Reduced-order Controller Research Articles

Control Strategy Based on $\text{H}\infty$ Repetitive Controller With Active Damping for Islanded Microgrid

To overcome the drawbacks of the proportional plus integral (PI) control based strategy, i.e., limitation for harmonic suppression and performance deterioration under load variation, a voltage control strategy based on the $\text{H}\infty $ repetitive controller with inverter-side current feedback damping is proposed for the inverter in islanded microgrid. The $\text{H}\infty $ repetitive controller provides good robustness against parameter perturbation and ensures the output voltage of low total harmonic distortion. Compared with other damping methods, a good resonance suppression and a better attenuation of the high-order harmonics can be achieved under the proposed strategy, which further improves the control performance of the voltage repetitive control system. A state space model including the damping coefficient is built to implement order reduction of the high-order controller, thereby simplifying the digital implementation while nearly without performance degradation. Moreover, the frequency response analysis shows that the order reduction can improve the adaptability of the controller to parameter variation. Finally, experiments and simulations verify the correctness of the analysis.

Koopman Reduced Order Control for Three Body Problem

In this paper, we use a Circle Restricted Three-Body Problem (CRTBP) to simulate the motion of a satellite. Then we reformulate this problem with the controller into the description using Koopman eigenfunction. Although the original dynamical system is nonlinear, the Koopman eigenfunction behaves linearly. Choosing Jacobi integral as the Koopman eigenfunction and using the zero velocity curve as the reference for control, we are allowed to combine well-developed Linear Quadratic Regulator (LQR) controller to design a nonlinear controller. Using this approach, we design the low thrust orbit transfer strategy for the satellite flying from the earth to the moon or from the earth to the sun.

Control of linear instabilities by dynamically consistent order reduction on optimally time-dependent modes

Identification and control of transient instabilities in high-dimensional dynamical systems remain a challenge because transient (non-normal) growth cannot be accurately captured by reduced-order modal analysis. Eigenvalue-based methods classify systems as stable or unstable on the sole basis of the asymptotic behavior of perturbations and therefore fail to predict any short-term characteristics of disturbances, including transient growth. In this paper, we leverage the power of the optimally time-dependent (OTD) modes, a set of time-evolving, orthonormal modes that capture directions in phase space associated with transient and persistent instabilities, to formulate a control law capable of suppressing transient and asymptotic growth around any fixed point of the governing equations. The control law is derived from a reduced-order system resulting from projecting the evolving linearized dynamics onto the OTD modes and enforces that the instantaneous growth of perturbations in the OTD-reduced tangent space be nil. We apply the proposed reduced-order control algorithm to several infinite-dimensional systems, including fluid flows dominated by normal and non-normal instabilities, and demonstrate unequivocal superiority of OTD control over classical modal control.

Efficient reduced order controller design for dissipative PDE systems with strong convective phenomena

The control of dissipative distributed parameter systems with strong convective phenomena is considered, employing model order reduction. The accuracy of the derived reduced order model (ROM) and the associated observer may decrease as the system behavior switches from diffusion-dominant to convection-dominant. To mitigate the issue, we propose to use adaptive proper orthogonal decomposition (APOD) to capture the changing behavior of the system. A Lyapunov controller is designed based on the ROM to control the system in the presence of disturbance and strong convective phenomena. Galerkin method is used to construct the ROM. The basis functions needed in Galerkin method are updated using APOD. A case study of regulating a tubular reactor at an open-loop unstable steady state is presented, where the performance of the ROM-based observer is evaluated. It's also demonstrated that APOD can improve the accuracy of the observer when an unexpected disturbance occurs.

Reduced order LQG control design for port Hamiltonian systems

The aim of this paper is to propose a reduced order control design method for large scale port Hamiltonian systems. To this end, a structure preserving reduction method and a modified LQG control design are combined to derive a reduced order model suitable for control purposes. We first recall the structure preserving reduction method for port Hamiltonian systems called effort constraint method and characterize the error bound associated to this reduction method. We then give sufficient conditions for non-standard LQG design which allow to design a passive controller equivalent to the control by interconnection of port Hamiltonian systems. This LQG method allows to define an LQG balanced realization by computing the LQG Gramians, the effort-constraint method is then used to derive a reduced order port Hamiltonian system and to design a reduced order passive LQG controller. Finally, the method is illustrated in simulation on a mass–spring–damper system. The performances of the reduced order controller are compared to the results obtained with a full order passive LQG controller.

