Asymptotic Tracking via Funnel Control

Funnel control is a powerful and simple method to solve the output tracking problem without the need of a good system model, without identification and without knowlegde how the reference signal is produced, but transient behavior as well as arbitrary good accuracy can be guaranteed. Until recently, it was believed that the price to pay for these very nice properties is that only practical tracking and not asymptotic tracking can be achieved. Surprisingly, this is not true! We will prove that funnel control – without any further assumptions – can achieve asymptotic tracking

Asymptotic Tracking via Funnel Control

Funnel control is a powerful and simple method to solve the output tracking problem without the need of a good system model, without identification and without knowlegde how the reference signal is produced, but transient behavior as well as arbitrary good accuracy can be guaranteed. Until recently, it was believed that the price to pay for these very nice properties is that only practical tracking and not asymptotic tracking can be achieved. Surprisingly, this is not true! We will prove that funnel control – without any further assumptions – can achieve asymptotic tracking

Experimental validation for the combination of funnel control with a feedforward control strategy

Current engineering design trends, such as light-weight machines and humanmachine-interaction, often lead to underactuated systems. Output trajectory tracking of such systems is a challenging control problem. Here, we use a twodesign-degree of freedom control approach by combining funnel feedback control with feedforward control based on servo-constraints. We present experimental results to verify the approach and demonstrate that the addition of a feedforward controller mitigates drawbacks of the funnel controller. We also present new experimental results for the real-time implementation of a feedforward controller based on servo-constraints on a minimum phase system

Stability/instability study of density systems and control law design

The paper considers some class of dynamical systems that called density systems. For such systems the derivative of quadratic function depends on so-called density function. The density function is used to set the properties of phase space, therefore, it influences the behaviour of investigated systems. A particular class of such systems is previously considered for (in)stability study of dynamical systems using the flow and divergence of a phase vector. In this paper, a more general class of such systems is considered, and it is shown that the density function can be used not only to study (in)stability, but also to set the properties of space in order to change the behaviour of dynamical systems. The development of control laws based on use the density function for systems with known and unknown parameters is considered. All obtained results are accompanied by the simulations illustrating the theoretical conclusions

Funnel control of nonlinear systems

Tracking of reference signals is addressed in the context of a class of nonlinear controlled systems modelled by $r$-th order functional differential equations, encompassing inter alia systems with unknown "control direction" and dead-zone input effects. A control structure is developed which ensures that, for every member of the underlying system class and every admissible reference signal, the tracking error evolves in a prescribed funnel chosen to reflect transient and asymptotic accuracy objectives. Two fundamental properties underpin the system class: bounded-input bounded-output stable internal dynamics, and a high-gain property (an antecedent of which is the concept of sign-definite high-frequency gain in the context of linear systems)