# lab3template - following questions e ss due to a step in ω...

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Lab 3 D IGITAL S IMULATION OF A C LOSED L OOP S YSTEM 1 of 2 Report By: Lab Partner: Lab TA: Section: Part 1. ___/15 Plots ___/6 (Attach time response plots to end or include them here) Fig. 1 Fig. 2 Time Response to a Unit step for ω r ___/6 Controller 1 Controller 2 Controller 3 Prelab Lab Prelab Lab Prelab Lab M p (%) % % % % % % t r (s) t s (s) K K r K d Table 1 Compare/contrast ___/3 M p , t r , and t s from Prelab with those from Lab Which controllers met the specifications? Part 2. ___/12 Deriving e ss components For the system in Figure 3.1, derive the relationship between steady-state error (e ss = ω r – ω) and natural frequency, ω n . Consider the error as a function of both ω r and τ d , and model these as step inputs. Since the Total ___/45

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Lab 3 D IGITAL S IMULATION OF A C LOSED L OOP S YSTEM 2 of 2 system is linear, superposition allows the two components to be calculated separately and then summed. Notice that e ss is not the same thing as “e” in the block diagram (e= K r ω r – ω). = 2 n ϖ (as an expression of K) (1) ( 29 ( 29 r s s - = (as an expression of ω r and τ d ) (2) Hint: Use the Final Value Theorem, (page 93, FPE). Make sure you answer the
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Unformatted text preview: following questions: e ss due to a step in ω r (τ d = 0) is: To minimize this error component, n should be…. e ss due to a step in τ d (ω r = 0) is: To minimize this error component, n should be…. Part 3. ___/18 For controller 3, derive the relationship between ζ, ω n , and the gains K and K d . ___/12 = + + 2 2 2 n n s s ξϖ (3) = n (as an expression of K and K d ) (4) = ξ (as an expression of K and K d ) (5) Hint: Increasing K does what to ω n 2 , what to ζ (and at what rate: linearly, exponentially, as K 2 , etc.) Increasing K d does what to ω n 2 , what to ζ (and at what rate) Using these equations, show how the pole locations change as K d >0 increases in value. ___/6 Poles = (as an expression of ζ and ω n ) (6) Discuss: As K d grows, the poles move…(remember there are two components of this, depending on the damping)...
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## This note was uploaded on 03/28/2011 for the course ECE 486 taught by Professor H during the Spring '09 term at University of Illinois at Urbana–Champaign.

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lab3template - following questions e ss due to a step in ω...

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