Active disturbance rejection guidance and control scheme for homing missiles with impact angle constraints

An active disturbance rejection guidance and control scheme for homing missiles with three-dimensional impact angle constraints is proposed. The six-degree-of-freedom dynamical and kinematical models containing model uncertainties and disturbances are established. A strict feedback relative dynamics between the target and homing missile in three-dimensional space are deduced. A reconstructed reduced-order attitude controller design model is proposed. A two-loop control structure with respect to the centroid guidance loop and rotational control loop is conducted to implement the six-degree-of-freedom guidance and control system with the help of second-order sliding mode approach and extended state observers. The tracking loop of the Euler angles of the missile can be elided and the number of six-degree-of-freedom control parameters can be reduced. Finally, the effectiveness and robustness of the newly proposed guidance and control scheme are investigated and verified via six-degree-of-freedom nonlinear simulation studies.

H∞ output-feedback control design for combustion systems using optical instrumentation

Abstract This paper proposes a complete robust control design procedure for combustion systems, present in a wide range of important applications. Using a non-linear model identified through optical instrumentation, it is proposed a linear model around an operating condition. To ensure robustness with respect to variations on the operation condition and to deal with external disturbances, a state-space linear representation is further developed, introducing uncertain parameters and exogenous inputs affecting the plant (as non-laminar air flow), giving rise to a poly topic uncertain linear system. Finally, it is proposed a reduced-order H∞ output-feedback control law for the resulting uncertain system, capable to assure closed-loop robust stability and performance in the whole uncertain domain. A numerical experiment is presented to show the effectiveness of the designed reduced-order controller, that is robust against uncertainties and have a low cost of implementation.

Digital redesign of analogue dynamic output-feedback controllers for polytopic systems

ABSTRACTThis paper is devoted to the problem known as digital redesign, i.e. given a previously designed stabilising continuous-time controller for a continuous-time plant, synthesise a digital controller that provides the hybrid closed-loop system with output trajectories as similar as possible to the continuous-time ones. To accomplish this goal, two distinct optimisation criteria are investigated: (i) the Euclidean norm of the difference between the dynamic matrix of the discretised closed-loop continuous-time system and the dynamic matrix that represents the discretised open-loop system fed back by the designed digital controller; (ii) the norm of the transfer function from the noise input to the error between the outputs of the two systems. As main novelties with respect to the existing results on digital redesign, the proposed conditions can deal with polytopic systems, and can synthesise reduced-order dynamic output-feedback digital controllers as well.

Advanced Control Synthesis for Reverse Osmosis Water Desalination Processes.

In this study, robust control synthesis has been applied to a reverse osmosis desalination plant whose product water flow and salinity are chosen as two controlled variables. The reverse osmosis process has been selected to study since it typically uses less energy than thermal distillation. The aim of the robust design is to overcome the limitation of classical controllers in dealing with large parametric uncertainties, external disturbances, sensor noises, and unmodeled process dynamics. The analyzed desalination process is modeled as a multi-input multi-output (MIMO) system with varying parameters. The control system is decoupled using a feed forward decoupling method to reduce the interactions between control channels. Both nominal and perturbed reverse osmosis systems have been analyzed using structured singular values for their stabilities and performances. Simulation results show that the system responses meet all the control requirements against various uncertainties. Finally the reduced order controller provides excellent robust performance, with achieving decoupling, disturbance attenuation, and noise rejection. It can help to reduce the membrane cleanings, increase the robustness against uncertainties, and lower the energy consumption for process monitoring.

LQG/LTR procedure using reduced-order Kalman filters

ABSTRACTThis paper discusses a linear-quadratic-Gaussian/loop transfer recovery (LQG/LTR) procedure using reduced-order Kalman filters by extending known exact-recovery result. The state-space realisation commonly used for reduced-order observer design is employed. The zero structure intrinsic to the realisation is revealed. Asymptotic recovery is achieved using a non-singular reduced-order Kalman filter with a parameterised set of covariance matrices. The proposed procedure provides a systematic method for directly designing reduced-order LQG controllers without additional coordinate transformations. A numerical design example for a simple multivariable plant is presented to compare the proposed design with the standard LQG/LTR design using a full-order Kalman filter.

