Mixed Sensitivity Optimization Research Articles

Research on H∞ Robust Control Strategy of Wind Turbine Hydraulic Variable Pitch System

The variable pitch system is an important part of the wind turbine. In consideration of the parameter uncertainty and external interference in the hydraulic variable pitch system, this paper proposes a H ∞ robust control strategy for the wind turbine variable pitch system. Firstly, the model of the system is given and the equation of state is obtained. According to the performance requirements, the weighted function which meets the system requirements in the process of the mixed sensitivity optimization is selected, and then the state space realization of the system generalized controlled object is obtained. Then, the H ∞ controller is obtained by solving Riccati equation. Finally, the designed system reduces the steady-state error, and improves the robustness of the system.

H∞ mixed sensitivity optimization for high speed tilting trains

The industrial norm of tilting high speed trains, nowadays, is that of Precedence tilt (also known as Preview tilt). Precedence tilt, although succesfull as a concept, tends to be complex (mainly due to the signal interconnections between vehicles and the advanced signal processing required for monitoring). Research studies of early prior to that of precedence tilt schemes, i.e. the so-called Nulling-type schemes, utilized local-per-vehicle signals to provide tilt action (this was essentially a typical disturbance rejection-scheme) but suffered from inherent delays in the control). Nulling tilt may still be seen as an important research aim due to the simple nature and most importantly due to the more straightforward fault detection compared to precedence schemes. The work in this paper presents a substantial extension conventional to robust H∞ mixed sensitivity nulling tilt control in literature. A particular aspect is the use of optimization is used in the design of the robust controller accompanied by rigorous investigation of the conflicting deterministic/stochastic local tilt trade-off

Robust disturbance rejection methodology for unstable non-minimum phase systems via disturbance observer

In this work, we propose a disturbance rejection methodology to deal with control problem of unstable non-minimum phase (NMP) systems. Firstly, we propose a two degrees-of-freedom control structure, which consists of an outer loop feedback controller and an inner loop disturbance observer (DOB). Specifically, the controller is designed for desired control performance, whereas the robust DOB is applied to deal with external disturbances and internal uncertainties. By analyzing the robust internal stability, several design requirements on both controller and DOB are presented for the control system. The H2 theory is adopted for controller design. Then, we propose a systematic DOB optimization method for unstable NMP systems. The proposed method synthesizes the relative order, robust internal stability and mixed sensitivity optimization together to formulate the cost function. The standard H∞ method is introduced to acquire the optimal solution that guarantying the design requirements. Simulations show that the proposed method can deal with the control system design for the unstable NMP systems, and it also has better performance comparing with the traditional method.

Disturbance rejection control with H∞ optimized observer for vibration suppression of piezoelectric smart structures

In this paper, a disturbance rejection (DR) control with H∞ optimized observer is developed for vibration suppression of smart structures considering model uncertainties and measurement noise. An electro-mechanically coupled dynamic finite element (FE) model of piezoelectric smart structures is firstly built for control design. Based on the dynamic FE model, the H∞ optimized observer is designed with a dynamic feedback gain which is calculated by H∞ mixed sensitivity optimization. Expected response speed and robustness to model uncertainties and measurement noise are obtained by configuring proper weighting functions. In the closed-loop system, estimated disturbances and state variables are fed back through a conventional DR controller to counteract disturbances and stabilize the system. In order to validate the DR control with H∞ optimized observer, vibration suppression simulations of a piezoelectric smart beam are implemented in the absence and presence of model uncertainties and measurement noise, respectively. Furthermore, DR control with generalized proportional integral observer and DR control with high-gain proportional integral observer are added for comparison. Results show that excellent vibration suppression performance and better robustness to model uncertainties and measurement noise are achieved by the DR control with H∞ optimized observer.

H∞ Robust Control of an LCL-Type Grid-Connected Inverter with Large-Scale Grid Impedance Perturbation

In the distributed power generation system (DPGS), there may be a large range perturbation values of equivalent grid impedance at the point of common coupling (PCC). Perturbation of the impedance will cause resonant frequency variation of the Inductance Capacitance Inductance (LCL) filter on a large scale, affecting the quality of the grid current of the grid-connected inverter (GCI) and even causing resonance. To deal with this problem, a novel H∞ robust control strategy based on mixed-sensitivity optimization is proposed in this paper. Its generalized controlled object is augmented by properly selecting weighting functions in order to consider both tracking performance around power frequency and the stability margin in a high frequency of the GCI. For convenient implementation, the H∞ robust controller is simplified by model reduction from the seventh order to the third order. By comparison with a traditional control strategy with a quasi-proportional resonance controller, the proposed H∞ robust control strategy avoids crossing 180 degrees at the resonant frequency point in the phase frequency characteristic of current loop, and moves the phase frequency characteristic left. It guarantees a sufficient margin of stability throughout the designed range of grid impedance perturbation values and avoids the difficulty of parameter setting. Finally, the experimental results support the theoretical analyses and demonstrate the feasibility of the proposed strategy.

