Precision-Drive-Dynamics: Nonlinear Actuator Dynamics, State-Space LQR & Neural-Adaptive Sliding Mode Control

Research Project | Advanced Nonlinear Control Systems, Non-Newtonian Friction & Physical Motion Intelligence

📄 Research Paper Manuscript: Read the full research manuscript draft (target venue: IEEE Transactions on Industrial Electronics): docs/paper/RESEARCH_PAPER.md | LaTeX Source with Theorem 1 (Finite-Time Sliding Convergence) and Theorem 2 (CBF Safe Invariance).
📐 Mathematical Derivations & Lyapunov Proofs: Complete Moreno-Osorio quadratic Lyapunov candidate proofs, LESO error boundedness lemmas, and Stribeck models: docs/NONLINEAR_DYNAMICS_AND_SMC_PROOFS.md.
⚙️ Three Implementation Tiers: Architecture comparison and firmware for V1, V2, and V3: docs/IMPLEMENTATION_VERSIONS.md.

Electromechanical actuators in high-precision robotics, surgical manipulators, and physical AI platforms must achieve sub-milliradian positioning, rapid speed settling, and immediate recovery from unknown external load torque shocks. While traditional introductory treatments assume idealized linear second-order plants governed by basic PID loops, real physical actuators exhibit acute nonlinearities:

• Stribeck & Coulomb friction: Induces stick-slip limit-cycle oscillations and steady-state deadband around zero-velocity crossovers.
• Actuator saturation: Voltage and current bounds cause severe integrator windup and thermal degradation.
• Thermal parameter drift: Armature copper resistance $R_a(T)$ shifts with temperature, while rotor inertia $J$ varies with dynamic payload grasping.

This research project develops a unified motion control framework combining:

1. High-Gain Linear Extended State Observer (LESO): Reconstructs unmodeled load torque shocks and friction in $<2,\text{ms}$.
2. Neural-Adaptive Super-Twisting 2-SMC (NA-STA): Eliminates high-frequency sliding mode chattering via continuous gain relaxation while guaranteeing finite-time convergence.
3. Control Barrier Function (CBF) Safety Filter: Enforces forward invariance of armature current ($|i_a| \le 8,\text{A}$) and inverter voltage saturation ($|V_a| \le 24,\text{V}$).
4. Three Real-World Implementation Tiers:
   • Tier 1 (Embedded Microcontroller Baseline): MISRA-C 20 kHz PWM timer ISR for STM32 FreeRTOS paired with an ISO 11898-2 CAN-bus telemetry driver with CRC-16 integrity.
   • Tier 2 (Stribeck LESO Hardware Driver): 10 kHz LESO state and disturbance observer with vectorized Stribeck friction benchmark.
   • Tier 3 (Neural-Adaptive CBF-STA): Differentiable QP safety filter ensuring strict electrical barrier adherence.

       Armature Circuit                           Rotor Mechanics
      +---/\/\/\---UUUU---+
      |     R        L    |
 +    |                   |                     +----------+
v_a(t)|               ( M ) e_b(t) = K_e*w      | Rotor J  |---> w(t), theta(t)
 -    |                   |                     +----------+
      +-------------------+                          |
                                                Load T_L(t) + Friction T_f(w)

$$\begin{aligned} L_a \frac{d i_a(t)}{dt} &= V_a(t) - R_a(T) i_a(t) - K_e \omega(t) \\ J \frac{d\omega(t)}{dt} &= K_t i_a(t) - \tau_f(\omega) - \tau_L(t) \end{aligned}$$

Where nominal motor parameters: $J = 0.015,\text{kg}\cdot\text{m}^2$, $K_t = 0.45,\text{N}\cdot\text{m/A}$, $K_e = 0.45,\text{V}\cdot\text{s/rad}$, $R_a = 1.25,\Omega$, $L_a = 8.0,\text{mH}$.

$$\tau_f(\omega) = \left[ T_c + (T_s - T_c) \exp\left(-\left(\frac{\omega}{\omega_s}\right)^2\right) \right] \operatorname{sgn}(\omega) + b_{\text{visc}} \omega$$

Where $T_c = 0.25,\text{N}\cdot\text{m}$ (Coulomb), $T_s = 0.55,\text{N}\cdot\text{m}$ (Static breakaway), $\omega_s = 6.0,\text{rad/s}$ (Stribeck velocity threshold), and $b_{\text{visc}} = 0.08,\text{N}\cdot\text{m}\cdot\text{s/rad}$.

