Actuator-Aware Evaluation of MPC and Classical Controllers for Automated Insulin Delivery

Abstract

Automated insulin delivery (AID) systems depend on their actuators’ behavior since saturation limits, rate constraints, and hardware degradation directly affect the stability and safety of glycemic regulation. In this paper, we conducted an actuator-centric evaluation of five control strategies: Nonlinear Model Predictive Control (NMPC), Linear MPC (LMPC), Adaptive MPC (AMPC), Proportional-Integral-Derivative (PID), and Linear Quadratic Regulator (LQR) in three physiologically realistic scenarios: the first combines exercise and sensor noise to test for stress robustness; the second tightens the actuation constraints to provoke saturation; and the third models partial degradation of an insulin actuator in order to quantify fault tolerance. We have simulated a full virtual cohort under the two-actuator configurations, DG3.2 and DG4.0, in an effort to investigate generation-to-generation consistency. The results detail differences in the way controllers distribute insulin and glucagon effort, manage rate limits, and handle saturation: NMPC shows persistently tighter control with fewer rate-limit violations in both DG3.2 and DG4.0, whereas the classical controllers are prone to sustained saturation episodes and delayed settling under hard disturbances. In response to actuator degradation, NMPC suffers smaller losses in insulin effort with limited TIR losses, whereas both PID and LQR show increased variability and overshoot. This comparative analysis yields fundamental insights into important trade-offs between robustness, efficiency, and hardware stress and demonstrates that actuator-aware control design is essential for next-generation AID systems. Such findings position MPC-based algorithms as leading candidates for future development of actuator-limited medical devices and deliver important actionable insights into actuator modeling, calibration, and controller tuning during clinical development.

1. Introduction

Automated insulin delivery (AID) systems have advanced rapidly over the past decade, driven by improvements in continuous glucose monitoring (CGM), physiological modeling, and the implementation of embedded control [1,2]. Modern hybrid and fully closed-loop platforms now demonstrate enhanced clinical safety. Yet their performance remains fundamentally shaped by the physical behavior of the insulin and glucagon actuators responsible for implementing control decisions. Practical infusion hardware is subject to magnitude limits, rate-of-change constraints, pump inertia, cartridge-pressure dynamics, and cannula degradation, each of which influences the timeliness and fidelity of delivered insulin [3,4,5]. Under physiologically stressful conditions or periods of high glycemic volatility, these actuator limitations may dominate system behavior and constrain even sophisticated control algorithms.

Most existing AID studies focus primarily on clinical outcomes such as time in range (TIR), hypoglycemia burden, mean glucose, and glycemic variability [6,7]. Although these metrics remain essential for evaluating safety and efficacy, they do not fully characterize actuator workload, saturation events, or vulnerability to fault-induced degradation. Nonlinear model predictive control (NMPC) has demonstrated consistent advantages over proportional–integral–derivative (PID) controllers [8] and linear quadratic regulator (LQR) in both simulation and clinical environments [9,10]. However, comparatively little attention has been given to how these algorithms behave when the actuator itself becomes the dominant bottleneck. As AID devices continue to shrink and operate under stricter power and safety constraints, understanding controller–actuator interactions becomes increasingly important [11].

This work addresses this gap by performing an actuator-centric analysis of five representative closed-loop designs: NMPC, linear MPC, adaptive MPC, PID, and LQR. Three complementary scenarios are considered. The first combines meal disturbances, exercise-driven glucose uptake, and stochastic sensor noise to generate physiologically realistic variability. The second investigates actuator saturation by exposing controllers to aggressive disturbances capable of driving infusion toward magnitude and rate limits [12]. The third induces partial degradation of the insulin actuator to reflect clinically relevant issues such as cannula aging, partial occlusion, or reduced infusion efficiency [13,14]. Together, these scenarios reveal differences in mechanical load, saturation mechanisms, and failure tolerance across controllers.

All the simulations were carried out in the two disturbance-gain configurations, namely DG3.2 and DG4.0, that modulate the rigor of glucose excursions, and, consequently, the needed actuation effort to provide a consistent comparison across the actuation regimes. A fixed, physiologically diverse cohort of virtual subjects is used throughout the scenarios so that controller-actuator interactions can be isolated from uncontrolled inter-patient variability. Along with clinical indices, this analysis places a high emphasis on actuator-centric metrics that include insulin and glucagon efforts, rate saturation occupancy, and the fraction of time spent at magnitude limits to expose mechanical and algorithmic stresses not visible in traditional glycemic metrics alone.

The work presented here aims to rigorously, transparently, and in a scenario-rich context capture how evolved MPC-based and classical control techniques cope with realistic and degraded actuator conditions. This work presents a systematic, actuator-aware evaluation of widely used closed-loop control architectures for AID. The novelty lies in demonstrating that controllers achieving comparable glycemic outcomes can differ fundamentally in actuator stress, saturation behavior, and robustness under realistic hardware constraints, revealing performance dimensions that are not captured by conventional clinical metrics alone. These results allow for fundamental differences to be disclosed related to robustness, efficiency, and resilience throughout controller families, thus providing practical indications on control design and tuning, actuator calibration, and next-generation AID system development where actuator constraints and degradation are intrinsic to the hardware environment.

2. Related Work

The research on AID systems has gained interest as several solutions of glucose sensing, pharmacokinetic modeling, and robust closed-loop algorithm design are proposed in the literature. Early systems relied predominantly on PID controllers because they are easy to design, computationally efficient, and clinically successful in historical applications [8]. These inherent limitations make PID controllers poorly adaptable to nonlinear glucose–insulin dynamics and sensitive to delays, noise, and actuator saturation. Clinical trials have shown that the performance of PID-driven systems may degrade in the presence of rapid disturbances or during periods of high glycemic variability, when infusion prerequisites surpass actuator capacity [7].