Research on Robust Control Strategies for VSC-HVDC

In the control system of VSC-HVDC, the phase locked loop provides phase signals to voltage vector control and trigger pulses to generate the required reference phase. The PLL is a typical second-order system. When the system is in unstable state, it will oscillate, make the trigger angle shift, produce harmonic, and make active power and reactive power coupled. Thus, considering the external disturbances introduced by the PLL in VSC-HVDC control system, the parameter perturbations of the controller and the model uncertainties, a H∞ robust controller of mixed sensitivity optimization problem is designed by using the Hinf function provided by the robust control toolbox. Then, compare it with the proportional integral controller through the MATLAB simulation experiment. By contrast, when the H∞ robust controller is added, active and reactive power of the converter station can track the change of reference values more accurately and quickly, and reduce overshoot. When the step change of active and reactive power occurs, mutual influence is reduced and better independent regulation is achieved.

Hybrid Robust Control Law with Disturbance Observer for High-Frequency Response Electro-Hydraulic Servo Loading System

Addressing the simulating issue of the helicopter-manipulating booster aerodynamic load with high-frequency dynamic load superimposed on a large static load, this paper studies the design of the robust controller for the electro-hydraulic loading system to realize the simulation of this kind of load. Firstly, the equivalent linear model of the electro-hydraulic loading system under assumed parameter uncertainty is established. Then, a hybrid control scheme is proposed for the loading system. This control scheme consists of a constant velocity feed-forward compensator, a robust inner loop compensator based on disturbance observer and a robust outer loop feedback controller. The constant velocity compensator eliminates most of the extraneous force at first, and then the double-loop cascade composition control strategy is employed to design the compensated system. The disturbance observer–based inner loop compensator further restrains the disturbances including the remaining extraneous force, and makes the actual plant tracking a nominal model approximately in a certain frequency range. The robust outer loop controller achieves the desired force-tracking performance, and guarantees system robustness in the high frequency region. The optimized low-pass filter Q(s) is designed by using the H∞ mixed sensitivity optimization method. The simulation results show that the proposed hybrid control scheme and controller can effectively suppress the extraneous force and improve the robustness of the electro-hydraulic loading system.

Multiple-Disturbance Rejection for High Precision Positioning of a VCM Servo Gantry

This paper presents an multiple disturbance rejection approach for rejecting narrow-band disturbances as well as norm-bounded random disturbances, with applications to high precision positioning of a Voice Coil Motor (VCM) actuated servo stage. An adaptive optimal phase filter design method is proposed for the rejection of frequency-varying narrow-band disturbances at unknown frequency range. With a parallel connection of the proposed adaptive filter, a robust H∞ controller can be synthesized with mixed sensitivity optimization for the purpose of both robust stability and rejection of norm-bounded random disturbances. The proposed control architecture is implemented to a VCM servo gantry to achieve high precision positioning in the presence of various disturbances.

Robust Stabilizer Design for High-Precision Tracking of a Linear Gantry

In this paper, we develop a robust ℋ∞ stabilizer design method for a parallel structure of internal model-based tracking control for a Voice Coil Motor (VCM) driven servo gantry. The physical model of the VCM gantry is discussed and the system augmentation with the internal-model control structure and the exosystem immersion is generated, where the plant model uncertainties are taken into consideration as well. A mixed sensitivity optimization method is introduced for the synthesis of robust stabilizers. Simulations and real time experiments demonstrate good performance of the proposed method for high precision tracking of the servo gantry system.

Robust <i>H</i><sub>∞</sub> Controller for High Precision Positioning System, Design, Analysis, and Implementation

In this paper, a systematic robust control design and analysis for a single axis precise positioner is presented. The effects of uncertainties on closed-loop stability and performance are considered in the H∞ robust controllers design. v-gap metric is utilized to validate the intelligently estimated uncertainty. The robust controllers are formulated within the frame- work of the standard H∞ mixed sensitivity optimization problem. Furthermore, a specially designed integral-H∞ and two-degree-of-freedom 2 DOF H∞ controllers are developed to provide improved robust performance and resolution properties. It is shown that the proposed design schemes are very effective for robust control and precise tracking performance of the servo positioning system.

Multiobjective optimization for automatic tuning of robust Model Based Predictive Controllers

In this paper a general procedure for tuning multivariable model predictive controllers (MPC) with constraints is presented. It has been applied to tune the control system of an activated sludge process control in a wastewater treatment plant. Control system parameters are obtained by solving a mixed sensitivity optimization problem, defined in terms of the H∞ norms of different weighted closed loop transfer functions matrices of the system, and a set of constraints, some of them expressed using the l1 norm. The use of multiple linearized models for the control allows for the specification of many robust performance criteria. The mathematical optimization for tuning all controller parameters is tackled in two iterative steps due to the existence of integer and real numbers. First, integer parameters are obtained using a special type of random search, and secondly a sequential programming method is used to tune the real parameters.

A Hamiltonian-based solution to the mixed sensitivity optimization problem for stable pseudorational plants

This paper considers the mixed sensitivity optimization problem for a class of infinite-dimensional stable plants. This problem is reducible to a two- or one-block H ∞ control problem with structured weighting functions. We first show that these weighting functions violate the genericity assumptions of existing Hamiltonian-based solutions such as the well-known Zhou–Khargonekar formula. Then, we derive a new closed form formula for the computation of the optimal performance level, when the underlying plant structure is specified by a pseudorational transfer function.

