Control System Analysis Preview
Professional control systems engineering example using step response analysis
Unity Feedback Control System
Problem: Analyze the step response of a unity feedback control system with plant transfer function G(s) = 1/(s(s+1)) and unit step input.
- • Type 1 system (zero steady-state error for step)
- • Second-order system with poles at s=0, s=-1
- • Closed-loop response: C(s)/R(s) = 1/(s(s+1))
Applications: Robotic positioning, drone autopilots, industrial automation
Analyze the Step Response
Find the time-domain response when this system is excited by a unit step input
Enter a function above and click "Compute" to see results
Control Systems Fundamentals
The transfer function G(s) = 1/(s(s+1)) represents a common second-order plant with an integrator. The step response reveals critical system behavior.
Expected Response:
- • Final value: 1 (zero steady-state error)
- • Rise time: depends on dominant pole
- • No overshoot (critically stable)
- • Exponential approach to steady state
Key Insights:
- • Pole at origin provides zero steady-state error
- • Real pole at s=-1 determines settling time
- • Response: c(t) = 1 - exp(-t)
Understanding step response helps engineers design controllers for desired transient and steady-state performance.
Industry Applications
SpaceX Falcon Rockets
Attitude control systems use similar transfer functions for precise rocket orientation during flight and landing.
Industrial Robotics
Boston Dynamics and factory automation systems use step response analysis for precise robotic positioning and movement control.
Autonomous Vehicles
Tesla Autopilot and Waymo use control system analysis for steering, acceleration, and braking system responses.
Drone Flight Control
DJI and military drone manufacturers analyze step responses for stable hover and precise maneuvering capabilities.
Expected Step Response Analysis
Rise Time
Time to reach 90% of final value
Steady State
Final value after settling
Overshoot
Maximum overshoot percentage
Want to compare with the RLC circuit example?
See how electrical engineers analyze oscillatory responses in power systems