can stiction lead to? |
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Definition
1. increase steady-state error
2. can lead to oscillation if integral control is used
3. can make system unstable |
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Term
| What are two solutions to cancelling out stiction? |
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Definition
1. use dither dignal
2. use offset |
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Term
| What are advantages of using dither signals? |
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Definition
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Term
| what are disadvantages of using dither signals? |
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Definition
1. need to change dither signal often
2. can lead to unstable |
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Term
| what are advantages of use of offset? |
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Definition
1. offsets are easy to measure
2. simple |
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Term
| what are disadvantages of use of offset? |
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Definition
1. not effective sometimes
2. need to change offset often |
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Term
| In terms of error of steady-state value, does use of dither do better or use of offset do better |
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Definition
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Term
| what happens if dither signal is big? |
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Definition
| steady state error is less |
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Term
| what happens if offset signal is big? |
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Definition
| steady state error is less |
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Term
| What are steps of linearization? |
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Definition
1. find an operating point(stationary point)
2. Write in "delta equation" at operating point
3. Write p(s) in terms of "delta equation" |
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Term
| In continuous system, what is stationary point? |
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Definition
| Not changing -> derivatives are 0 |
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Term
| In discrete systems, what is stationary point? |
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Definition
| [K+1] = [K] = [k+2] = ... |
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Term
| Compare linearization between cancellation |
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Definition
Linearization Adv:
1. systematic
2. works for any non-linear system
Cancellation Adv:
1. cancels NL exactly
2. Can estimate range of inputs
Linearization Disadv:
1. works for only close range
Cancellation Disadv:
1. inverse function might not exist
2. sensitivity concerns |
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Term
| Why would saturator be introduced in real life? |
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Definition
| don't want to exceed dangerous limites |
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Term
| What are ways to deal with saturators? |
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Definition
1. ignore the saturator and ensure saturation is avoided
2. add a feedback to saturator so it won't go to saturation |
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Term
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Definition
| oscillation produced by NL elem that's really hard to get rid of |
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Term
| What is a describing function? |
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Definition
| put the limit cycle to describing function |
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Term
| what are advantages of describing function? |
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Definition
| 1. can use linear analysis methods |
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Term
| what are disadvantages of describing function? |
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Definition
| 1. not 100% accurate since it's an approximate |
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Term
| In limit cycle, is controller the NL element or plan the NL element? |
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Definition
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Term
| What are assumptions for describing function approach? |
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Definition
1. input and output are oscillating
2. only first harmonic passes -> only first term in Fourier series
3. external inputs are 0, no dynamics, has odd symmetry |
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Term
| What's equation for fourier series? |
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Definition
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Term
| what does describing function depends on? |
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Definition
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Term
| If non-linearity is memory-less, then what's the describing function? |
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Definition
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Term
| if the non-linearity is dynamic, then besides A, what can it depend on? |
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Definition
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Term
| what's the general form of describing function? |
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Definition
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Term
| derive describing function |
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Definition
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Term
| If a limit cycle exists, what are equations to find frequency and amplitude? |
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Definition
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Term
| What are conditions for stability of limit cycle at Ao? |
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Definition
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