Robust energy- and power-based control design: Port Hamiltonian and Brayton-Moser systems

PhD ceremony: Mr. D.A. Dirksz, 13.15 uur, Academiegebouw, Broerstraat 5, Groningen

Title: Robust energy- and power-based control design: Port Hamiltonian and Brayton-Moser systems

Promotor(s): prof. J.M.A. Scherpen

Faculty: Mathematics and Natural Sciences

 

A recent trend in industry is model-based design, having a model of a physical system at the center of the design process. Model-based design enables faster and more cost-effective development of dynamical systems. The design of control systems is also one of the disciplines that rely heavily on system models. Because of the advances in technology, systems are becoming more complex, making them harder to model, which then makes the control design process also more difficult.

Although still popular, it is becoming harder for linear control design techniques to deal with the increasing complexity. The complexity of systems is very often related to nonlinearities in the system description. In the last decades different nonlinear control techniques have been developed to deal with many types of nonlinearities. However, nonlinear control design often relies on an exact description of the system dynamics. It is well-known that such a description is difficult to obtain, since models are just a (useful) simplified representation of the real system. It is impossible to model everything, and the model uncertainties can negatively affect the implementation of the designed controller.

This thesis deals with energy-based and power-based control design of physical systems. Both are nonlinear control design methods based on shaping the energy function and the mixed-potential function of a system, respectively,into a desired form. The energy-based control method is based on systems described inport-Hamiltonian form, while the power-based method is based on systems described in Brayton-Moser form. One of the main contributions of this thesis is to improve the robustness of energy-and power-based control by extending them to include integral and adaptive control.

Integral action is well-known to compensate for steady-state errors caused by unknown disturbances or model uncertainties. Adaptive control compensates for errors caused by uncertainty in the system parameters, by estimating the real parameter values. Furthermore, adaptive control offers advantages for tracking control, where the reference signal is constantly changing. The integral and adaptive control methods are described in such way that the port-Hamiltonian or the Brayton-Moser structure is preserved for the closed-loop system.

Both modeling frameworks have a clear physical structure with advantages for system analysis and control design, which explains whyit is desired to preserve the particular structure. Furthermore, canonical transformations are described in this thesis for systems described in Brayton-Moser form. This was inspired by canonical transformations for port-Hamiltonian systems, which in some cases can provide a better insight for system analysis and control design.

In many cases nonlinear control also depends on full-state feedback. Mechanical systems are usually equipped with only position measurement encoders, while velocities are obtainedby numerical differentiation. Differentiation of measurement errors and noise can add a lot of uncertainty to the obtained velocity signal, which can then have a negative effect on performance.

In this context the thesis shows how tracking control of mechanical systems, with only position measurements, can be realized by applying the canonical transformation theory for port-Hamiltonian systems in combination with dynamic feedback.

Such results have been obtained in the past for Euler-Lagrange mechanical systems, based on a redefined Coriolis term in combination with dynamic feedback. The contribution in this case is that, contrary to the Euler-Lagrange results, it is shown in that the specific choice for the Coriolis term naturally follows from the port-Hamiltonian canonical transformation framework.

The different control methods presented in this thesis are applied on a manipulator experimental setup to verify their effectiveness. The experiments show improvements in steady-state errors compared to the well-known PID control, confirming the robustness of the described methods. Contrary to the developed methods here, there is no good theoretical justification for PID control.