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Research on Optimized Fuzzy PID Temperature Control Strategy Based on Improved Particle Swarm Optimization

Renjie Jin

arXiv:2609.00001v1cs.NE

TL;DR

Industrial thermal control must handle inertia, delays, nonlinearities, and parameter drift that challenge fixed-parameter and standard optimization approaches. The paper combines a FOPDT-based evaluation with LMPSO, whose Levy flights and Elite Memory Pool support improved fuzzy PID tuning; simulations report a 105.5 s response figure and robustness under model mismatch.

  • Problem

    Industrial thermal processes involve inertia, time delays, nonlinearities, and aging-related parameter drift, while standard PSO can prematurely converge on flat fuzzy-parameter fitness landscapes.

  • Method

    The paper evaluates fuzzy PID tuning with LMPSO, combining Levy flights, an Elite Memory Pool, and a FOPDT model of the thermal process.

  • Results

    105.5 s is the reported rise time, 42.5% faster than IPSO, with 1.63% overshoot; the strategy also maintains high performance when process time constants increase by 25%.

  • Takeaways & Limitations

    LMPSO offers a simulation-supported approach for fuzzy PID control of delayed, time-varying industrial thermal processes, combining faster response with reported robustness.

  • Takeaways & Limitations

    The optimization comparison remains constrained by standard PSO's documented stagnation and local-optimum vulnerability in complex fitness landscapes.

Abstract

from arXiv · show

Precise temperature control is critical in industrial automation, governing product quality in processes from chemical reactors to furnaces. However, high-order inertia, time delays, and parameter drift render traditional PID and manual fuzzy controllers inadequate. To surmount these hurdles, this study presents a robust framework: a Fuzzy PID strategy optimized by a novel Levy-flight Improved Particle Swarm Optimization (LMPSO) algorithm. Addressing the "curse of dimensionality" in fuzzy tuning, LMPSO integrates Levy flight mutation to shatter premature convergence and an Elite Memory Pool to secure evolutionary efficiency. Simulations on a First-Order Plus Dead Time (FOPDT) model reveal the algorithm's potency: it slashes settling time to 105.5 s -- approximately 46.7% faster than standard PSO and 42.5% faster than competitive improved PSO variants -- while achieving an optimal ITAE value. Robustness tests confirm superior stability under severe model mismatches, proving its viability for high-precision industrial applications.

I. INTRODUCTION

Industrial temperature control must handle inertia, delays, nonlinearities, and aging-related parameter drift, while conventional and manually tuned fuzzy controllers remain limited. The paper proposes LMPSO to improve fuzzy-parameter optimization by combining Levy flights with an Elite Memory Pool.

  • Thermal processes combine significant inertia, time delays, nonlinearities, and slow parameter drift caused by equipment aging.
  • Fuzzy PID adapts controller gains to system states, but manual membership-function tuning is inefficient and subjective.
  • Standard PSO can prematurely converge on the flat fitness landscapes associated with fuzzy parameters.
  • LMPSO combines Levy flights with an Elite Memory Pool to balance global exploration and local exploitation.
  • Prior optimization work includes PSO variants and alternative meta-heuristics such as GWO, Enhanced Dung Beetle Optimization, and ISSA.

III. SYSTEM MODELING AND FUZZY CONTROLLER DESIGN

The study models the thermal process with a First-Order Plus Dead Time model and evaluates robustness under a composite perturbation representing equipment aging. The nominal model includes substantial thermal inertia and delay, while the stress test changes both gain and time constant.

  • The thermal process is represented by a First-Order Plus Dead Time model used as a standard approximation for industrial thermal processes.
  • The nominal model uses process gain K = 1.5, time constant T = 120s, and pure time delay τ = 30s.
  • The delay-to-time-constant ratio is τ/T = 0.25, indicating a significant delay relative to the process time constant.
  • The composite perturbation attenuates gain K by 10% to 1.35 and increases time constant T by 25% to 150 s.

B. Design of the Self-Adjusting Fuzzy PID Controller

The self-adjusting controller combines fuzzy inference with conventional PID control to modulate gains from instantaneous error information. Its nonlinear rule base makes control aggressive during large errors and more cautious near the setpoint.

  • The architecture combines a fuzzy inference engine with a conventional PID structure for real-time parameter modulation.
  • The closed-loop controller uses error e(t) and its rate of change ec(t) to compute correction factors.
  • The MATLAB/Simulink implementation contains the FOPDT plant, fuzzy inference subsystem, and signal routing for performance monitoring.
  • Baseline parameters Kx0 and fuzzy outputs ΔKx are scaled by Ke, Kec, and Ku, which serve as optimization decision variables.
  • Large errors boost ΔKp and minimize ΔKd, whereas steady-state operation increases ΔKp and ΔKi to overcome static friction.

