Location of Repository

In this thesis we focussed on two control related problems in the context of port-Hamiltonian systems with dissipation (PHSD): (1) Observer design and output feedback stabilization, (2) Energy shaping by using alternate passive input-output pairs. With regard to the first problem, we concentrated mainly on mechanical systems in Chapters 3 and 5 whereas in Chapter 4 we studied observer design for special class of port-Hamiltonian systems which also included electro-mechanical systems. We focussed on the second problem in Chapter 6 where we explored the possibility of generating new passive input-output pairs for a PHSD and investigated their role in shaping the system's energy via the control by interconnection method.

Topics:
Hamilton-vergelijkingen, Input-output-analyse; Waarnemers; Proefschriften (vorm); mathematische fysica

Year: 2010

DOI identifier: 10.3166/ejc.16.665-677

OAI identifier:
oai:ub.rug.nl:dbi/4bbdd23c62ccf

Provided by:
University of Groningen Digital Archive

- (6.1) is satisfied} where
- 1085.4 Observers and alternate passive input-output pairs for PHSD The Cholesky factorization of ˜ M is obtained as T =
- 1145.4 Observers and alternate passive input-output pairs for PHSD As a result ¯
- 1326.2 Alternate passive input-output pairs for PHSD with dissipation where ¯ fP, ˜ fP ∈ Rm, ¯ fR, ˜ fR ∈ Rp represent the ﬂows and ¯
- (1993). 155Bibliography [11]
- 6.4 Physical Examples 1396. Energy shaping of PHSD by using alternate passive input-output pairs 6.4.1 Parallel RLC circuit [69] Consider the parallel RLC circuit with dynamics,
- (1999). A comprehensive introduction to differential geometry, 3rd ed edition, volume 2. Publish or Perish,
- (2010). A globally exponentially convergent immersion and invariance speed observer for n–degrees of freedom mechanical systems with nonholonomoic constraints. Automatica,
- (2009). A globally exponentially convergent immersion and invariance speed observer for n–degrees of freedom mechanical systems.
- A new feedback method for dynamic control of manipulators.
- (1996). A nonlinear small gain theorem for the analysis of control systems with saturation.
- (1993). A passivity approach to controllerobserver design for robots.
- (2003). A remark on the converging–input converging–output property.
- (1992). A simple observer for nonlinear systems applications to bioreactors.
- (1421). Achievable Casimirs and its implications on control of port-Hamiltonian systems.
- Adaptive motion control of rigid robots.
- An energy-balancing perspective of interconnection and damping assignment control of nonlinear systems.
- An intrinsic Hamiltonian formulation of the dynamics of LC-circuits.
- (2002). An Introduction to differential manifolds and Riemannian geometry,
- Archive for Rational Mechanics and Analysis,
- Asymptotically stable walking for biped robots: Analysis via systems with impulse effects.
- (2000). Besanc ¸on. Global output feedback tracking control for a class of Lagrangian systems.
- (2004). C.Hong, L.Xie, andF.L.Lewis. ControlofaMEMS optical switch.
- Canonical form observer design for nonlinear time-variable systems.
- (1997). Constructive nonlinear control.
- Control by interconnection and standard passivity-based control of port-Hamiltonian systems.
- (2005). Control of robot manipulators in joint space.
- (2000). Controlled Lagrangians and the stabilization of mechanical systems I: The ﬁrst matching theorem.
- (2001). Controlled Lagrangians and the stabilization of mechanical systems II: Potential shaping.
- Dirac Manifolds.
- (2009). Dynamic scaling and observer design with application to adaptive control.
- (1999). Dynamics and control of a class of underactuated mechanical systems.
- (1972). Dynamics of nonholonomic systems,
- (1996). Energy based control of a class of underactuated mechanical systems.
- (2009). Energy shaping of porthamiltonian systems by using alternate passive outputs.
- Energy-based Lyapunov functions for forced Hamiltonian systems with dissipation.
- Figure 5.4: Time histories of q(t), ˆ y(t) (top graphs) and of ˙ ˆ q(t), T −1(y(t))ˆ x(t) (bottom graphs). The dashed lines are for k1 =5and the dotted lines are for k1 =1 0 . 1165.4 Observers and alternate passive input-output pairs for
- (2010). Full order observer design for a class of port–Hamiltonian systems.