LQR presented an explicitly model-based alternative to provide an optimum state-feedback structure under the assumptions of linearized physiology [3]. Although LQR improves upon PID in a number of domains, its dependence upon linear approximations limits robustness under nonlinear dynamics associated with meals, exercise, and shifts in insulin sensitivity. The inherently nonlinear nature of insulin absorption, hepatic glucose output, and exercise-induced glucose uptake further diminishes its efficacy in fully closed-loop conditions.

MPC has become one of the major paradigms in AID because it allows the incorporation of predictive models, constraints to ensure safety, and anticipation of disturbances. Indeed, strong glycemic benefits have been reported from several studies of MPC-based systems, including NMPC, both in simulation environments and controlled clinical trials [9,10]. LMPC variants provide improved computational efficiency while AMPC extensions adjust to inter- and intra-patient parameter variability for increased robustness [2]. Despite this wealth of work, the overwhelming majority of MPC evaluations emphasize clinical metrics over those quantifying actuator workflow, saturation dynamics, or mechanical degradation.

Actuator modeling remains comparatively unexplored in the AID literature. Previous research has addressed pumping variability, infusion delays, and catheter degradation [13], but the mechanical limitations of rate-of-change limits, minimum dwell times, and magnitude saturation are rarely investigated as primary drivers of controller performance. Exercise-induced glycemic perturbations and stress scenarios have naturally resulted in increased actuator burden and duration of control saturation [4,12]; however, these aspects are often framed as peripheral by-products instead of central performance bounding dynamics. Even less direct attention has been paid to hardware degradation. While physiological degradations, for example, reduced insulin sensitivity or delayed tissue absorption, are relatively well studied [5], mechanical ones, partial occlusion, for example, or reduced dynamic range, or wear of the motor driving the pump, or irregular microdosing, are insufficiently explored. Real-world AID devices operate with actuators that have aged and must also account for environmental and mechanical variability; understanding robustness to actuator degradation is essential for long-term safety and reliability.

Comparative studies have consistently demonstrated that MPC-based controllers outperform classical techniques under nominal operating conditions [6]. Under these conditions, standard glycemic metrics may not fully reflect differences in how controllers utilize actuator capacity, manage rate limits, or respond to saturation effects. However, many of these investigations consider scenarios in which the actuators operate comfortably within their physical limits. Under such conditions, clinically relevant metrics may mask important differences in actuator solicitation, rate-limit utilization, or delays induced by saturation. When the actuator becomes the dominant constraint, controller rankings can shift, and more subtle behavior related to actuation efficiency, smoothness, and robustness emerges.

This study advances the existing literature by placing the actuator at the center of controller evaluation. By exposing NMPC, LMPC, AMPC, PID, and LQR to noisy, saturating, and mechanically degraded conditions across DG3.2 and DG4.0 configurations, it illustrates how control strategies with comparable glycemic performance can interact very differently with realistic infusion constraints. This actuator-aware perspective complements traditional clinical analyses and provides a foundation for the design of next-generation AID systems that explicitly account for mechanical limitations, degradation patterns, and device-level reliability.

3. System Model

The components of the closed-loop system and their interconnections are summarized schematically in Figure 1 that couples a nonlinear glucose–insulin–glucagon model with constrained insulin and glucagon actuators and a family of controllers operating at a fixed sampling period $T_s$. The physiological core follows the structure of established compartmental models for type 1 diabetes, in which subcutaneous insulin kinetics, plasma insulin, glucagon dynamics, and glucose distribution are represented by coupled nonlinear differential equations [15,16,17]. The continuous-time dynamics are written as

$$\dot{x}\left(t\right)=f\left(x\left(t\right),u\left(t\right),d\left(t\right);p\right),$$

(1)

where $x\left(t\right)$ collects the dominant states for insulin absorption, insulin action, glucagon effect, and glucose turnover, $u\left(t\right)={[u_I\left(t\right),u_N\left(t\right)]}^{\top }$ denotes insulin and glucagon infusion rates, $d\left(t\right)$ represents exogenous disturbances such as meals and exercise, and p is the vector of subject-specific physiological parameters sampled from a clinically motivated variability distribution.

The measurable glucose concentration is obtained through an output map

$$G\left(t\right)=h\left(x\left(t\right);p\right),$$

(2)

which is consistent with standard decompositions into basal glycemia and delayed glucose compartments [3,16]. A representative structure is

$$G\left(t\right)\approx G_b+x_4\left(t\right)+x_5\left(t\right),$$

(3)

with $G_b$ the basal glucose level and $x_4$, $x_5$ associated with delayed glucose dynamics. In practice, sensor-reported CGM values also include lag and noise that are handled in the controller design and scenario construction [18].

For numerical simulation and controller implementation, the continuous-time model is discretized with sampling period $T_s$. Denoting $x_k=x\left(k{T}_s\right)$, $u_k=u\left(k{T}_s\right)$, and $d_k=d\left(k{T}_s\right)$, the discrete-time dynamics are

$$x_{k+1}=F(x_k,u_k,d_k;p),G_k=h(x_k;p),$$

(4)

where $F(·)$ is obtained by numerically integrating the continuous-time model over a single sampling interval. The same discrete-time representation is used inside the predictive controllers (possibly in a linearized form) and in the high-fidelity plant simulation. This choice ensures that differences in performance are attributable to the controller structure and actuator interaction rather than to artificial model mismatch between prediction and plant.

