Variable impedance model predictive control (MPC) formulations often treat joint stiffness as an instantaneous decision variable. The resulting feasible set strictly contains the physically realizable set under first-order actuator dynamics. We identify this as a formulation error rather than a modeling approximation, formalize the distinction between the parameter-based feasible set F_param and the realizable set F_real, and characterize the regime of mismatch via the dimensionless parameter α = ωsT (actuator bandwidth times task timescale). For the 1D hopping monoped, we prove that below an analytical threshold α_crit derived in closed form from task physics, no admissible stiffness command realizes the parameter-based prediction. Numerical validation in 1D shows monotonic deviation growth as α decreases, with the predicted scaling holding across ten parameter combinations (log-log R2 = 0.986). Mechanism transfer to planar spring-loaded inverted pendulum dynamics confirms center-of-mass and stance-timing deviation as the primary consequence, with regime-dependent friction effects as a tertiary observable. A second threshold α_infeas < α_crit establishes a floor below which restricting the admissible stiffness range cannot repair realizability, closing the conservative-tuning objection. Augmenting the prediction state with stiffness closes the mismatch by construction.

翻译：可变阻抗模型预测控制（MPC）公式常将关节刚度视为瞬时决策变量，由此得到的可行集严格包含一阶执行器动力学下的实际可实现集。我们识别出这属于公式化误差而非建模近似，形式化区分了基于参数的可行集F_param与可实现集F_real，并通过无量纲参数α=ω_sT（执行器带宽乘以任务时间尺度）刻画了不匹配区间。针对一维弹跳单足系统，我们证明当α低于从任务物理中闭式导出的解析阈值α_crit时，不存在可容许刚度指令能实现基于参数的预测。一维数值验证显示偏差随α减小单调增长，且预测标度关系在十组参数组合中成立（对数-对数R²=0.986）。机制迁移至平面弹簧负载倒立摆动力学后，确认质心轨迹和支撑相时序偏差为主要影响，随区间变化的摩擦效应为三级可观测现象。第二个阈值α_infeas<α_crit确立了限制可容许刚度范围无法修复可实现性的下限，从而否定了保守调参的反对意见。通过将刚度增广至预测状态，可构造性地消除该不匹配。