State-Space Analysis & Control Systems Engineering

Key Engineering Contributions

1. 01
   Mathematical Modeling & Verification: Derived the state-space representation of a coupled double spring-mass-damper system. Verified the mathematical model's accuracy by running comparative step-response simulations against the physical Simscape plant.
2. 02
   PID Control & Frequency Analysis: Analytically designed and iteratively tuned a PID controller to minimize steady-state error while managing the trade-offs between tracking accuracy and system damping. Evaluated the control system's tracking limits across varying input frequencies using Bode plots, successfully identifying the 12.2 rad/s cutoff frequency.
3. 03
   State-Feedback Control Implementation: Engineered a modern state-feedback controller using analytical pole placement (s = -45, -50, -55, -60) to enforce strict performance constraints. Calculated optimal gain matrices to achieve a rapid settling time of less than 0.1 seconds while ensuring critical damping.

Visual Documentation

Figure 1

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Simulink model of the PD controller

Figure 2

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Chart of error propagation over time when reference step is r(t) = 0.1. The Kp value is about 1000 while the Kd value is about 70 which produces a 10% error as requested by the system desired paramete

Figure 3

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To minimize steady state error, a Ki value of 100 was chosen. The error propagation may be seen above over time.

Figure 4

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Bode Diagram of the Closed Transfer Function which shows the cut off frequency of 12.2 rad/s (1.94 Hz).

Figure 5.1

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Part 1 of 3

Figure 5.2

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Part 2 of 3

Figure 5.3

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Part 3 of 3

Figure 6

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The Simulink model of the state-feedback controller and its output over time