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�a. System showing�input and output;�b. pole-zero plot�of the system;�c. evolution of a�system response.�Follow blue arrows�to see the evolution�of the response�component generated�by the pole or zero.�

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�Effect of a real-axis�pole upon transient�response

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�a. First-order system;�b. pole plot

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�First-order system�response to a unit�step

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�Laboratory results�of a system step�response test

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�Second-order�systems, pole plots,�and step�responses

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�Second-order�step response �components�generated by�complex poles

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�Step responses�for second-order�system�damping cases

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�General form of step response

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�General second order system

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�Second-order response as a function of damping ratio

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�

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�

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�Second-order�underdamped�responses for�damping ratio �values

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�Second-order underdamped response specifications

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�Second-order underdamped response specifications Tp

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�Second-order underdamped response specifications %OS

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�Percent�overshoot vs.�damping ratio

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�Second-order underdamped response specifications Ts

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�Second-order underdamped response specifications Tr

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�Normalized rise�time vs. damping�ratio for a�second-order�underdamped�response

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�Pole plot for an�underdamped �second-order�system

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Lines of constant�peak time,T_p, settling�time,T_s , and percent�overshoot, %OS�Note: T_s₂ < T_s₁ ;�T_p₂< T_p₁; %OS₁<�%OS₂

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�Step responses�of second-order�underdamped �systems�as poles move:�a. with constant �real part;�b. with constant �imaginary part;�c. with constant �damping ratio

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�Rotational�mechanical system.

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�The Cybermotion�SR3 security robot�on patrol. The�robot navigates by�ultrasound and path�programs transmitted�from a computer,�eliminating the need�for guide strips on�the floor. It has video�capabilities as well as�temperature, humidity,�fire, intrusion, and gas�sensors.

Courtesy of Cybermotion, Inc.

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�Component responses of a three-pole system:�a. pole plot;�b. component�responses: nondominant pole is near�dominant second-order pair (Case I), far from the pair (Case II), and�at infinity (Case III)

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�Step responses�of system T₁(s),�system T₂(s), and�system T₃(s)

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�Effect of adding�a zero to a �two-pole system

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�Step response�of a�non minimum-phase system

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Figure 4.29�a. Effect of amplifier�saturation on load angular velocity�response;�b. Simulink block�diagram