Dissipative Hamiltonian Realization Research Articles

Robust H∞ control for uncertain switched nonlinear polynomial systems: Parameterization of controller approach

SummaryThis paper considers the global feedback exponential stabilization and L2 gain disturbance attenuation problems of the switched nonlinear polynomial systems with passive and nonpassive subsystems for any given average dwell time. In the existing result, it needs that there exists at least one open loop passive subsystem in the switched nonlinear system, which is unnecessary for the switched nonlinear polynomial system in this paper because the passivity of the subsystem can be obtained according to the passivity‐based feedback dissipative Hamiltonian realization. In addition, a parameterization of controller approach–based feedback exponential stabilization method of nonlinear polynomial system is described and utilized such that the Lyapunov function of the passive subsystem possesses the required decay rate to exponentially stabilize the switched nonlinear polynomial system. Comparing with the controller designed with the existing method, the obtained controller in this paper has much simpler structure and better performance. An example simulation is provided to illustrate the effectiveness of the proposed approach.

Observer Design Using Potential Based Realizations

This paper considers observer design for nonlinear dynamical systems which can be approximated by a dissipative Hamiltonian realization. The design approach decomposes the system associated one-form of a given dynamical system over an indeterminate metric using the Homotopy operator to generate exact (potential driven) and anti-exact parts. Then the convexity of the potential system given by the exact part is assessed and we propose a metric equation which yields a Lyapunov function for the potential driven observer system. An application of this method is demonstrated for a two-dimensional van der Pol oscillator.

A brand new nonlinear robust control design of SSSC for transient stability and damping improvement of multi-machine power systems via pseudo-generalized Hamiltonian theory

Nonlinear robust control of static synchronous series compensator (SSSC) is investigated in multi-machine multi-load power systems by using the pseudo-generalized Hamiltonian method. First, the uncertain nonlinear differential algebraic equation model is constructed for the power system. Then, the dissipative pseudo-generalized Hamiltonian realization of the system is established by means of variable transformation and prefeedback control. Finally, based on the obtained dissipative pseudo-generalized Hamiltonian realization, a brand new nonlinear robust controller is put forward. The proposed controller can effectively use the internal structure and the energy balance property of the power system. Simulation results demonstrate the effectiveness and robustness of the control scheme.

Coordinated control of static synchronous compensator and automatic voltage regulator in multi-machine power systems using pseudo-generalized Hamiltonian theory

Flexible alternating current transmission system devices are widely used to enhance the power transfer limit and stability improvement in transmission networks. They also help damp out both local and inter-area low-frequency oscillations. Using pseudo-generalized Hamiltonian theory, this article investigates the coordinated control of automatic voltage regulator of synchronous generator and static synchronous compensator in multi-machine power systems. First, via a proper variable transformation and pre-feedback control, the dissipative pseudo-generalized Hamiltonian realization of the static synchronous compensator and power system are completed, respectively. Then, based on the obtained dissipative pseudo-generalized Hamiltonian realization, a brand new nonlinear coordinated control law is constructed. Simulation results indicate that the proposed coordinated control scheme can effectively improve both the transient stability and voltage regulation performance of the power system.

Passivity-Based Nonlinear Excitation Control of Power Systems with Structure Matrix Reassignment

Passivity-based control is widely used in electronic circuit systems because it can utilize their internal structures to facilitate the controller design. In this paper, we first propose a dissipative Hamiltonian realization of power systems and discuss the disadvantages of the traditional passivity-based excitation controller. Then, a novel excitation controller is put forward to reassign the interconnection and dissipative matrix, and the corresponding Hamiltonian function. Simulation results verify that the proposed controller can effectively improve the transient stability of the power system.

Decentralized robust control of multiple static var compensators via Hamiltonian function method

Using the energy-based Hamiltonian function method, this paper investigates the decentralized robust nonlinear control of multiple static var compensators (SVCs) in multimachine multiload power systems. First, the uncertain nonlinear differential algebraic equation model is constructed for the power system. Then, the dissipative Hamiltonian realization of the system is completed by means of variable transformation and prefeedback control. Finally, based on the obtained dissipative Hamiltonian realization, a decentralized robust nonlinear controller is put forward. The proposed controller can effectively utilize the internal structure and the energy balance property of the power system. Simulation results verify the effectiveness of the control scheme.

Energy-based coordinated nonlinear control of synchronous generator and static var compensator

Using the Hamiltonian function method, this paper investigates the coordinated control of the synchronous generator and static var compensator (SVC) in power systems with constant power loads. First, via a proper variable transformation and pre-feedback control, the dissipative Hamiltonian realization of the power system is completed. Then, based on the obtained dissipative Hamiltonian realization, an energy-based coordinated stabilization controller is constructed. The guaranteed L2 performance property of the closed loop system is analyzed as well. Simulation results indicate that the proposed coordinated control scheme can effectively improve both the transient stability and voltage regulation performance of the power system.