Benchmarking under severe transient disturbance shocks ($0.45,\text{N}\cdot\text{m}$ step load impact at $t=1.2,\text{s}$):

1. $90.88%$ Disturbance Sag Reduction: High-gain LESO observer estimates unknown load torque within $<2,\text{ms}$, dynamically injecting feedforward cancellation.
2. $95.4%$ Chattering Elimination: Continuous Super-Twisting algorithm eliminates high-frequency actuator heating and gear tooth wear.
3. Deterministic Electrical Safety: The CBF quadratic program guarantees strict adherence to inverter voltage ($|V_a| \le 48,\text{V}$) and current limits.

Precision-Drive-Dynamics/
├── README.md                                         # Master research documentation
├── requirements.txt                                  # Python dependencies
├── classical_frequency_response.py                   # Bode, Nyquist & root locus analysis
├── modern_control_analysis.py                        # LQR, CARE & Monte Carlo robustness
├── nonlinear_friction_smc_benchmark.py               # Stribeck friction & NDOB observer
├── super_twisting_smc_eso.py                         # Super-Twisting 2-SMC & LESO benchmark
├── adaptive_cbf_super_twisting.py                    # Neural-Adaptive CBF-STA QP verification
├── docs/
│   ├── NONLINEAR_DYNAMICS_AND_SMC_PROOFS.md          # Formal Lyapunov stability & CBF proofs
│   ├── IMPLEMENTATION_VERSIONS.md                    # Architecture guide for V1, V2, and V3
│   └── paper/
│       ├── RESEARCH_PAPER.md                         # Full IEEE TIE format research draft
│       └── Precision_Drive_Dynamics_TIE.tex          # LaTeX manuscript source
├── pid_figures/                                      # Publication-grade simulation plots
│   ├── fig_adaptive_cbf_super_twisting.png           # NA-STA CBF verification
│   ├── fig_precision_drive_benchmark.png             # Tier 2 hardware benchmark
│   ├── fig_super_twisting_chattering_free.png        # Chattering suppression comparison
│   └── fig_eso_disturbance_estimation.png            # LESO reconstruction accuracy
└── implementations/                                  # Three concrete implementation versions
    ├── v1_embedded_stm32_freertos/                   # 20 kHz PWM ISR + ISO 11898 CAN HAL
    │   ├── firmware_stm32_foc.c
    │   ├── can_motor_telemetry.py
    │   └── main_embedded_drive_runner.py
    ├── v2_stribeck_leso_hardware_driver/             # Stribeck friction & 10 kHz LESO driver
    │   ├── stribeck_friction_model.py
    │   ├── high_gain_leso_driver.py
    │   └── precision_drive_benchmark.py
    └── v3_neural_adaptive_cbf_sta/                   # Neural-Adaptive CBF QP Safety Stack
        ├── neural_adaptive_super_twisting.py
        └── cbf_qp_safety_filter.py

# Run Tier 1 Embedded CAN-Bus Telemetry Loop:
python -m implementations.v1_embedded_stm32_freertos.main_embedded_drive_runner

# Run Tier 2 Stribeck LESO Hardware Benchmark:
python -m implementations.v2_stribeck_leso_hardware_driver.precision_drive_benchmark

# Run Tier 3 Neural-Adaptive CBF-STA Verification:
python adaptive_cbf_super_twisting.py

@misc{koduru2026precision,
  author = {Koduru, Yagnesh Kumar},
  title  = {Neural-Adaptive Super-Twisting Sliding Mode Control with Control Barrier Functions for High-Precision Motor Drives},
  year   = {2026},
  note   = {Research manuscript draft; not peer reviewed},
  url    = {https://github.com/yagneshkumarkoduru/Precision-Drive-Dynamics}
}