Zero Dynamics of Physical Systems From Bond Graph Models—Part II: MIMO Systems

1999 ◽  
Vol 121 (1) ◽  
pp. 18-26 ◽  
Author(s):  
S. Y. Huang ◽  
K. Youcef-Toumi
Keyword(s):  
System Analysis ◽  
Controller Design ◽  
Mimo Systems ◽  
Bond Graph ◽  
Relative Degree ◽  
Zero Dynamics ◽  
Input Output ◽  
Feedback Systems ◽  
Graph Models ◽  
Physical Systems

Zero dynamics is an important feature in system analysis and controller design. Its behavior plays a major role in determining the performance limits of certain feedback systems. Since the intrinsic zero dynamics can not be influenced by feedback compensation, it is important to design physical systems so that they possess desired zero dynamics. In the Part I paper, a method is proposed to derive the zero dynamics of SISO systems from bond graph models. Using this approach, the design of physical systems, including the consideration of zero dynamics, can be performed in a systematic way. In this paper, the extension of the proposed method for MIMO systems is presented. It is shown that for MIMO systems, the input-output configurations determine the existence of vector relative degrees. If a system has a vector relative degree, it’s zero dynamics can be identified by a straightforward extension of the proposed method. If a system does not have a vector relative degree, a dynamic extension procedure may be used to fix the structure. By doing so, the zero dynamics can still be identified in a similar manner. It is also shown that if the input-output configurations are ill-designed, not only the relative degrees do not exist, but also the zero dynamics can not be reasonably defined. In that case, independent tracking controls for all the outputs are impossible. Therefore, the results in this paper provide a guideline for the design of the input-output configurations as well as the zero dynamics of MIMO systems.

Zero Dynamics of Physical Systems From Bond Graph Models—Part I: SISO Systems

1999 ◽  
Vol 121 (1) ◽  
pp. 10-17 ◽  
Author(s):  
S. Y. Huang ◽  
K. Youcef-Toumi
Keyword(s):  
System Analysis ◽  
Mimo Systems ◽  
Geometric Approach ◽  
Bond Graph ◽  
Graph Representation ◽  
Zero Dynamics ◽  
Feedback Systems ◽  
State Equations ◽  
Graph Models ◽  
Physical Systems

Zero dynamics is an important feature in system analysis and controller design. Its behavior plays a major role in determining the performance limits of certain feedback systems. Since the intrinsic zero dynamics can not be influenced by feedback compensation, it is important to design physical systems so that they possess desired zero dynamics. However, the calculation of the zero dynamics is usually complicated, especially if a form which is closely related to the physical system and suitable for design is required. In this paper, a method is proposed to derive the zero dynamics of physical systems from bond graph models. This method incorporates the definition of zero dynamics in the differential geometric approach and the causality manipulation in the bond graph representation. By doing so, the state equations of the zero dynamics can be easily obtained. The system elements which are responsible for the zero dynamics can be identified. In addition, if isolated subsystems which exhibit the zero dynamics exist, they can be found. Thus, the design of physical systems including the consideration of the zero dynamics become straightforward. This approach is generalized for MIMO systems in the Part II paper.

"Bond graph approach for input-output decoupling of linear MIMO systems with Derivative State Feedback"

2018 ◽  
Author(s):  
Christophe Sueur
Keyword(s):  
State Feedback ◽  
System Analysis ◽  
Mimo Systems ◽  
Bond Graph ◽  
State Feedback Control ◽  
Pole Placement ◽  
Control Law ◽  
Input Output ◽  
Placement Problem

"This paper presents a new solution for the well-known input-output decoupling problem of linear multivariable systems with a derivative state feedback control law. A simple solution to the pole placement problem is highlighted in the monovariable and multivariable cases with application to a mechanical system. Analysis up to control design are achieved structurally in the bond graph domain for the case study."

A Lumped Parameter Electromechanical Model for Describing the Nonlinear Behavior of Piezoelectric Actuators

1997 ◽  
Vol 119 (3) ◽  
pp. 478-485 ◽  
Author(s):  
M. Goldfarb ◽  
N. Celanovic
Keyword(s):  
System Analysis ◽  
Nonlinear Behavior ◽  
Piezoelectric Actuators ◽  
Bond Graph ◽  
Lumped Parameter Model ◽  
Input Output ◽  
Mechanical Stiffness ◽  
Analysis And Design ◽  
Lumped Parameter ◽  
Proposed Model

A lumped-parameter model of a piezoelectric stack actuator has been developed to describe actuator behavior for purposes of control system analysis and design, and in particular for control applications requiring accurate position tracking performance. In addition to describing the input-output dynamic behavior, the proposed model explains aspects of nonintuitive behavioral phenomena evinced by piezoelectric actuators, such as the input-output rate-independent hysteresis and the change in mechanical stiffness that results from altering electrical load. Bond graph terminology is incorporated to facilitate the energy-based formulation of the actuator model. The authors propose a new bond graph element, the generalized Maxwell resistive capacitor, as a lumped-parameter causal representation of rate-independent hysteresis. Model formulation is validated by comparing results of numerical simulations to experimental data.

scholarly journals Analysing and simulating energy-based models in biology using BondGraphTools

