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MECH431_topic6_PID

# MECH431_topic6_PID - K G(s Chapter 10 PID controls and...

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K G(s) + - MECH 431 PID Slide 1 Chapter 10 PID controls and two-degrees- of-freedom control systems

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K G(s) + - MECH 431 PID Slide 2 Tuning rules for PID controllers It is not always possible to model the plant of a system by mathematical equations. So, it is not always possible to apply analytical techniques to design the necessary PID controller. + - Plant
K G(s) + - MECH 431 PID Slide 3 Ziegler-Nichols controller tuning Controller tuning is the process of selecting controller parameters to meet performance specifications. Ziegler and Nichols suggested rules for tuning PID controllers based on experimental step responses. Such rules are handy when mathematical models are not available.

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K G(s) + - MECH 431 PID Slide 4 Ziegler-Nichols controller tuning Ziegler and Nichols rules suggest values of K p , T i , and T d that yield a stable system. However, the system might still exhibit large maximum overshoot M P and you might need to perform some fine tuning.
K G(s) + - MECH 431 PID Slide 5 Method 1 We first obtain experimentally the response of the plant to a unit-step input. If the plant involves neither integrator nor dominant complex-conjugate poles, then the step response curve may look S-shaped. If this S shape does indeed exist, we can find 2 constants: (1) delay time L and time constant T .

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K G(s) + - MECH 431 PID Slide 6 Method 1 •Draw a tangent at the inflection point of the S-shaped curve and determine the intersections with the time axis and line c ( t ) = K .
K G(s) + - MECH 431 PID Slide 7 Method 1 The transfer function can be approximated by a 1 st order system with a transport lag. The tune the controller based on the following table.

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K G(s) + - MECH 431 PID Slide 8 Method 2 In this method first set T i = and T d = 0. Using the proportional control action, increase K p from 0 to a critical value K cr at which the output FIRST (if it does at all) exhibit sustained oscillations. + - Plant r ( t ) u ( t ) c ( t )
K G(s) + - MECH 431 PID Slide 9

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K G(s) + - MECH 431 PID Slide 10 Observation Method 2 If the system has a known mathematical model, we can use the root locus method to find the critical gain K cr . We can also find the frequency of sustained oscillations w cr where 2 π / w cr = P cr .
K G(s) + - MECH 431 PID Slide 11 Example 10-1 • Tune this PID controller for 25% M p for a unit step input. + - R ( s ) u ( t ) c ( t ) PID controller •Given: Solution: • Since the plant TF has an integrator lets try the second method of Z.N.

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