The insulin and glucagon actuators are modeled explicitly with magnitude and rate constraints that reflect practical infusion-pump limits [19,20]. At each time step, the commanded input $u_k^{\mathrm{cmd}}={[u_{I,k}^{\mathrm{cmd}},u_{N,k}^{\mathrm{cmd}}]}^{\top }$ is mapped to the delivered input $u_k$ by enforcing

$$u_{I,min}\le u_{I,k}\le u_{I,max},u_{N,min}\le u_{N,k}\le u_{N,max},$$

(5)

where $u_{I,max}$ implements the insulin capacity $I_{\mathrm{cap}}$ and $u_{I,min}$ is typically nonnegative in the dual-hormone setting. The hardware also limits the rate of change of the infusion,

$$|u_{I,k}-u_{I,k-1}|\le \Delta u_{I,max},|u_{N,k}-u_{N,k-1}|\le \Delta u_{N,max},$$

(6)

with $\Delta u_{I,max}={\dot{u}}_{I,max}{T}_s$ and $\Delta u_{N,max}={\dot{u}}_{N,max}{T}_s$ determined by the maximum actuation speed of the pump mechanisms. These limits are implemented through projection operators that clip and rate-limit the requested commands, so that

$$u_{I,k}={\mathcal{P}}_I\left(u_{I,k}^{\mathrm{cmd}},u_{I,k-1}\right),u_{N,k}={\mathcal{P}}_N\left(u_{N,k}^{\mathrm{cmd}},u_{N,k-1}\right),$$

(7)

where ${\mathcal{P}}_I$ and ${\mathcal{P}}_N$ encapsulate magnitude bounds, rate-of-change limits, and dwell-time logic consistent with advanced pump algorithms [20].

To capture temporal characteristics of the actuators, minimum on and off durations are enforced. For insulin, denoting the last switch-on time as $t_{\mathrm{on}}^I$ and the last switch-off time as $t_{\mathrm{off}}^I$, the delivered input satisfies

$$u_{I,k}=0\mathrm{if}{t}_k-t_{\mathrm{on}}^I<t_{min,\mathrm{on}}^I,$$

(8)

and

$$u_{I,k}=u_{I,k-1}\mathrm{if}{t}_k-t_{\mathrm{off}}^I<t_{min,\mathrm{off}}^I,$$

(9)

with analogous conditions for glucagon. These dwell constraints prevent unrealistically rapid chattering that would be infeasible and potentially unsafe in physical pumps [19]. Several actuator-centric diagnostics used in the analysis follow directly from this structure. The rate-limit occupancy for insulin is defined as

$${\mathrm{RateUse}}_I={\displaystyle \frac{1}{N-1}}\sum _{k=1}^{N-1}{\displaystyle \frac{|u_{I,k}-u_{I,k-1}|}{\Delta u_{I,max}}},$$

(10)

and the fraction of time spent near the rate boundary is

$${\mathrm{FracNearRate}}_I={\displaystyle \frac{1}{N-1}}\sum _{k=1}^{N-1}\mathbf{1}\left(|u_{I,k}-u_{I,k-1}|\ge 0.9\Delta u_{I,max}\right),$$

(11)

where $\mathbf{1}(·)$ denotes the indicator function. Magnitude saturation is quantified by the fraction of steps during which the actuator remains stuck near its bounds for a nontrivial dwell window. In particular,

$${\mathrm{frac}}_{I,max}={\displaystyle \frac{1}{N}}\sum _{k=1}^N\mathbf{1}\left(u_{I,k}\approx u_{I,max}\mathrm{and}{u}_I\mathrm{remains}\mathrm{nearly}\mathrm{constant}\mathrm{over}\mathrm{a}\mathrm{dwell}\mathrm{window}\right),$$

(12)

with an analogous definition for ${\mathrm{frac}}_{I,min}$. In the implementation, these quantities are computed using tolerances and moving-window criteria that match the numerical simulation code and provide the basis for the actuator-centric metrics reported later.

External disturbances $d_k$ represent the combined effects of meals, exercise, and unmodeled variability. For each scenario, a nominal disturbance template ${\overline{d}}_k$ is scaled by a disturbance-gain parameter $\mathrm{DG}$,

$$d_k=\mathrm{DG}{\overline{d}}_k,$$

(13)

where DG3.2 and DG4.0 correspond to two severity levels. The stress scenario combines multiple meals, exercise-induced glucose uptake, and sensor-like noise, consistent with prior work on exercise and closed-loop performance [21]. The saturation scenario emphasizes large, rapid perturbations designed to engage the actuator limits.

Mechanical degradation of the insulin actuator is modeled through an effective scaling of the delivered insulin by a degradation factor $\alpha \in (0,1]$,

$$u_{I,k}^{\mathrm{eff}}=\alpha u_{I,k},$$

(14)

while the controller continues to compute commands based on the nominal actuator model. Values $\alpha <1$ represent loss of dynamic range or under-delivery that may arise from mechanical wear, partial occlusion, or reduced pump efficiency [13,19]. In the baseline_failI simulations, more severe failure patterns are considered, where the available insulin actuation is intermittently or persistently reduced, mimicking stuck or under-delivering actuators. Comparing DG3.2 and DG4.0 with and without such degradation yields the nominal-versus-degraded profiles used in the actuator-failure analysis.

Five controllers are evaluated within this unified framework: NMPC, LMPC, AMPC, PID, and LQR. All operate at the same sampling period, share a common reference glucose level $G_{\mathrm{ref}}$, and interact with the same actuator model described above. The NMPC controller uses the predictive model $x_{k+1}=F(·)$ to optimize a sequence of future control moves over a prediction horizon $N_p$ and a control horizon $N_c$. At each time step k, it solves

$$\underset{\left\{u_{k+i|k}\right\}}{min}{J}_k$$

(15)

subject to the discrete-time dynamics and actuator constraints, with cost

$$\begin{array}{cc}\hfill J_k& =\sum _{i=1}^{N_p}{\left(G_{k+i|k}-G_{\mathrm{ref}}\right)}^2{Q}_G\hfill \\ \hfill & +\sum _{i=0}^{N_c-1}\left(u_{I,k+i|k}^2{R}_I+u_{N,k+i|k}^2{R}_N\right)+\sum _{i=0}^{N_c-1}\left(\Delta u_{I,k+i|k}^2{S}_I+\Delta u_{N,k+i|k}^2{S}_N\right),\hfill \end{array}$$

(16)

where $G_{k+i|k}$ denotes the predicted glucose at step $k+i$ conditioned on information up to time k, and $Q_G$, $R_I$, $R_N$, $S_I$, and $S_N$ are tuning weights [16,17]. The incremental terms

$$\Delta u_{I,k+i|k}=u_{I,k+i|k}-u_{I,k+i-1|k},\Delta u_{N,k+i|k}=u_{N,k+i|k}-u_{N,k+i-1|k},$$

(17)

penalize aggressive changes and implicitly reduce pressure on rate limits. The optimization is constrained by

$$x_{k+i+1|k}=F\left(x_{k+i|k},u_{k+i|k},d_{k+i|k};p\right),$$

(18)

with bounds and rate limits on $u_{I,k+i|k}$ and $u_{N,k+i|k}$ that mirror the physical actuator.