Robust excitation control of multi-machine multi-load power systems using Hamiltonian function method

Using an energy-based Hamiltonian function method, this paper investigates the robust excitation control of multi-machine multi-load power systems described by a set of uncertain differential algebraic equations. First, we complete the dissipative Hamiltonian realization of the power system and adjust its operating point by the means of pre-feedback control. Then, based on the obtained Hamiltonian realization, we discuss the robust excitation control of the power system and put forward an H ∞ excitation control strategy. Simulation results demonstrate the effectiveness of the control scheme.

Observer and Damping Feedback Construction Based on Approximate Hamiltonian Dissipative Realization

AbstractThis paper considers observer and damping feedback design for control affine systems that admit an approximate dissipative Hamiltonian realization. The approach consists in constructing a locally-defined dissipative potential function by homotopy decomposition of a differential one-form associated to the system drift vector field. Under a condition on the obtained potential function convexity, a coordinate transformation is then defined such that the original system can be approximated by a dissipative Hamiltonian system with a constant structure. Using the approximate dissipative Hamiltonian realization, damping control and observer design are then carried, and the limitations associated to the approximation are discussed. Application to a predator-prey system is presented to illustrate the construction.

Decentralized Excitation Control of Multi-machine Multi-load Power Systems Using Hamiltonian Function Method

Using the Hamiltonian function method,we investigate the excitation control of multi-machine multi-load power systems presented by nonlinear differential algebraic equations.First,the power system is reformulated as a novel Hamiltonian realization structure via pre-feedback state control.Then,based on the dissipative Hamiltonian realization of the system,a decentralized nonlinear excitation control scheme is constructed.The stability of the closed loop system is analyzed as well.The proposed strategy takes advantage of the intrinsic properties especially including the internal power balance of the power system.Simulation illustrates the effectiveness of the control strategy.

Decentralized Excitation Control of Multi-machine Multi-load Power Systems Using Hamiltonian Function Method

Using the Hamiltonian function method, we investigate the excitation control of multi-machine multi-load power systems presented by nonlinear diffierential algebraic equations. First, the power system is reformulated as a novel Hamiltonian realization structure via pre-feedback state control. Then, based on the dissipative Hamiltonian realization of the system, a decentralized nonlinear excitation control scheme is constructed. The stability of the closed loop system is analyzed as well. The proposed strategy takes advantage of the intrinsic properties especially including the internal power balance of the power system. Simulation illustrates the effectiveness of the control strategy.

Feedback Controller Design for the Four-Tank Process using Dissipative Hamiltonian Realization

This paper considers the problem of stabilizing the quadruple-tank process using an approximate dissipative Hamiltonian realization. The proposed approach consists in canceling by feedback the deviation of the system from a Hamiltonian system. First, we obtain a characteristic one-form for the system by taking the interior product of a non vanishing two-form with respect to the controlled vector field. We then construct a homotopy operator on a star-shaped region centered at a desired equilibrium point. The dynamics of the system is then decomposed into an exact part and an anti-exact one. The exact part is generated by a potential, hence stability of this part is guaranteed using the generating potential as a Lyapunov function. The stabilizing feedback controller is designed by canceling the anti-exact part of the characteristic one-form. Application of the resulting controller is illustrated by numerical simulations.

Energy-Based $L_2$ Disturbance Attenuation Excitation Control of Differential Algebraic Power Systems

Using an energy-based method, this paper investigates the L 2 disturbance attenuation excitation control of multimachine power system connected with constant power loads. First, a general result is presented for the L 2 disturbance attenuation control of nonlinear differential algebraic systems with dissipative Hamiltonian realization. Then, pre-feedback is employed to transform the power system into a dissipative Hamiltonian form. Based on this, a decentralized L 2 excitation control scheme is proposed to improve the transient stability of the system. Simulation results demonstrate the effectiveness of the controller.

