Multiobjective State Feedback Control Research Articles

Individual Blade Pitch Control of a Spar-Buoy Floating Wind Turbine

The spar-buoy floating wind turbine is one of the three main floating wind turbine concepts and one of the first to proceed to a full-scale prototype stage. Multiobjective linear state feedback controllers are implemented on the spar-buoy floating wind turbine with individual blade pitching (IBP). The spar-buoy's deep draft results in a low platform pitch and roll natural frequencies. The low-frequency pitch and roll modes interact with other low-frequency modes of the system (i.e., surge and sway, respectively). Therefore, the linear state-space model used for control design must include the surge and sway degrees of freedom. Furthermore, a low platform pitch natural frequency limits the effectiveness of IBP at regulating the platform pitch around the first tower fore-aft (FA) resonant frequency. Simulations using a high-fidelity model are carried out according to design load case 1.2 of the IEC-61400-3 standard for fatigue load testing under normal operating conditions. Simulation results relative to a gain-scheduled proportional-integral controller show that a multiobjective state feedback controller is able to reduce tower FA and side-side bending fatigue loads by an average of 9%. This improvement is mainly due to IBP despite its limited effectiveness around the first tower FA resonant frequency.

Robust multi-objective H2/H∞ tracking control based on the Takagi–Sugeno fuzzy model for a class of nonlinear uncertain drive systems

In this paper a robust H2/H∞ multi-objective state-feedback controller and tracking design are presented for a class of multiple input/multiple output nonlinear uncertain systems. First, some states (error of tracking) are augmented to the system in order to improve tracking control. Next, uncertain parameters and the quantification of uncertainty on physical parameters are defined by the affine parameter-dependent systems method. Then, to apply the H2/H∞ controller, the uncertain nonlinear system is approximated by the Takagi–Sugeno fuzzy model. After that, based on each local linear subsystem with augmented state, an H2/H∞ multi-objective state-feedback controller is designed by using a linear matrix inequalities approach. Finally, parallel distributed compensation is used to design the controller for the overall system and the total linear system is obtained by use of the weighted sum of the local linear subsystems. Several results show that the proposed method can effectively meet performance requirements such as robustness, good load disturbance rejection, good tracking and fast transient responses for a three-phase interior permanent magnet synchronous motor system.

Multi-objective state feedback control for linear delay systems

This paper provides new linear matrix inequalities (LMI)-based formulae for mixed H2/H∞ state-feedback synthesis of linear continuous-time systems with state delays of any size. The proposed delay-independent LMI-based conditions enable us to parameterize a memoryless state-feedback controller without involving the Lyapunov variables in the formula. Compared with previous results based on a common Lyapunov variable, the proposed formula provides less conservative results. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

On multiobjective synthesis for parameter-dependent descriptor systems

This note proposes dilated (or extended) linear matrix inequality (LMI) characterisations of admissibility, D-admissibility, H∞ and H2 norms for continuous-time descriptor systems. As for state-space systems, these LMIs achieve less conservative results when dealing with robust admissibility/performance analysis of affine parameter-dependent descriptor systems. Furthermore, an iterative design procedure for multiobjective state-feedback control of parameter-dependent descriptor systems is presented based on these dilated LMI conditions. The main idea underlying the proposed method is to linearise the products of controller parameter and the auxiliary variable by assigning the last one. In the initialisation step of the proposed algorithm, the assignment takes into account an explicit characterisation of the auxiliary variable. The effectiveness of the proposed conditions and design method is shown through some numerical examples.

Vibration control of beams using multiobjective state-feedback control

An active vibration suppression system is designed using a multiobjective state-feedbackcontroller. The governing equation of motion for a piezo/beam system is derived usingHamilton’s principle. The control gains of the resulting system are selected using the theoryof robust controls. In this regard, a robust controller is designed using a feedback control law that satisfies additional constraints on the closed-loop pole locationin the face of model uncertainties, which are derived for a general class of convexregions of the complex plane. These constraints are expressed in terms of thelinear matrix inequalities approach for multiobjective synthesis. The validity andapplicability of this approach for vibration suppression for the piezo/beam systemby damping out the multiple vibrational modes of the piezo/beam system arediscussed.

Analytical development of a robust controller for smart structural systems

This paper aims at demonstrating the feasibility of active control of beams with a multiobjective state-feedback control technique. The multiobjective state-feedback controller is designed on a linear matrix inequality (LMI) approach for the multiobjective synthesis. The design objectives are to achieve a mix ofH∞ performance andH2 performance satisfying constraints on the closed-loop pole locations in the face of model uncertainties. The controller is also designed to reject the effects of the noise and external of disturbances. For the theoretical analysis, the governing equation of motion is derived by Hamilton’s principle to describe the dynamics of a smart structural system. Numerical examples are presented to demonstrate the effectiveness of the integrated robust controller in damping out the multiple vibration modes of the piezo/beam system.

Stable controller synthesis for linear time-invariant systems

This paper is concerned with the problem of suboptimal stable mixed H 2 / H X control for linear time-invariant systems. The designed controller with the same order as that of the considered system is required to satisfy a prescribed H X performance bound or a prescribed degree of stability. By reducing the stable controller synthesis problem to a multiobjective state feedback control problem for two different state models, sufficient conditions for the solvability of the considered problem are given in terms of solutions to algebraic Riccati equations and matrix inequalities. An LMI-based iterative algorithm is developed to solve the stable controller synthesis problem. The proposed algorithm is shown to be convergent. Examples are given to illustrate the proposed methods.

Multiobjective State-Feedback Control Design with Non-Common LMI Solutions: A Subspace Approach

This paper presents a new approach with non-common linear matrix inequality (LMI) solutions to the multiobjective state-feedback control design problem. A conventional approach is adopting common LMI solutions to avoid a difficulty of non-convex constraints at the sacrifice of conservatism. To reduce the conservatism, in this paper, we introduce some additional constraints to variables so that we convexify the problem and obtain LMI conditions that leave the feedback gain directly as one of the variables. Because of the freedom in the variables satisfying the constraints, our approach turns out to give a set of LMI conditions that allow non-common LMI solutions. Furthermore, an effective iterative algorithm follows immediately from the present approach, with which we can reduce the conservatism considerably.