A Passivity-based Nonlinear Admittance Control with Application to Powered Upper-limb Control under Unknown Environmental Interactions

This paper presents an admittance controller based on the passivity theory for a powered upper-limb exoskeleton robot which is governed by the nonlinear equation of motion. Passivity allows us to include a human operator and environmental interaction in the control loop. The robot interacts with the human operator via F/T sensor and interacts with the environment mainly via end-effectors. Although the environmental interaction cannot be detected by any sensors (hence unknown), passivity allows us to have natural interaction. An analysis shows that the behavior of the actual system mimics that of a nominal model as the control gain goes to infinity, which implies that the proposed approach is an admittance controller. However, because the control gain cannot grow infinitely in practice, the performance limitation according to the achievable control gain is also analyzed. The result of this analysis indicates that the performance in the sense of infinite norm increases linearly with the control gain. In the experiments, the proposed properties were verified using 1 degree-of-freedom testbench, and an actual powered upper-limb exoskeleton was used to lift and maneuver the unknown payload.Comment: Accepted in IEEE/ASME Transactions on Mechatronics (T-MECH

Guaranteed passive parameterized macromodeling by using Sylvester state-space realizations

A novel state-space realization for parameterized macromodeling is proposed in this paper. A judicious choice of the state-space realization is required in order to account for the assumed smoothness of the state-space matrices with respect to the design parameters. This technique is used in combination with suitable interpolation schemes to interpolate a set of state-space matrices, and hence the poles and residues indirectly, in order to build accurate parameterized macromodels. The key points of the novel state-space realizations are the choice of a proper pivot matrix and a well-conditioned solution of a Sylvester equation. Stability and passivity are guaranteed by construction over the design space of interest. Pertinent numerical examples validate the proposed Sylvester realization for parameterized macromodeling

Discrete port-Hamiltonian systems: mixed interconnections

Either from a control theoretic viewpoint or from an analysis viewpoint it is necessary to convert smooth systems to discrete systems, which can then be implemented on computers for numerical simulations. Discrete models can be obtained either by discretizing a smooth model, or by directly modeling at the discrete level itself. The goal of this paper is to apply a previously developed discrete modeling technique to study the interconnection of continuous systems with discrete ones in such a way that passivity is preserved. Such a theory has potential applications, in the field of haptics, telemanipulation etc. It is shown that our discrete modeling theory can be used to formalize previously developed techniques for obtaining passive interconnections of continuous and discrete systems

Synchronization of Nonlinear Circuits in Dynamic Electrical Networks with General Topologies

Sufficient conditions are derived for global asymptotic synchronization in a system of identical nonlinear electrical circuits coupled through linear time-invariant (LTI) electrical networks. In particular, the conditions we derive apply to settings where: i) the nonlinear circuits are composed of a parallel combination of passive LTI circuit elements and a nonlinear voltage-dependent current source with finite gain; and ii) a collection of these circuits are coupled through either uniform or homogeneous LTI electrical networks. Uniform electrical networks have identical per-unit-length impedances. Homogeneous electrical networks are characterized by having the same effective impedance between any two terminals with the others open circuited. Synchronization in these networks is guaranteed by ensuring the stability of an equivalent coordinate-transformed differential system that emphasizes signal differences. The applicability of the synchronization conditions to this broad class of networks follows from leveraging recent results on structural and spectral properties of Kron reduction---a model-reduction procedure that isolates the interactions of the nonlinear circuits in the network. The validity of the analytical results is demonstrated with simulations in networks of coupled Chua's circuits

Compensation of position errors in passivity based teleoperation over packet switched communication networks

Because of the use of scattering based communication channels, passivity based telemanipulation systems can be subject to a steady state position error between master and slave robots. In this paper, we consider the case in which the passive master and slave sides communicate through a packet switched communication channel (e.g. Internet) and we provide a modification of the slave impedance controller for compensating the steady state position error arising in free motion because of packets loss

Impedance-Based Stability Analysis and Controller Design of Three-Phase Inverter-Based Ac Systems

Three-phase voltage-source power inverters are widely used for energy conversion in three-phase ac systems, such as renewable energy systems and microgrids. These three-phase inverter-based ac systems may suffer from small-signal instability issues due to the dynamic interactions among inverters and passive components in the systems. It is crucial for system integrators to analyze the system stability and design the inverter controller parameters during system planning and maintenance periods to guarantee stable system operation. The impedance-based approach can analyze the stability of source-load systems, by applying the Nyquist stability criterion or the generalized Nyquist stability criterion (GNC) to the impedance ratio of the source and load impedances. This dissertation investigates the impedance-based methods for stability analysis and inverter controller design of three-phase inverter-based multi-bus ac systems. Improved sequence impedance and d-q impedance models of both three-phase voltage-controlled inverters and current-controlled inverters are developed. A simple method for sequence impedance measurement of three-phase inverters is developed by using another inverter as the measurement unit, connected in a paralleled structure with common-dc and common-ac sides. For three-phase radial-line renewable systems with multiple current-controlled inverters, an impedance-based sufficient stability criterion is proposed in the d-q frame, without the need for pole calculation of the return-ratio matrices. An inverter controller parameter design method is developed based on the phase margin information obtained from the stability analysis. For general three-phase multi-bus ac power systems consisting of both voltage-controlled inverters and current-controlled inverters, several impedance-based stability analysis methods and inverter controller parameter design approaches are further proposed, based on the sequence impedances, the d-q impedances and the measured terminal characteristics, to avoid the unstable harmonic resonance, the low-frequency oscillation and the oscillation of the fundamental frequency, respectively. All these proposed stability analysis methods enable the system stability assessment without the need for the internal control information of inverters. Moreover, an impedance-based adaptive control strategy of inverters with online resonance detection and passivity or phase compensation is proposed for stable integration of both voltage-controlled inverters and current-controlled inverters into unknown grid-connected or islanded systems with other existing inverters in operation