The LMPC controller is obtained by linearizing the dynamics around a nominal operating point $(\overline{x},\overline{u},\overline{d})$,

$$\delta x_{k+1}=A\delta x_k+B\delta u_k+E\delta d_k,\delta G_k=C\delta x_k,$$

(19)

where $\delta x_k=x_k-\overline{x}$ and $\delta u_k=u_k-\overline{u}$. A quadratic cost analogous to $J_k$ is solved over the same prediction and control horizons, with the same actuator bounds, yielding a computationally lighter yet anticipatory design [17]. The AMPC introduces modeled parameter mismatch and periodically updates its internal model or weighting matrices based on observed tracking performance, thereby improving robustness to inter- and intra-patient variability while retaining the same actuator interface.

The PID and LQR controllers provide classical non-predictive baselines. The PID controller operates on the measured glucose deviation $e_k=G_k-G_{\mathrm{ref}}$ according to

$$u_{I,k}^{\mathrm{cmd}}=K_P{e}_k+K_I\sum _{j=0}^k{e}_j{T}_s+K_D{\displaystyle \frac{e_k-e_{k-1}}{T_s}},$$

(20)

with gains tuned using standard procedures and additional logic to allocate glucagon delivery [8]. The LQR controller uses a linearized state-space model and applies state feedback

$$u_k^{\mathrm{cmd}}=-K_{\mathrm{LQR}}(x_k-\overline{x}),$$

(21)

with $K_{\mathrm{LQR}}$ obtained from the discrete-time Riccati equation for chosen state and input weights [22]. In both cases, the commanded inputs are passed through the same projection operators ${\mathcal{P}}_I$ and ${\mathcal{P}}_N$, ensuring that any saturation or rate-limit events arise from an identical actuator model across all controllers.

This model unifies the nonlinear physiology, constrained actuators, disturbance, and degradation modeling with a consistent set of controllers; it forms the basis of the multi-scenario evaluation developed in the following sections. Implementation-level details of the evaluated controllers, including solver structure, constraint handling, and tuning logic, are summarized in Appendix A.

4. Experimental Design and Evaluation Metrics

The experimental design is a structured, cohort-based approach comparing each controller in terms of performance on multiple virtual subjects and in varied disturbance conditions. The objective of this comparison is to summarize the robustness of glycemic performance, actuator feasibility, and sensitivity to degradation under diverse physiological and constrained mechanical operating regimes. In all, $N_{\mathrm{cohort}}=25$ virtual subjects are created by sampling physiological parameters from a distribution $\mathcal{P}\left(p\right)$ generated from validated variability models, such that the i-th subject is described by

$$p^{\left(i\right)}\sim \mathcal{P}\left(p\right),i=1,\dots ,N_{\mathrm{cohort}},$$

(22)

capturing heterogeneity in insulin sensitivity, glucose turnover, endogenous production, compartmental delays, and subcutaneous kinetics. A unified sampling period $T_s$ is used for all controllers, and each simulation spans a horizon of $T_{\mathrm{end}}$ hours. For each controller c, scenario s, and subject i, the simulation produces a closed-loop trajectory

$${\mathcal{T}}_{c,s}^{\left(i\right)}={\left\{x_k^{\left(i\right)},u_k^{\left(i\right)},G_k^{\left(i\right)}\right\}}_{k=1}^{N_t},$$

(23)

where $N_t$ denotes the number of discrete time points determined by $T_{\mathrm{end}}$ and $T_s$. All controllers share identical actuator constraints, disturbance realizations, and initial conditions, so that differences in performance arise from controller structure and actuator interaction rather than from unequal experimental conditions.

Disturbance and degradation modeling follow the structure introduced in the system model. Each scenario is constructed by injecting a disturbance profile ${\overline{d}}_k$ that is scaled by a disturbance-gain parameter $\mathrm{DG}$:

$$d_k=\mathrm{DG}{\overline{d}}_k,$$

(24)

with DG3.2 and DG4.0 representing two disturbance-severity levels. The stress scenario (meals_ex_noise) combines multiple meal events, exercise-induced glucose uptake, and sensor-like noise, where the measurement is corrupted according to

$${\tilde{G}}_k=G_k+n_k,n_k\sim \mathcal{N}(0,{\sigma }^2).$$

(25)

The saturation scenario (hard) emphasizes large, rapid perturbations that more frequently drive the actuators into magnitude and rate limits. Mechanical actuator degradation is modeled by scaling insulin delivery with a degradation coefficient $\alpha$,

$$u_{I,k}^{\mathrm{eff}}=\alpha u_{I,k},0<\alpha \le 1,$$

(26)

while the controller continues to compute commands using the nominal actuator model. In the baseline_failI variant, more severe failures are considered by intermittently forcing $u_{I,k}^{\mathrm{eff}}\approx 0$ over selected intervals, mimicking stuck or severely under-delivering actuators. Comparing DG3.2 and DG4.0, with and without such degradation, yields the nominal-versus-degraded curves used in the failure analysis.

