محاكاة المتحكم التناسبي التكاملي التفاضلي باستخدام سيمولينك-PID Simulation Using Simulink

Overview

This video demonstrates how to simulate a PID controller in Simulink using Simulink-PID blocks. It starts from a previously built P-D (PDI) controller, then adds integral action, followed by an analysis of how tuning each PID gain affects the system response.

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What’s built / how it’s implemented

• The model starts with an already-designed PDI controller (Proportional–Differential–Integral).
• To add integration action, the presenter uses a transfer function block in Simulink that represents an integral term:
  • integration = constant / s
  • implemented via a “transform function” / transfer function block.
• The overall Simulink model includes:
  • the plant (referred to as a reactor, or potentially any physical system such as a motor),
  • a reference input (target setpoint),
  • controller blocks for P, D, and I actions.

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Simulation and performance checks

The simulation is repeatedly run, and standard transient-response metrics are evaluated:

• Overshoot (described as the “big jump” / peak deviation)
• Rise time (time to reach near the setpoint)
• Steady-state response (final value)
• Steady-state error compared to an allowed tolerance of 1%
  • Acceptance mentioned as ≥ 0.99 (meaning error is within 1%)

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Key tuning experiments and observed effects

1. Adjusting an integral-related parameter to fix steady-state error

• Initial response is described as “decent” but slightly outside tolerance.
• Example values mentioned:
  • steady-state around 0.9615, still above allowable error (i.e., not meeting the tolerance requirement)
• By changing the relevant gain (example: set to 8):
  • overshoot is about 3.6% (below a 5% threshold)
  • rise time remains < 0.5 s
  • steady-state response is essentially 1 (excellent tracking)

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2. Increasing simulation time

• With a longer run (example: 100 seconds):
  • rise time still stays < 0.5 s
  • overshoot worsens slightly but still remains < 5%
  • steady-state remains acceptable, near the limit around 0.99

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3. Increasing Proportional gain (P)

• Reported effects:
  • rise time decreases (faster response)
  • overshoot increases (larger peak)
• Example mentioned:
  • raising P to around 40 increases overshoot
    • reported overshoot around ~7%
    • peak read from the plot around ~11.79%
  • rise time improves to roughly 0.25 s
  • steady-state error improves to < 1%

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4. Increasing Differential gain (D)

• Reported effects:
  • more damping / smoother response
  • overshoot should reduce due to damping, but interactions with P can limit how much overshoot drops
• Example mentioned:
  • setting D to 8 yields a smoother, more damped response
  • steady-state error stays < 1%
  • rise time becomes much slower (possibly approaching ~1 s)
• Important interaction note:
  • because P and D interact, overshoot may not automatically fall below the 5% limit even if damping increases.

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5. Increasing Integral action (I)

• Warning: I must not be made too large.
  • integral action “adds a pole” / affects stability.
• Example:
  • pushing the integral-related value far beyond a remembered limit (example: 400 vs allowed limit around 130)
  • results in instability
  • the simulation shows divergence behavior, and plot scaling becomes extreme (indicating instability)
• Conclusion:
  • larger I can worsen transient response (slower/poorer instantaneous behavior) even if steady-state accuracy improves.

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Overall takeaways / tutorial conclusions

• Adding integral action (I) using a transfer-function block improves steady-state accuracy and can eliminate steady-state error.
• P gain trade-off: faster rise time but more overshoot.
• D gain trade-off: smoother/damped behavior but often slower rise time.
• I gain constraint: too large integral gain can destabilize the closed-loop system.

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Main speakers / sources

• Main speaker: the unnamed presenter/teacher in the video (speaking throughout the subtitles).
• Referenced tool/implementation: Simulink / Simulink PID using transfer-function blocks.