论文标题
关于表现出输入多重性的过程的控制的注释
A note on the control of processes exhibiting input multiplicity
论文作者
论文摘要
在非线性系统中可能发生稳态多样性，这给反馈控制带来了挑战。当可以使用不同值的系统输入达到相同的稳态输出值时，就会出现输入多样性。配备有积分操作的控制器的输入多重性的动态系统具有多个固定点，可能是局部稳定的。这对于操作是不可取的。对于具有三个固定点的2x2示例系统，我们演示了如何设计一组两个单个循环控制器，因此只有一个固定点在局部稳定，从而有效地消除了用于控制的“输入多样性问题”。我们还表明，当将MPC用于示例系统时，所有三个闭环固定点都是稳定的。根据输入变量的初始值，MPC下的闭环系统可能会收敛到不同的稳态输入实例（但相同的输出稳态）。因此，我们在计算上探索了此封闭环系统的盆地边界。目前尚不清楚如何设计MPC或其他现代非线性控制器，以便仅特定的平衡点稳定。
Steady state multiplicity can occur in nonlinear systems, and this presents challenges to feedback control. Input multiplicity arises when the same steady state output values can be reached with system inputs at different values. Dynamic systems with input multiplicities equipped with controllers with integral action have multiple stationary points, which may be locally stable or not. This is undesirable for operation. For a 2x2 example system with three stationary points we demonstrate how to design a set of two single loop controllers such that only one of the stationary points is locally stable, thus effectively eliminating the "input multiplicity problem" for control. We also show that when MPC is used for the example system, all three closed-loop stationary points are stable. Depending on the initial value of the input variables, the closed loop system under MPC may converge to different steady state input instances (but the same output steady state). Therefore we computationally explore the basin boundaries of this closed loop system. It is not clear how MPC or other modern nonlinear controllers could be designed so that only specific equilibrium points are stable.