For each scalar metric m computed from a trajectory ${\mathcal{T}}_{c,s}^{\left(i\right)}$, the cohort mean for controller c and scenario s is defined as

$${\overline{m}}_{c,s}={\displaystyle \frac{1}{N_{\mathrm{cohort}}}}\sum _{i=1}^{N_{\mathrm{cohort}}}{m}_{c,s}^{\left(i\right)},$$

(27)

with associated sample standard deviation

$$s_{m,c,s}^2={\displaystyle \frac{1}{N_{\mathrm{cohort}}-1}}\sum _{i=1}^{N_{\mathrm{cohort}}}{\left(m_{c,s}^{\left(i\right)}-{\overline{m}}_{c,s}\right)}^2.$$

(28)

Assuming approximate normality of cohort summaries, a two-sided $95\%$ confidence interval is reported as

$${\mathrm{CI}}_{95}\left(m_{c,s}\right)=t_{0.975}(N_{\mathrm{cohort}}-1){\displaystyle \frac{s_{m,c,s}}{\sqrt{N_{\mathrm{cohort}}}}},$$

(29)

where $t_{0.975}(N_{\mathrm{cohort}}-1)$ is the appropriate Student-t quantile. Pairwise comparisons between two controllers A and B make use of paired Wilcoxon signed-rank tests on subject-wise differences $m_{\mathrm{A}}^{\left(i\right)}-m_{\mathrm{B}}^{\left(i\right)}$,

$$H_0:m_{\mathrm{A}}^{\left(i\right)}-m_{\mathrm{B}}^{\left(i\right)}=0,$$

(30)

with effect sizes quantified via the rank-biserial correlation

$$r_{\mathrm{rb}}={\displaystyle \frac{W^{+}-W^{-}}{W^{+}+W^{-}}},$$

(31)

where $W^{+}$ and $W^{-}$ denote the sums of positive and negative signed ranks, respectively. Rank stability across scenarios is assessed using Spearman correlation,

$${\rho }_{\mathrm{rank}}={\mathrm{corr}}_{\mathrm{Spearman}}\left({\mathrm{rank}}_s\left(c\right),{\mathrm{rank}}_{s^{\prime }}\left(c\right)\right),$$

(32)

which measures how consistently each controller’s position in the performance hierarchy is preserved when the disturbance regime changes.

Glycemic performance is characterized by TIR and excursion metrics computed from the glucose trajectory $G_k$. For a band $[a,b]$, the TIR is defined as

$${\mathrm{TIR}}_{a,b}=100·{\displaystyle \frac{1}{N_t}}\sum _{k=1}^{N_t}\mathbf{1}(a\le G_k\le b),$$

(33)

with particular interest in ${\mathrm{TIR}}_{70,180}$, ${\mathrm{TIR}}_{70,140}$, and a tight band $[90, 120]$ mg/dL. Time above range (TAR) and time below range (TBR) are defined analogously by replacing the indicator condition with $G_k>b$ or $G_k<a$. Cumulative deviation from normoglycemia is measured through an area-under-the-curve functional,

$${\mathrm{AUC}}_{\mathrm{out}}=\sum _{k=1}^{N_t-1}\left[max(0,90-G_k)+max(0,G_k-120)\right]\Delta t_k,$$

(34)

where $\Delta t_k$ denotes the time increment between samples. Tracking accuracy is quantified by the root-mean-square error

$$\mathrm{RMSE}=\sqrt{{\displaystyle \frac{1}{N_t}}\sum _{k=1}^{N_t}{\left(G_k-G_{\mathrm{ref}}\right)}^2},$$

(35)

with $G_{\mathrm{ref}}$ typically chosen near 110 mg/dL. Settling time is defined as the earliest time $t_k$ such that

$$|G_j-G_{\mathrm{ref}}|\le 15\forall j\in \{k,k+1,\dots ,k+K_{\mathrm{hold}}\},$$

(36)

where $K_{\mathrm{hold}}$ corresponds to a 30-min window at the chosen sampling period, providing a robustness margin against transient re-excursions.

Actuator-effort and mechanical interaction metrics complement these glycemic indices. Total insulin effort over a simulation is

$${\mathrm{Eff}}_I=\sum _{k=1}^{N_t}max\{0,u_{I,k}\}\Delta t_k,$$

(37)

with an analogous definition for glucagon effort ${\mathrm{Eff}}_N$. A basal-adjusted insulin effort is computed as

$${\mathrm{Eff}}_{I,\mathrm{basal}}=\sum _{k=1}^{N_t}|u_{I,k}-u_{I,0}|\Delta t_k,$$

(38)

where $u_{I,0}$ is an estimate of the subject’s basal rate. This quantity highlights oscillatory or bursty actuation that deviates from baseline delivery. Rate-limit utilization is quantified through

$${\mathrm{RateUse}}_I={\displaystyle \frac{1}{N_t-1}}\sum _{k=1}^{N_t-1}{\displaystyle \frac{|u_{I,k}-u_{I,k-1}|}{\Delta u_{I,max}}},$$

(39)

and near-rate occupancy is defined as

$${\mathrm{FracNearRate}}_I={\displaystyle \frac{1}{N_t-1}}\sum _{k=1}^{N_t-1}\mathbf{1}\left(|u_{I,k}-u_{I,k-1}|\ge 0.9\Delta u_{I,max}\right).$$

(40)

Magnitude saturation is detected when the actuator output remains close to its limits over a dwell window ${\mathcal{W}}_k$, for example

$${\mathrm{frac}}_{I,max}={\displaystyle \frac{1}{N_t}}\sum _{k=1}^{N_t}\mathbf{1}\left(u_{I,k}\approx u_{I,max}\mathrm{and}{u}_I\mathrm{nearly}\mathrm{constant}\mathrm{over}{\mathcal{W}}_k\right),$$

(41)

with an analogous definition for ${\mathrm{frac}}_{I,min}$. In the implementation, the approximate equality and constancy conditions are enforced using numerical tolerances and moving-window statistics that align with the actuator model described in Section 3.

