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Modeling and Mixed-Integer Nonlinear MPC of Positive-Negative Pressure Pneumatic Systems

Yu Mei, Xinyu Zhou, Xiaobo Tan

TL;DR

The paper tackles the regulation of positive and negative pressure in soft pneumatic systems, where bidirectional actuation and affordable valves yield nonlinear, switching dynamics. It develops a mixed-integer nonlinear model predictive controller that co-optimizes mode scheduling and PWM inputs on a physics-grounded switched plant, employing a Combinatorial Integral Approximation to relax discrete decisions. The approach yields a control-affine hybrid model, a MINLP that is tractable via the CIA NLP and a rounding step, and demonstrates superior trade-offs in tracking accuracy, energy use, and switching compared to baselines in simulation using real-system parameters. Although computational demand is higher, the results highlight the practical potential for model-based control in multi-channel soft actuators, with future work aimed at real-time validation, solver acceleration, and stability analysis.

Abstract

Positive-negative pressure regulation is critical to soft robotic actuators, enabling large motion ranges and versatile actuation modes. However, it remains challenging due to complex nonlinearities, oscillations, and direction-dependent, piecewise dynamics introduced by affordable pneumatic valves and the bidirectional architecture. We present a model-based control framework that couples a physics-grounded switched nonlinear plant model (inflation/deflation modes) with a mixed-integer nonlinear model predictive controller (MI-NMPC). The controller co-optimizes mode scheduling and PWM inputs to realize accurate reference tracking while enforcing input constraints and penalizing energy consumption and excessive switching. To make discrete mode decisions tractable, we employ a Combinatorial Integral Approximation that relaxes binary mode variables to continuous surrogates within the valve-scheduling layer. With parameters identified from the physical system, simulations with step and sinusoidal references validate the proposed MI-NMPC, showing a consistently favorable trade-off among accuracy, control effort, and switching, and outperforming conventional PID and NMPC with heuristic mode selection.

Modeling and Mixed-Integer Nonlinear MPC of Positive-Negative Pressure Pneumatic Systems

TL;DR

The paper tackles the regulation of positive and negative pressure in soft pneumatic systems, where bidirectional actuation and affordable valves yield nonlinear, switching dynamics. It develops a mixed-integer nonlinear model predictive controller that co-optimizes mode scheduling and PWM inputs on a physics-grounded switched plant, employing a Combinatorial Integral Approximation to relax discrete decisions. The approach yields a control-affine hybrid model, a MINLP that is tractable via the CIA NLP and a rounding step, and demonstrates superior trade-offs in tracking accuracy, energy use, and switching compared to baselines in simulation using real-system parameters. Although computational demand is higher, the results highlight the practical potential for model-based control in multi-channel soft actuators, with future work aimed at real-time validation, solver acceleration, and stability analysis.

Abstract

Positive-negative pressure regulation is critical to soft robotic actuators, enabling large motion ranges and versatile actuation modes. However, it remains challenging due to complex nonlinearities, oscillations, and direction-dependent, piecewise dynamics introduced by affordable pneumatic valves and the bidirectional architecture. We present a model-based control framework that couples a physics-grounded switched nonlinear plant model (inflation/deflation modes) with a mixed-integer nonlinear model predictive controller (MI-NMPC). The controller co-optimizes mode scheduling and PWM inputs to realize accurate reference tracking while enforcing input constraints and penalizing energy consumption and excessive switching. To make discrete mode decisions tractable, we employ a Combinatorial Integral Approximation that relaxes binary mode variables to continuous surrogates within the valve-scheduling layer. With parameters identified from the physical system, simulations with step and sinusoidal references validate the proposed MI-NMPC, showing a consistently favorable trade-off among accuracy, control effort, and switching, and outperforming conventional PID and NMPC with heuristic mode selection.

Paper Structure

This paper contains 12 sections, 17 equations, 6 figures, 3 tables, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. POSITIVE-NEGATIVE PRESSURE PNEUMATIC SYSTEM
  3. System Description
  4. Switched System Modeling
  5. Control-affine Hybrid Formulation
  6. MIXED-INTEGER NONLINEAR MODEL PREDICTIVE CONTROL
  7. Mixed-integer Optimal Control Problem
  8. Mixed-Integer NMPC with Combinatorial Integral Approximation
  9. SIMULATION
  10. Baseline Controllers: PID and NMPC
  11. Numerical Setup and Results
  12. CONCLUSION

Figures (6)

  • Figure 1: Positive-negative pressure pneumatic system schematic.
  • Figure 2: Block diagram of the mathematical model of a solenoid valve subsystems.
  • Figure 3: Schematic of the mass flow contributions to the air receiver.
  • Figure 4: Simulation results of tracking step reference with zoomed-in snapshot. For each case, the subplots from top to bottom show: output pressure, tracking error, control input (PWM), and mode sequence over time.
  • Figure 5: Simulation results of tracking the sinusoidal reference.
  • ...and 1 more figures