Daniel Dirksz

Structure Preserving Adaptive Control of Port-Hamiltonian Systems

In this technical note, an adaptive control scheme is presented for general port-Hamiltonian systems. Adaptive control is used to compensate for control errors that are caused by unknown or uncertain parameter values of a system. The adaptive control is also combined with canonical transformation theory for port-Hamiltonian systems. This allows for the adaptive control to be applied on a large class of systems and for being included in the port-Hamiltonian framework.

Adaptive tracking control of fully actuated port-Hamiltonian mechanical systems

In the presence of parameter uncertainty tracking control can result in significant tracking errors. To overcome this problem adaptive control is applied, which estimates and compensates for the errors of the uncertain parameters. A new adaptive tracking control scheme is presented for standard fully actuated port-Hamiltonian mechanical systems. The adaptive control is such that the closed loop error system is still port-Hamiltonian and asymptotically stable.

Power-Based Setpoint Control: Experimental Results on a Planar Manipulator

In the last years the power-based modeling framework, developed in the sixties to model nonlinear electrical RLC networks, has been extended for modeling and control of a larger class of physical systems. In this brief we apply power-based integral control to a planar manipulator experimental setup. An integrator is known to compensate for steady-state errors, which usually occur in real applications. Recent developments in power-based control have shown the possibility of applying integral control to globally asymptotically stabilize a nonlinear system, without losing the original structure. In contrast, the more common PI or PID controllers do not provide such global properties. Both simulation and experimental results show an improvement in transient performance compared to PID control.

Power-based adaptive and integral control of standard mechanical systems

Recently a power-based modeling framework was introduced for mechanical systems, based on the Brayton-Moser framework. In this paper it is shown how this power-based framework is used for control of standard mechanical systems. For systems which are affected by parameter uncertainty or other unknown disturbances adaptive control and integral control are also described in this framework. The power-based control approach is also compared with the energy-shaping control of port-Hamiltonian systems. The most interesting difference is the possibility of having adaptive and integrator dynamics depending on position errors, while preserving the physical structure.

Interconnection and Damping Assignment Passivity-Based Control for port-Hamiltonian mechanical systems with only position measurements

A dynamic extension for position feedback of port-Hamiltonian mechanical systems is studied. First we look at the consequences for the matching equations when applying Inter-connection and Damping Assignment Passivity-Based Control (IDA-PBC). Then we look at the possibilities of asymptotically stabilizing a class of port-Hamiltonian mechanical systems without having to know the velocities, as once presented for Euler-Lagrange (EL) systems. Here it is shown how the idea of damping injection by dynamic extension works when shaping the total energy in the port-Hamiltonian framework.

Position Control via Force Feedback in the Port-Hamiltonian Framework

In this chapter, position control strategies via force feedback are presented for standard mechanical systems in the port-Hamiltonian framework. The presented control strategies require a set of coordinate transformations, since force feedback in the port-Hamiltonian framework is not straightforward. With the coordinate transformations force feedback can be realized while preserving the port-Hamiltonian structure. The port-Hamiltonian formalism offers a modeling framework with a clear physical structure and other properties that can often be exploited for control design purposes, which is why we believe it is important to preserve the structure. The proposed control strategies offer an alternative solution to position control with more tuning freedom and exploit knowledge of the system dynamics.

Identification of cyclic disturbances in positioning systems via compressive sensing

In industrial precision positioning systems the measurement position is hardly ever the same as the location of the actuator. The properties and imperfections of the actuator and the underlying components between the sensor and the actuator mainly lead to deterministic reproducible position errors. The advantage of these systematic cyclic disturbances is that they can be compensated for, once identified. In this paper we use nonuniform sampling combined with Compressive Sensing (CS) to identify high spatial frequency disturbances in positioning systems when the spatial sample period is limited. The proposed strategy is implemented on the paper positioning unit of a wide format printer, to identify the cyclic disturbances in the positioning of paper with respect to the printheads. Based on CS, we present a strategy to identify the cyclic disturbances in the paper positioning from randomly obtained relative position error measurements. Experiments with a limited spatial sample period show that the high disturbance frequencies are also successfully identified.

Notch Filters for Port-Hamiltonian Systems

In this paper a standard notch filter is modeled in the port-Hamiltonian framework. By having such a port-Hamiltonian description it is proven that the notch filter is a passive system. The notch filter can then be interconnected with another (nonlinear) port-Hamiltonian system, while preserving the overall passivity property. By doing so we can combine a frequency-based control method, the notch filter, with the nonlinear control methodology of passivity-based control.