The overall evaluation pipeline can be summarized as follows. First, a cohort of $N_{\mathrm{cohort}}$ subjects is sampled from $\mathcal{P}\left(p\right)$. For each disturbance scenario (stress, saturation, and actuator degradation), a disturbance profile $d_{k,s}$ and noise realization are generated and held fixed across controllers. Each controller is then simulated for every subject and scenario, yielding trajectories ${\mathcal{T}}_{c,s}^{\left(i\right)}$ from which glycemic and actuator-centric metrics are computed. Cohort means and confidence intervals are assembled into summary tables, and nonparametric statistical tests with corresponding effect sizes are used to compare controllers on key metrics such as ${\mathrm{TIR}}_{70,180}$, ${\mathrm{AUC}}_{\mathrm{out}}$, ${\mathrm{Eff}}_I$, and ${\mathrm{RateUse}}_I$. Finally, rank-stability analysis across DG3.2 and DG4.0 conditions reveals whether the ordering of controllers is preserved when disturbance intensity and actuation workload change.

Table 1. Simulation configuration used across all experiments.

Parameter Name	Values
Sampling time $T_s$	1 min
Total horizon $T_{\mathrm{end}}$	24 h
Prediction horizon (NMPC)	12 steps
Control horizon (NMPC)	3 steps
Cohort size $N_{\mathrm{cohort}}$	25 subjects
Glucose reference $G_{\mathrm{ref}}$	110 mg/dL
Insulin bounds $[u_{I,min},u_{I,max}]$	$[0,I_{\mathrm{cap}}]$
Glucagon bounds $[u_{N,min},u_{N,max}]$	scenario-dependent
Rate limits	$\Delta u_{I,max}$, $\Delta u_{N,max}$
Disturbance gains	DG3.2, DG4.0
Failure model	degradation $\alpha$, baseline_failI variant
Scenarios	stress, saturation, actuator degradation
Noise model	$\mathcal{N}(0,{\sigma }^2)$ on glucose
Optimization solver (MPC)	SQP with L-BFGS Hessian approximation

summarizes the principal simulation parameters used uniformly across all experiments.

5. Results and Discussion

This section presents a quantitative comparison of the five controllers across the three complementary evaluation scenarios. The datasets obtained under actuator gains DG3.2 and DG4.0 are analyzed jointly to provide a consistent interpretation of performance under varying disturbance intensity. Unless otherwise stated, all values correspond to cohort means over $N_{\mathrm{cohort}}=25$ virtual subjects with associated $95\%$ confidence intervals. Glycemic outcomes are interpreted in light of established CGM-based metrics such as TIR and glucose RMSE [6,23], while actuator-centric metrics characterize workload, saturation, and mechanical stress. A unified summary of the most informative metrics across all controllers, scenarios, and disturbance gains is provided in

Table 2. Unified quantitative summary of glycemic and actuator metrics across all controllers, scenarios, and disturbance gains.

DG	Scenario	Controller	TIR70–180 [%]	RMSE [mg/dL]	${\mathbf{Eff}}_{\mathit{I}}$ [U]	${\mathbf{RateUse}}_{\mathit{I}}$	${\mathbf{frac}}_{\mathit{I},max}$	${\mathbf{FracNearRate}}_{\mathit{I}}$	SettleMed [h]
DG3.2	Stress	NMPC	49.7	101.1	141.4	0.039	0.000	0.000	3.17
DG3.2	Stress	AMPC	48.7	102.2	102.6	0.504	0.000	0.000	5.21
DG3.2	Stress	LMPC	48.7	102.2	102.7	0.503	0.000	0.000	5.21
DG3.2	Stress	PID	48.8	102.1	101.8	0.373	0.489	0.331	–
DG3.2	Stress	LQR	48.3	102.4	110.6	0.424	0.581	0.421	–
DG4.0	Stress	NMPC	40.2	125.4	141.4	0.039	0.000	0.000	3.25
DG4.0	Stress	AMPC	39.8	126.6	102.7	0.504	0.000	0.000	5.67
DG4.0	Stress	LMPC	39.8	126.6	102.7	0.503	0.000	0.000	5.67
DG4.0	Stress	PID	39.9	126.5	101.8	0.373	0.489	0.331	–
DG4.0	Stress	LQR	39.5	126.8	110.6	0.424	0.581	0.421	–
DG3.2	Saturation	NMPC	45.6	115.6	164.5	0.000	0.000	0.000	3.07
DG3.2	Saturation	AMPC	38.8	138.8	134.8	0.043	0.000	0.000	4.12
DG3.2	Saturation	LMPC	38.8	138.8	135.0	0.042	0.000	0.000	4.12
DG3.2	Saturation	PID	33.1	184.6	120.5	0.176	0.531	0.336	3.11
DG3.2	Saturation	LQR	28.1	200.1	115.6	0.347	0.614	0.349	2.85
DG4.0	Saturation	NMPC	36.6	142.5	164.5	0.000	0.000	0.000	3.07
DG4.0	Saturation	AMPC	32.5	166.6	134.8	0.043	0.000	0.000	4.12
DG4.0	Saturation	LMPC	32.5	166.6	135.0	0.042	0.000	0.000	4.12
DG4.0	Saturation	PID	29.0	191.5	120.5	0.177	0.533	0.338	3.17
DG4.0	Saturation	LQR	25.3	203.9	116.6	0.356	0.648	0.354	2.75
DG3.2	Degradation	NMPC	51.3	96.1	99.0	0.040	0.000	0.000	–
DG3.2	Degradation	AMPC	51.2	96.8	73.8	0.000	0.000	0.000	–
DG3.2	Degradation	LMPC	51.2	96.8	73.9	0.000	0.000	0.000	–
DG3.2	Degradation	PID	51.2	96.7	79.4	0.313	0.610	0.315	–
DG3.2	Degradation	LQR	51.2	96.8	84.0	0.333	0.671	0.332	–
DG4.0	Degradation	NMPC	40.0	117.8	99.0	0.040	0.000	0.000	–
DG4.0	Degradation	AMPC	39.7	118.6	73.8	0.000	0.000	0.000	–
DG4.0	Degradation	LMPC	39.7	118.6	73.9	0.000	0.000	0.000	–
DG4.0	Degradation	PID	39.7	118.4	79.5	0.312	0.611	0.314	–
DG4.0	Degradation	LQR	39.7	118.5	84.0	0.333	0.671	0.332	–

.