구조적 분석에 기초한 외란관측기의 설계

Disturbance observer (DOB) has been studied extensively and applied to many motion control fields during the last decades, but relatively few studies have been devoted to the development of analytic, systematic design methods for DOB itself, This paper thus aims to provide an analytic, systematic design method for DOB. To do this, DOB is structurally analyzed and the generalized disturbance compensation framework named robust internal-loop compensator (RIC) is introduced. Through this, the inherent equivalence between DOB and RIC is found, and the mixed sensitivity optimization problem of DOB is solved. Q-filter design is completely separated from the mixed sensitivity optimization problems of DOB although the proposed method has implicit .elation with Q-filter. Also, although the Q-fille. is separately designed with sensitivity function, the proposed DOB framework has the exactly same characteristic as the original DOB.

Advanced disturbance observer design for mechanical positioning systems

Disturbance-observer (DOB)-based controller design is one of the most popular methods in the field of motion control. In this paper, the generalized disturbance compensation framework, named the robust internal-loop compensator (RIC) is introduced and an advanced design method of a DOB is proposed based on the RIC. The mixed sensitivity optimization problem, which is the main issue of DOB design, is also solved through the parametrization of the DOB in the RIC framework. Differently from conventional methods, the Q-filter is separated from the mixed sensitivity optimization problem and a systematic design law for the DOB is proposed. This guarantees the robustness and optimality of the DOB and enables the design for unstable plants.

On the mixed sensitivity optimization problem for stable pseudorational plants

In this paper, we consider the mixed sensitivity optimization (two-block H∞) problem for stable plants with pseudorational transfer functions. This class of transfer functions plays an important role in dealing with delay systems. We derive a closed-form expression to compute the optimal performance level, by extending the well-known Zhou-Khargonekar formula to the two-block problems with pseudorational plants. A numerical example is given to illustrate the result.

Mixed Sensitivity Optimization to Avoid Pole/Zero Cancellation

We give a detailed discussion of the mixed sensitivity formulation proposed by Kwakernaak and explore the useful ideas behind it. We prove that this two-block mixed sensitivity problem is closely related to a four-block problem, and therefore to some extent can attain a balanced design among all transfer functions of a closed-loop system. We make some interesting comparisons between this approach and the well-known loop shaping design of McFarlane and Glover. We also show that this mixed sensitivity approach is superior to others because it can provide us with extra flexibility in shaping the sensitivity functions and lead to a controller of minimal order. © 1997 Elsevier Science Ltd.

A Practical H.INF. Two Degrees of Freedom Controller Design and Its Applications to Servo Systems.

We consider the problem of applying H∞ optimization techniques to design a TDOF controller for robust servo systems. We introduce a two-step H∞ optimization procedure: a feedback controller is designed to satisfy feedback properties and a prefilter is used to improve reference tracking performance. We describe a mixed sensitivity optimization scheme that is used for the feedback controller design, and propose a frequency shaping philosophy that highlights key issues for the prefilter design. We discuss the uncertainties in DC motor model and explain how to treat the parametric and non-parametric uncertainties in H∞ optimization framework. We also show a design example for a DC motor with parametric uncertainties and analyze the tracking property in terms of design strategy and parameters change.

Krein space approach to H/sup ∞/ mixed sensitivity minimization for a class of infinite dimensional systems

Motivated by the computation of the H/sup /spl infin// optimal performance and optimal mixed sensitivity for a class of infinite dimensional systems, the author considers the explicit computation of the norm and minimal symbols of a class of Hankel plus Toeplitz type operators with irrational symbols using the Krein space approach. The author shows how to explicitly compute the norm and parameterize all the minimal symbols. The results are used to obtain a complete solution to the H/sup /spl infin// optimal mixed sensitivity synthesis problem for a class of infinite dimensional systems: an explicit formula for computing the H/sup /spl infin// optimal performance and explicit parameterization of all optimal and suboptimal mixed sensitivities. An illustrative example is given. >

Optimal mixed sensitivity for SISO-distributed plants

The authors extend previous results for the single-input/single-output (SISO) mixed sensitivity problem for distributed parameter systems to a more general setting in which the transfer function of the plant to be controlled has both irrational stable and irrational unstable parts. These developments were originally motivated by the computation of the infimal H/sup /spl infin//-norm of the weighted mixed sensitivity for the irrational transfer function model of a damped flexible beam. >

Mixed-sensitivity optimization for a class of unstable infinite-dimensional systems

In this paper we solve the H ∞ mixed-sensitivity minimization problem for a class of unstable distributed systems. The solution is based on an extension of the skew Toeplitz methodology. The key mathematical fact used is that the skew Toeplitz operators arising in the unstable case are finite-rank perturbations of the classical skew Toeplitz operators obtained from compressions of rational functions. A system of linear equations (the singular system) is derived for this class of operators, from which one can compute the associated singular values and vectors. An example is included to illustrate the results.