Offset-free nonlinear model predictive control (NMPC) can eliminate the tracking offset associated with the presence of plant-model mismatch or other persistent disturbances by augmenting the plant model with disturbances and employing an observer to estimate both the states and disturbances. Despite their importance, a systematic approach for the generation of suitable disturbance models is not available.

We propose an optimization-based method to generate disturbance models based on sufficient observability conditions and generalize the theory of offset-free NMPC by allowing for (i) more measured variables than controlled variables and (ii) unmeasured controlled variables. Based on the sufficient conditions, we formulate a generalized semi-infinite program, which we reformulate and solve as a simpler semi-infinite program using a discretization algorithm. The solution furnishes the optimal disturbance model, which maximizes the set of those state, manipulated variable, and disturbance realizations, for which a sufficient observability condition is satisfied. The disturbance model is generated offline and can be used online for offset-free NMPC.

We apply the approach using three case studies ranging from small scale chemical reactor cases to a medium scale polymerization reactor case. The results demonstrate the validity and usefulness of the generalized theory and show that the model generation approach successfully finds suitable disturbance models for offset-free NMPC.

无偏移非线性模型预测控制（NMPC）可以通过用干扰增加工厂模型并雇用观察者来估计状态和干扰，从而消除与工厂模型不匹配或其他持续性干扰相关的跟踪偏移。尽管它们很重要，但尚无用于生成合适干扰模型的系统方法。

我们提出了一种基于优化的方法来基于足够的可观察性条件生成干扰模型，并通过允许（i）比控制变量更多的测量变量和（ii）未测量的控制变量来推广无偏移NMPC的理论。在充分条件的基础上，我们制定了一个广义的半无限程序，使用离散化算法将其重新简化并求解为一个更简单的半无限程序。该解决方案提供了最佳干扰模型，该模型使状态，操纵变量和干扰实现的集合最大化，为此满足了充分的可观察性条件。干扰模型是离线生成的，可以在线用于无偏移的NMPC。

我们使用从小型化学反应器案例到中型聚合反应器案例的三个案例研究来应用该方法。结果证明了广义理论的有效性和实用性，并表明该模型生成方法成功地找到了适用于无偏移NMPC的扰动模型。