A. Standard PSO Limitations and the LMPSO Solution

LMPSO addresses standard PSO stagnation by adding Levy-flight mutation and an Elite Memory Pool. Its iterative process evaluates ITAE, preserves superior solutions, and applies mutation when stagnation is detected.

  • A. Standard PSO Limitations and the LMPSO Solution: Standard PSO can stagnate when particles collapse into local optima in complex fitness landscapes.
  • A. Standard PSO Limitations and the LMPSO Solution: LMPSO uses Levy flights with Mantegna’s Algorithm to generate heavy-tailed mutation step sizes.
  • A. Standard PSO Limitations and the LMPSO Solution: Long-distance Levy jumps are triggered after stagnation detection to move particles toward unexplored regions.
  • A. Standard PSO Limitations and the LMPSO Solution: The Elite Memory Pool preserves top-performing solutions to balance exploration with exploitation, with sensitivity analysis suggesting a 10% pool size.
  • A. Standard PSO Limitations and the LMPSO Solution: The optimization cycle initializes fuzzy scaling factors, evaluates ITAE in Simulink, updates the Elite Pool, and conditionally applies Levy mutation or velocity updates.

V. SIMULATION EXPERIMENTS AND RESULT ANALYSIS

The study evaluates LMPSO-based fuzzy PID temperature control in MATLAB/Simulink using ITAE optimization and specified simulation parameters.

  • ITAE is used as the optimization objective to penalize long-duration errors and encourage faster settling.
  • The experiments are conducted in a MATLAB/Simulink simulation environment.
  • LMPSO and simulation parameters are documented in Table I for comparison across control strategies.

B. Parameter Selection and Sensitivity Analysis

The Levy flight index controls LMPSO mutation behavior, and β = 1.5 provides the reported best balance between exploration and convergence performance.

  • Parameter Selection and Sensitivity Analysis: β ∈{1.0, 1.5, 2.0} is tested because the Levy flight index governs mutation step size.
  • Parameter Selection and Sensitivity Analysis: β = 1.5 achieves the lowest ITAE by balancing excessive randomness at β = 1.0 against local-optimum trapping at β = 2.0.
  • Parameter Selection and Sensitivity Analysis: LMPSO is compared with Standard PSO and an IPSO variant using Dynamic Inertia Weight as the benchmark strategy.
  • Parameter Selection and Sensitivity Analysis: Standard PSO drops rapidly but flatlines around generation 10, indicating premature convergence.
  • Parameter Selection and Sensitivity Analysis: IPSO converges faster than Standard PSO but becomes trapped in a local optimum around generation 15.
  • Parameter Selection and Sensitivity Analysis: Around generation 16, LMPSO triggers Levy flight after stagnation detection and discovers a deeper minimum.

D. Dynamic Response Analysis

Dynamic-response comparisons examine multiple control schemes and show that LMPSO identifies an optimum less sensitive to parameter drift.

  • Dynamic Response Analysis: The evaluation compares Conventional PID, Empirical Fuzzy, Standard PSO, and IPSO using step-response curves and Table II metrics.
  • Dynamic Response Analysis: Scheme A (PID) exhibits 27% overshoot, while Scheme C (Standard PSO) is overly conservative.
  • Dynamic Response Analysis: 183.5 s is the IPSO settling time, which improves on Standard PSO.
  • Dynamic Response Analysis: Fig. 6 presents the step-response comparison, while Fig. 8 presents system responses under model-parameter perturbation.
  • Dynamic Response Analysis: LMPSO identifies a robust optimum that is less sensitive to parameter drift than the IPSO solution.

VI. CONCLUSION

The study addresses fuzzy PID optimization for industrial thermal processes with large delays and time-varying parameters using LMPSO. Simulations report faster, stable control performance.

  • LMPSO combines Levy-flight exploration with Elite Memory Pool exploitation to address fuzzy PID optimization challenges in industrial thermal processes.The approach targets processes characterized by large delays and time-varying parameters.
  • LMPSO reduces settling time by over 40% against competitive IPSO variants without compromising stability.
  • 105.5 s rise time was achieved, 42.5% faster than IPSO, while maintaining 1.63% overshoot.

E. Disturbance Rejection and Robustness

LMPSO improves temperature-response recovery after load disturbances and remains close to nominal performance under severe model mismatch. The study notes that these findings are currently simulation-based.

  • Disturbance rejection: 3.24◦C was the temperature deviation under a 20% negative load disturbance, with LMPSO recovering the setpoint significantly faster.The disturbance was injected at t = 400 s; IPSO recovered reasonably well but more slowly.
  • Robustness: Under Gain -10% and Time Constant +25% mismatch, LMPSO maintained a response profile remarkably similar to nominal performance.The degradation in ITAE was minimized under the perturbed conditions.
  • Scope boundary: The reported robustness results are limited to a theoretical model environment without real-world hardware validation.Future work is planned on a Hardware-in-the-Loop PLC platform.
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