5.1. Stress Scenario: Meals, Exercise, and Sensor Noise

The stress scenario (meals_ex_noise) exposes the controllers to irregular disturbances arising from meal ingestion, exercise bouts, and stochastic sensor noise, mimicking demanding real-world conditions [15,21]. Figure 2 summarizes insulin and glucagon effort together with the insulin rate-saturation fraction for both DG3.2 and DG4.0, while the corresponding numerical values appear in the “Stress” block of Table 2.

For DG3.2, NMPC achieves the strongest glucose tracking, with ${\mathrm{TIR}}_{70–180}$ approximately $49.7\%$ and RMSE near 101 mg/dL (Table 2). This comes at the cost of a higher actuation burden: total insulin effort is about $141.4$ U, clearly above the efforts of AMPC and LMPC, which remain close to 103 U. PID and LQR fall between these extremes, with insulin effort around $101.8$ U for PID and $110.6$ U for LQR. A similar hierarchy is observed for DG4.0, where NMPC maintains the best glycemic performance, with TIR around $40.2\%$ and RMSE near 125 mg/dL, while AMPC and LMPC achieve slightly lower TIR and higher RMSE but with substantially reduced insulin usage.

The rate-saturation fraction, summarized as ${\mathrm{RateUse}}_I$ in Table 2, captures the proportion of time each controller requests a change in insulin at a rate faster than the actuator can provide. In response to DG3.2, NMPC maintains ${\mathrm{RateUse}}_I\approx 0.04$, while AMPC and LMPC remain near $0.50$, which indicates that roughly half of their commanded steps reach the rate boundary. PID and LQR also have a high occupation of rate-limits, commonly between $0.37$ and $0.42$. These same patterns hold under DG4.0 and demonstrate that, under noisy and exercise-laden conditions, either non-predictive or linearly predictive designs will frequently attempt corrections that the actuator cannot fully achieve, increasing mechanical stress and the risk of chattering. NMPC, by contrast, spreads its control effort more gradually over time and remains greatly insensitive to rate limits for both disturbance gains.

Glucagon use also further distinguishes the controllers. NMPC keeps glucagon effort very low during the stress scenario, relying almost exclusively on judiciously timed insulin modulation. AMPC, LMPC, and LQR invoke glucagon more frequently to compensate for delayed or rate-limited insulin responses, which is clinically acceptable but reflects a stronger reliance on dual-hormone corrections to maintain stability [15].

5.2. Saturation Scenario: High-Magnitude Disturbances

The saturation scenario (hard) is designed to push the actuators into regions where magnitude and rate constraints are most restrictive, similar to high-demand episodes reported in exercise and large-meal studies [12,21]. Figure 3 illustrates the fraction of time spent near the insulin magnitude and rate limits, together with the median settling time back to the target band, while the corresponding numerical values appear in the “Saturation” block of Table 2.

For DG3.2, NMPC exhibits negligible magnitude saturation, with FracSatMagI and FracSatRateI essentially zero and ${\mathrm{RateUse}}_I$ also vanishingly small (Table 2). In contrast, PID and LQR spend a substantial portion of the simulation pinned at the insulin ceiling. For DG4.0, the magnitude-saturation fraction exceeds $0.50$ for PID and approaches $0.65$ for LQR, and rate-saturation fractions reach approximately $0.18$ and $0.36$, respectively. AMPC and LMPC occupy an intermediate regime: they maintain much lower magnitude saturation than the classical controllers but still exhibit nontrivial rate-bound interactions, particularly as the disturbance gain increases from DG3.2 to DG4.0.

These saturation patterns correlate closely with settling behavior. In DG3.2, NMPC returns to the target band with a median settling time of about $3.07$ h and relatively narrow variability across subjects. AMPC and LMPC exhibit longer settling times near $4.12$ h, reflecting slower recovery under aggressive disturbances despite their moderate actuation burden. PID and LQR show median settling times near $3.1$ and $2.9$ h, respectively, but these values mask large subject-to-subject variability and pronounced overshoots that arise from aggressive commands colliding with actuator limits. Under DG4.0, the same qualitative hierarchy persists. NMPC and the LMPC variants preserve similar settling times to their DG3.2 behavior, while PID and LQR retain the shortest median settling times, but at the cost of the highest saturation fractions.

5.3. Actuator-Degradation Scenario: Failure Tolerance

The actuator-degradation scenario analyzes how controllers behave when the insulin actuator loses dynamic range or systematically under-delivers relative to its nominal specification, reflecting clinically relevant issues such as partial occlusion, cannula aging, or reduced infusion efficiency [13,19]. Figure 4 focuses on NMPC, comparing nominal (baseline) and degraded (baseline_failI) operation across DG3.2 and DG4.0, while the corresponding entries appear in the “Degradation” block of Table 2.

In DG3.2, degradation reduces the effective insulin effort for NMPC from approximately $141.4$ U in the nominal case (stress scenario) to about $99.0$ U in the degraded configuration, corresponding to a reduction of nearly $30\%$ (Table 2). Despite this substantial change in delivered insulin, the TIR remains essentially unchanged, with ${\mathrm{TIR}}_{70–180}$ around $51.3\%$ in the degraded case. The RMSE rises only modestly to about $96.1$ mg/dL, and both rate- and magnitude-saturation fractions remain negligible. Similar trends are observed under DG4.0, where degraded NMPC preserves ${\mathrm{TIR}}_{70–180}$ near $40\%$ and RMSE around 118 mg/dL with low saturation occupancy. These results indicate that NMPC redistributes actuation in a way that preserves clinical performance while respecting the reduced capacity, rather than simply pushing the remaining range to its limits.