- (2004). Geometric control of mechanical Systems: Modeling, analysis and design for simple mechanical control systems,
- Global stabilization of nonlinear cascaded systems.
- (2000). Growth rateconditions for uniform asymptotic stability of cascaded time-varying systems.
- (2003). Immersion and Invariance: A new tool for stabilization and adaptive control of nonlinear systems.
- (2001). Interconnection and damping assignment approach to control of PM synchronous motors.
- Interconnection and damping assignment control of electromechanical systems.
- (2008). Interconnection and damping assignment passivity-based control for port-Hamiltonian mechanical systems with only position measurements. 47thIEEEConference on Decision and Control,
- (2004). Interconnection and damping assignment passivity-based control: A survey.
- (2003). Introduction to smooth manifolds.
- Invariant manifold based reduced-order observer design for nonlinear systems.
- is a system with no constraints (k =0 ) and hence we choose (as stated in Remark 5.4) our coordinates as (x,y)=( q,T(y)˙ q) and further obtain L =
- J3}LLp×m ⎤ ⎦. (6.68) 1386.4 Physical Examples Next, for the special case of ˜ u = u, we have the matrices ˜ J1, ˜ J2 and ˜ J3 as given in (6.49). Upon substituting them in (6.67), we obtain the condition, ⎡ ⎣ J(x) g (x) g R(x)
- (1983). Linearization by output injection and nonlinear observers.
- (1990). Matrix analysis.
- (1999). New directions in nonlinear observer design,
- Nonholonomic control of 3 link planar manipulator with a free joint.
- (2003). Nonholonomic mechanics and control.
- (2008). Nonlinear and adaptive control with applications.
- (1995). Nonlinear control of a swinging pendulum.
- (1989). Nonlinear observer design by observer error linearization.
- (2005). Nonlinear observer design using invariant manifolds and applications.
- Nonlinear observer design using Lyapunov’s auxiliary theorem.
- (2007). Nonlinear observers and applications,
- (1985). Nonlinear observers with linearizable error dynamics.
- (1999). Nonlinear systems: analysis, stability and control.
- (1996). Nonlinear systems.
- Nonlinearobservers: acirclecriteriondesign and robustness analysis.
- Observer design for nonlinear systems.
- Observer design for systems with multivariable monotone nonlinearities. Systems and Control Letters,
- (2001). Observer-based control of systems with slope-restricted nonlinearities.
- Observers for linearly unobservable nonlinear systems.
- (1998). Observers for Lipschitz nonlinear systems.
- (1964). Observing the state of a linear system.
- Observing the state of non-linear dynamic systems.
- (1999). On output transformations forstatelinearization upto output injection.
- On the existence of a KazantzisKravaris/Luenberger observer.
- On the Hamiltonian formulation of nonholonomic mechanical systems.
- (1998). Passivity and disturbance attenuation via output feedback for uncertain nonlinear systems.
- (1998). Passivity–based control of Euler–Lagrange systems.
- (1991). Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems.
- (1992). Port controlled Hamiltonian systems: modeling origins and system theoretic properties.
- (2004). Port-based modeling and analysis of snakeboard locomotion.
- (2001). Putting energy back in control.
- (1992). Remarks on robot dynamics: canonical transformations and Riemannian geometry.
- Representations of Dirac structures on vector spaces and nonlinear LC circuits.
- Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment.
- Table 5.3: Simulation parameters for the Walking Robot example where the constants
- (2008). The Hamiltonian formulation of energy conserving physical systems with external ports.
- The observer is constructed following the steps in Section 4, yielding ¯
- to obtain M2(x)=1 . We further compute using (6.59)-(6.61)that,
- (2007). Total energy shaping control of mechanical systems: simplifying the matching equations via coordinate changes.
- (2002). Tracking control of second-order chained form systems by cascaded backstepping.
- (1998). Underactuated mechanical systems,
- Using the condition (6.68), we can easily check that the achievable Casimirs for the MEMS system will not depend on the mechanical position coordinates (q,p) for any given matrices ˜
- Velocity Observers for Mechanical Systems with Kinematic Constraints Δy

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.