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Lecture 9: Time-Response Characteristics (II) TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AA A AAA A A A A A A A A
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Sampled-Data Systems Dominant closed-loop poles: the closed-loop pole(s) furthest away from 0 Transient response largely determined by the dominant closed-loop pole(s) Problem: quantify the response characteristics based on dominant pole locations
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Continuous-Time Feedback Systems Dominant closed-loop poles: the closed-loop pole(s) furthest to the right Transient response largely determined by the dominant closed-loop pole(s)
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Time Specifications of Continuous-Time Systems
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Time Specifications for a Real Dominant Pole Time Specifications:
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Time Specifications for Complex Dominant Poles Dominant closed-loop poles: Time Specifications:
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Example
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Relating the Closed-Loop Poles Sampled-data system Continuous-time system Closed-loop poles: Characteristic equation: Closed-loop poles: Transfer function: hold
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to the closed-loop poles of the sampled-data system (approximately)
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Inverse Map (General Case)
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Time Specifications of Sampled-Data Systems
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First Order System Example Approximate settling time for the system response to unit step input?
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Second Order Example Closed-loop transfer function: Taking the inverse transform:
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Second Order Example: Simulation
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Constant Damping Loci
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Constant Frequency Loci Constant frequency loci correspond to closed-loop poles with the same oscillation frequency in step response (or the same peak time)
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Constant Damping Ratio Loci
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Time responses for different closed-loop pole locations
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Systems Considered So Far
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Characteristic Equation of General Sampled-Data Systems (independent of input)
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Finding Characteristic Equation via SFG Signal Flow Graph: 2. Find the transfer function from the output of the sampler to its input: 3. Take star transform:
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Example with Multiple Samplers Characteristic equation:
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