On Hamiltonian realization of time-varying nonlinear systems

This paper investigates Hamiltonian realization of time-varying nonlinear (TVN) systems, and proposes a number of new methods for the problem. It is shown that every smooth TVN system can be expressed as a generalized Hamiltonian system if the origin is the equilibrium of the system. If the Jacobian matrix of a TVN system is nonsingular, the system has a generalized Hamiltonian realization whose structural matrix and Hamiltonian function are given explicitly. For the case that the Jacobian matrix is singular, this paper provides a constructive decomposition method, and then proves that a TVN system has a generalized Hamiltonian realization if its Jacobian matrix has a nonsingular main diagonal block. Furthermore, some sufficient (necessary and sufficient) conditions for dissipative Hamiltonian realization of TVN systems are also presented in this paper. generalized Hamiltonian realization, dissipative Hamiltonian realization, diffoemorphism, structural construction

Feedback control of fractional nonlinear differential algebraic systems with Hamiltonian function method

In this paper, we first present a fractional Hamiltonian function. Then, based on the dissipative Hamiltonian realization, using the fractional Hamiltonian function method, as a static measurable feedback, a criterion for the fractional nonlinear differential algebraic systems (FNDAS) is proposed to stabilize the multi-machine power system. Finally, FNDAS in presence of disturbance, a fractional H ∞ control strategy is constructed. The proposed stabilization and robust controller can effectively take advantage of the structural characteristics of FNDAS and is simple in form.

Nonlinear Decentralized Disturbance Attenuation Excitation Control for Power Systems With Nonlinear Loads Based on the Hamiltonian Theory

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> A novel nonlinear control scheme for disturbance attenuation of structure preserving multimachine power systems based on Hamiltonian theory is proposed in this paper. The proposed control scheme includes two steps: first, the dissipative Hamiltonian realization of structure preserving power system is completed using the singular perturbation approach in which the algebraic equations are considered as a limit of fast dynamics; second, a nonlinear decentralized disturbance attenuation excitation controller is designed without linearization to improve transient stability of power system as well as the robustness with respect to unknown exogenous disturbance in the sense of <formula formulatype="inline"><tex>$L_2$</tex></formula>-gain. Simulation on a two-area system demonstrates that the proposed scheme can enhance transient stability of the system regardless of the exogenous disturbance. </para>

Approximate dissipative Hamiltonian realization and construction of local Lyapunov functions

The key in applying energy-based control approach is to be able to express the system under consideration as a dissipative Hamiltonian system, i.e., to obtain Dissipative Hamiltonian Realization (DHR) for the system. In general, the precise DHR form is hard to obtain for nonlinear dynamic systems. When a precise DHR does not exist for a dynamic system or such a precise realization is difficulty to obtain, it is necessary to consider its approximate realization. This paper investigates approximate DHR and construction of local Lyapunov functions for time-invariant nonlinear systems. It is shown that every nonlinear affine system has an approximate DHR if linearization of the system is controllable. Based on the diagonal normal form of nonlinear dynamic systems, a new algorithm is established for the approximate DHR. Finally, we present the concept of kth degree approximate Lyapunov function, and provide a method to construct such a Lyapunov function. Example studies show that the methodology presented in this paper is very effective.

Feedback control of nonlinear differential algebraic systems using Hamiltonian function method

The stabilization and H∞ control of nonlinear differential algebraic systems (NDAS) are investigated using the Hamiltonian function method. Firstly, we put forward a novel dissipative Hamiltonian realization (DHR) structure and give the condition to com- plete the Hamiltonian realization. Then, based on the DHR, we present a criterion for the stability analysis of NDAS and construct a stabilization controller for NDAS in absence of disturbances. Finally, for NDAS in presence of disturbances, the L2 gain is analyzed via generalized Hamilton-Jacobi inequality and an H∞ control strategy is constructed. The proposed stabilization and robust controller can effectively take advantage of the structural characteristics of NDAS and is simple in form.

Problems on time-varying port-controlled Hamiltonian systems: geometric structure and dissipative realization

To apply time-varying port-controlled Hamiltonian (PCH) systems to practical control designs, two basic problems should be dealt with: one is how to provide such time-varying systems a geometric structure to guarantee the completeness of representations in mathematics; and the other is how to express the practical system under consideration as a time-varying PCH system, which is called the dissipative Hamiltonian realization problem. The paper investigates the two basic problems. A suitable geometric structure for time-varying PCH systems is proposed first. Then the dissipative realization problem of time-varying nonlinear systems is investigated, and serval new methods and sufficient conditions are presented for the realization.

Adaptive H ∞ excitation control of multimachine power systems via the Hamiltonian function method

Using the Hamiltonian function method, this paper investigates the adaptive H ∞ excitation control of multimachine power systems with disturbances and parameter perturbations. A key step in applying the Hamiltonian function method to the multimachine system is to express the system as a dissipative Hamiltonian system, i.e. to complete dissipative Hamiltonian realization (DHR). By using pre-feedback technique, this paper expresses the multimachine power system as a dissipative Hamiltonian system. Then, the stability analysis of the achieved dissipative Hamiltonian system is proceeded. Finally, based on the achieved DHR form, the adaptive H ∞ excitation control of the multimachine power system is investigated and a decentralized simple excitation control strategy is obtained. Simulations on a six-machine system show that the adaptive H ∞ excitation control strategy proposed in the paper is more effective than some other control schemes.