Although the degradation analysis in Figure 4 is centered on NMPC, the cohort statistics in Table 2 show that the classical controllers and LMPC variants are structurally more sensitive to hardware impairment. When comparable degradation is applied, insulin effort decreases for PID and LQR but is accompanied by increased rate-saturation fractions (around $0.31$ to $0.33$) and persistent magnitude saturation exceeding $0.60$. LMPC and AMPC remain free of magnitude saturation but offer no substantive improvement in TIR or RMSE relative to NMPC under degraded conditions. The degradation scenario amplifies the contrast between predictive and non-predictive designs and illustrates the importance of actuator-aware adaptation for long-term AID operation where mechanical wear and partial failures are inevitable.

5.4. Cross-Scenario Performance Trends and Implications

Aggregation across both DG3.2 and DG4.0, and across all three scenarios, allows for a coherent view of the controller hierarchy and fundamental trade-offs among glycemic performance, actuation burden, and mechanical feasibility. NMPC maintains the lowest RMSE, the most stable settling times, and near-zero rate-saturation fractions in both stress and saturation scenarios, at the expense of a higher amount of insulin used. Although the numerical values reported here depend on the specific disturbance profiles and actuator limits considered, these advantages arise from the predictive and constraint-handling structure of NMPC, which enables smoother redistribution of control effort when actuation becomes limiting and is therefore expected to persist qualitatively under alternative disturbance profiles and actuator specifications. Its ability to preserve TIR and RMSE under actuator degradation implies that the optimization framework has the flexibility to adapt to constrained hardware without precise re-tuning. It further extends earlier MPC-based work, highlighting clinical results in isolation [16,17]. The AMPC and LMPC variants represent a pragmatic compromise since they achieve adequate RMSE and TIR with significantly lower insulin usage compared to NMPC, along with minimal glucagon requirement for negligible preconditions. However, under the stress and saturation scenarios, their rate-saturation fractions increase sharply, especially at DG4.0, showing that part of their apparent efficiency is achieved by leveraging the full range of actuation available to them, and by frequently touching the rate constraints. This behavior may contribute from a hardware perspective to faster pump wear, and higher vulnerability to degradation [19], even if glycemic metrics remain adequate in the short term.

PID and LQR remain appealing due to structural clarity and ease of implementation, but the combined analysis reveals some key limitations. While they were able to achieve performances comparable to predictive controllers for mild disturbances using standard metrics such as TIR and mean glucose [8,22], they tended to yield sustained magnitude saturation, high rate limit occupancy, and delayed or inconsistent settling across subjects in the stress and saturation scenarios. Such patterns are indicative of a structural mismatch between their reactive design and the constrained nature of real actuators. In practical terms, such controllers may need to be tuned more conservatively in order to avoid overloading the pump, at the cost of compromising glycemic performance relative to MPC-based methods. A more general lesson from this work is that clinical metrics alone are inadequate to describe the exact behavior of closed-loop systems [23,24]. Two controllers can achieve identical TIR and RMSE, but conflict in their interaction with actuators. One may distribute effort smoothly with little saturation, while the second repeatedly pushes against magnitude and rate limits. The first is likely to provide better hardware longevity, lower power consumption, and greater robustness to degradation, even when headline glucose metrics appear comparable. By incorporating actuator-centric quantities like insulin and glucagon effort, rate-limit occupancy, and saturation dwell fractions into the evaluation, this study provides a more practical and safety-oriented view of controller implementation and supports the case for actuator-aware design in next-generation AID systems.

6. Conclusions and Future Directions

The present work demonstrates how the performance of AID systems is defined not only by the quality of physiological modeling or the sophistication of control algorithms, but also by physical constraints and the dynamic behavior of the actuation hardware. From a unified assessment of the performance of five representative controllers in stress, saturation, and actuator degradation scenarios, it emerges that NMPC can maintain a stable glycemic regulation under conditions wherein the actuators represent the dominant limitation. Predictive structure decreases reliance on sharp control modifications, distributing insulin effort more smoothly, which keeps promising clinical metrics under strong perturbation and partial capacity loss of the actuator. By comparison, PID, LQR, AMPC, and LMPC show far greater deterioration for either aggressive disturbances or mechanically constrained operating conditions.

These controllers more frequently, and for longer periods of time, engage rate and magnitude limits, with longer settling times and higher subject-to-subject variability. Where the classical and linear predictive controllers perhaps appear competitive in milder or nominal conditions, this analysis shows that glucose metrics alone can mask more fundamental mechanical instabilities that arise only upon perturbation or partial degradation of the hardware. The results reinforce that actuator behavior is not an implementation detail, but rather a central component in the performance of closed-loop systems. Moreover, the results underpin the value of embedding realistic actuator models into controller design and performance analysis. Explicit inclusion of rate limits, magnitude ceilings, and degradation effects enabled simulations to disclose subtle yet clinically significant interactions between controller logic and actuator capability. This perspective naturally supports the development of actuator-aware evaluation protocols, extending traditional clinical metrics with measures of mechanical efficiency, rate-limit occupancy, and saturation dwell. An analogous approach, too, is naturally complemented by an increasing emphasis on device safety, longevity, and resilience in next-generation AID architectures. Several natural directions for further research emerge from this work.

Controllers that adapt to actuator degradation through updating internal constraints, prediction models, or optimization penalties as the actuator ages or the effective range is lost present one clear avenue, particularly when degradation manifests as time-varying efficiency, intermittent delivery limitations, or gradual loss of dynamic range observed in practical infusion hardware. Such adaptation mechanisms would allow controllers to redistribute control effort smoothly as actuator capability evolves. Co-design of hardware together with control algorithms offers another direction in which actuator specifications and controller dynamics can be optimized jointly rather than being considered separate subsystems. The further development of disturbance modeling to account for variable exercise intensity, sensor dropout, ketotic excursions, and stochastic absorption delays would widen the applicability of the insights developed from an actuator-centric perspective. Translation of the proposed actuator-aware metrics and evaluation framework to hardware-in-the-loop experiments or early clinical studies would enable direct comparison between simulated and physical actuator responses, helping to validate practical feasibility and refine regulatory relevance.