Switched nonlinear control of high-pressure grinding rolls under multi-objective particle size constraints

Controlling the particle size distribution (PSD) of high-pressure grinding rolls (HPGR) presents a fundamental challenge in mineral processing, requiring the simultaneous coordination of three conflicting quality objectives: target size fraction yield tracking, coarse particle suppression, and over-grinding mitigation. This paper formulates the HPGR PSD control problem as a switched affine nonlinear system with three operating modes (coarse particle breakage, over-grinding mitigation, and efficiency maintenance), and proposes a co-design methodology integrating mode-dependent state feedback control with multiple Lyapunov functions (MLF) based switching law. First, a switched affine nonlinear model is established with explicit control objective constraints. Second, mode-dependent feedback gains are synthesized via linear matrix inequalities (LMIs). Third, a three-layer composite switching law is constructed incorporating particle size thresholds, MLF constraints, and minimum dwell time, with theoretical proofs of exponential stability under ideal conditions and uniform ultimate boundedness under bounded disturbances and estimation errors. Model-based numerical evaluation using nonlinear HPGR models identified from industrial data shows that the proposed method achieves an aggregate constraint violation rate of 4.10%, compared with 7.50% for the Mamdani fuzzy-expert HPGR controller and 17.07% for gain-scheduled PID, while reducing IAE by 86.5% and 89.0%, respectively. The simulations also demonstrate robustness to the tested parameter perturbations and state-estimation errors. These results describe simulated closed-loop performance under the stated model assumptions.