We consider tracking control for uncertain linear systems with known relative degree which are possibly non-minimum phase, i.e., their zero dynamics may have an unstable part. For a given sufficiently smooth reference signal we design a low-complexity controller which achieves that the tracking error evolves within a prescribed performance funnel. We present a novel approach where a new output is constructed, with respect to which the system has a higher relative degree, but the unstable part of the zero dynamics is eliminated. Using recent results in funnel control, we then design a controller with respect to this new output, which also incorporates a new reference signal. We prove that the original output stays within a prescribed performance funnel around the original reference trajectory and all signals in the closed-loop system are bounded. The results are illustrated by some simulations.

我们考虑对具有已知相对度的不确定线性系统进行跟踪控制，该线性度可能是非最小相位，即其零动态可能具有不稳定的部分。对于给定的足够平滑的参考信号，我们设计了一个低复杂度的控制器，该控制器可实现跟踪误差在规定的性能漏斗内演变。我们提出了一种新颖的方法，其中构造了新的输出，相对于该输出，系统具有较高的相对度，但是消除了零动态的不稳定部分。利用漏斗控制的最新结果，我们针对该新输出设计了一个控制器，该控制器还包含了一个新的参考信号。我们证明原始输出保持在围绕原始参考轨迹的规定性能漏斗内，并且闭环系统中的所有信号都受到限制。