2021 ◽  
Author(s):  
Peter Cudmore ◽  
Michael Pan ◽  
Peter J. Gawthrop ◽  
Edmund J. Crampin
Keyword(s):  
Systems Biology ◽  
Mathematical Models ◽  
Bond Graph ◽  
Experimental Measurements ◽  
Bond Graphs ◽  
Graph Models ◽  
Conservation Of Energy ◽  
Conservation Of Mass ◽  
Physical Systems ◽  
Complex Interactions

AbstractLike all physical systems, biological systems are constrained by the laws of physics. However, mathematical models of biochemistry frequently neglect the conservation of energy, leading to unrealistic behaviour. Energy-based models that are consistent with conservation of mass, charge and energy have the potential to aid the understanding of complex interactions between biological components, and are becoming easier to develop with recent advances in experimental measurements and databases. In this paper, we motivate the use of bond graphs (a modelling tool from engineering) for energy-based modelling and introduce, BondGraphTools, a Python library for constructing and analysing bond graph models. We use examples from biochemistry to illustrate how BondGraphTools can be used to automate model construction in systems biology while maintaining consistency with the laws of physics.

Lagrange’s Equations for Complex Bond Graph Systems

1977 ◽  
Vol 99 (4) ◽  
pp. 300-306 ◽  
Author(s):  
Dean Karnopp
Keyword(s):  
Bond Graph ◽  
Writing System ◽  
Complex Mechanism ◽  
State Equations ◽  
Graph Models ◽  
Physical Systems ◽  
Lagrange’S Equations ◽  
Alternative Means ◽  
Lagrange's Equations ◽  
State Functions

The standard means of imposing causality to extract state equations for bond graph models of physical systems can be inconvenient when algebraic loops and derivative causality in combination with nonlinear constraints are present. This paper presents an alternative means of writing system differential equations using energy and coenergy state functions and Lagrange’s equations. For certain types of systems, particularly mechanical and electromechanical systems, this indirect means of finding state equations turns out to be very convenient. In this technique, causality is used in a new way to establish generalized coordinates and generalized efforts for nonconservative elements. Finally, it is shown that in some cases in which a Lagrangian can be written by inspection for a complex mechanism, a detailed bond graph for this component is unnecessary and yet the equations of the mechanism can be easily coupled to the bond graph equations for the remainder of the system.

HYBRSIM—a modelling and simulation environment for hybrid bond graphs

2002 ◽  
Vol 216 (1) ◽  
pp. 35-46 ◽  
Author(s):  
P. J. Mosterman
Keyword(s):  
Numerical Analysis ◽  
Event Detection ◽  
Bond Graph ◽  
Modelling And Simulation ◽  
Simulation Environment ◽  
Dynamic Coupling ◽  
Bond Graphs ◽  
Switching Element ◽  
Graph Models ◽  
Physical Systems

Bond graphs are a powerful formalism to model continuous dynamics of physical systems. Hybrid bond graphs introduce an ideal switching element, the controlled junction, to approximate continuous behaviour that is too complex for numerical analysis (e.g. because of non-linearities or steep gradients). HYBRSIM is a tool for hybrid bond graph modelling and simulation implemented in Java and is documented in this paper. It performs event detection and location based on a bisectional search, handles run-time causality changes, including derivative causality, performs physically consistent (re-)initialization and supports two types of event iteration because of dynamic coupling. It exports hybrid bond graph models in Java and C/C++ code that includes discontinuities as switched equations (i.e. pre-enumeration is not required).

Asymptotic Properties of Sampling Zero Dynamics for Nonlinear Systems in the Case of Time Delay and Relative Degree Two

2014 ◽  
Vol 1061-1062 ◽  
pp. 893-898
Author(s):  
Xiu Yun Li ◽  
Cheng Zeng ◽  
Tong Zhou ◽  
Yan Jun Ren ◽  
Yu Xuan Li
Keyword(s):  
Time Delay ◽  
Nonlinear Systems ◽  
Data Model ◽  
Controller Design ◽  
Asymptotic Properties ◽  
Sampling Period ◽  
Relative Degree ◽  
Zero Dynamics ◽  
Sampled Data ◽  
The Stability

It is well-known that stability of zero dynamics is often inevitable to the controller design. And most real world plants often involve a time delay. This paper investigates the zero dynamics, as the sampling period tends to zero, of a sampled-data model composed of a zero-order hold (ZOH), a continuous-time plant with a time delay and a sampler in cascade. We first present how an approximate sampled-data model can be obtained for the nonlinear system with relative degree two, and the local truncation error between the output of obtained model and the true system output is of order , where T is the sampling period and r is the relative degree. Furthermore, we also propose the additional zero dynamics in the sampling process, which are called the sampling zero dynamics, and the condition for assuring the stability of sampling zero dynamics for the desired model is derived. The results presented here generalize a well-known notion of sampling zero dynamics from the linear case to nonlinear systems.

Duality in system analysis for bond graph models

2010 ◽  
Vol 347 (2) ◽  
pp. 377-414 ◽  
Author(s):  
S. Lichiardopol ◽  
C. Sueur
Keyword(s):  
System Analysis ◽  
Bond Graph ◽  
Graph Models
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