Robust control for four-wheel-independent-steering electric vehicle with steer-by-wire system

A four-wheel-independent-steering (4WIS) electric vehicle (EV) with steer-by-wire (SBW) system is proposed in this paper. The fast terminal sliding mode controller (FTSMC) is designed for the SBW system to suppress external disturbances. Taking unstructured and structured uncertainties into consideration, a robust controller is designed for the 4WIS EV utilizing μ synthesis approach and the controller order reduction is implemented based on Hankel-Norm approximation. Since sideslip angle is the feedback signal of robust controller and it is hard to measure, the extended Kalman filter (EKF) is employed to estimate sideslip angle. To evaluate the vehicle performance with the designed control system, step and sinusoidal steering maneuvers are simulated and analyzed. Simulation results show that the designed control system have good tracking ability, strong robust stability and good robust performance to improve vehicle stability and handing performance.

Reduced order controller design for Timoshenko beam: A port Hamiltonian approach

This paper deals with the structure and passivity preserving model reduction and the reduced order controller design for a class of distributed controlled port Hamiltonian systems - Timoshenko beam. The boundary conditions of the beam lead to physical constraints which are hardly considered in the reduction procedure. In this work we propose to use the descriptor system realization of port Hamiltonian system to conserve the physical constraints. A passive LQG control design method is proposed for this type of system. This LQG method defines a balanced coordinate which allows us to reduce the system. Using the obtained reduced model, a reduced order passive controller which stabilizes the full order system is designed using the LQG method. At last we give the numerical simulations to show the effectiveness of the proposed reduced passive controller.

An Improved Parameterized Controller Reduction Technique via New Frequency Weighted Model Reduction Formulation

AbstractIn this paper, an improved parameterized controller reduction technique via a new frequency weighted model reduction formulation is developed for the feedback control of MIMO discrete time systems particularly for non‐unity feedback control system configurations which have the controller located in the feedback path. New frequency weights which are a function of a free parameter matrix are derived based on a set of equivalent block diagrams and this leads to a generalized double sided frequency weighted model reduction formulation. Solving this generalized double sided frequency weighted model reduction problem for various values of the free parameter results in obtaining controllers which correspond to each value of the free parameter. It is shown that the proposed formulation has a useful characteristic such that selecting a controller which corresponds to a large value of the free parameter results in obtaining an optimal reduced order controller and using this optimal reduced order controller in a closed loop system results in significant reduction in the infinity norm of the approximation error between the original closed loop system and the closed loop system which uses an optimal reduced order controller (when compared to existing frequency weighted model reduction methods).

Robust trajectory tracking control of a dual-arm space robot actuated by control moment gyroscopes

It is a new design concept to employ control moment gyroscopes (CMGs) as reactionless actuators for space robots. Such actuation has several noticeable advantages such as weak dynamical coupling and low power consumption over traditional joint motor actuation. This paper presents a robust control law for a CMG-actuated space robot in presence of system uncertainties and closed-chain constraints. The control objective is to make the manipulation variables to track the desired trajectories, and reduce the possibility of CMG saturation simultaneously. A reduced-order dynamical equation in terms of independent motion variables is derived using Kane's equations. Desired trajectories of the independent motion variables are derived by minimum-norm trajectory planning algorithm, and an adaptive sliding mode controller with improved adaptation laws is proposed to drive the independent motion variables tracking the desired trajectories. Uniformly ultimate boundedness of the closed loop system is proven using Lyapunov method. The redundancy of the full-order actual control torques is utilized to generate a null torque vector which reduces the possibility of CMG angular momentum saturation while producing no effect on the reduced-order control input. Simulation results demonstrate the effectiveness of the proposed algorithms and the advantage of weak dynamical coupling of the CMG-actuated system.

Order reduction of plant and controller in closed loop identification based on joint input-output approach

This paper presents the order reduction for plant and controller models estimated by the joint input-output approach in the closed loop identification, named the controllability or observability intensity truncation (COIT) method in which the index for order reduction is the controllability intensity or the observability intensity. The use of these intensities depends on the estimated models obtained by the joint input-output approach. In the application of the closed loop identification with the balanced truncation (BT) and the COIT methods; a numerical example and an inverted pendulum experimental system, the COIT method appropriately reduces the order of the estimated plant and controller models and is superior to the BT method.

Observer-based two-time scale robust control of free-flying flexible-joint space manipulators with external disturbances

SUMMARYObserver-based two-time scale robust control is proposed for free-flying flexible-joint space manipulators with unknown payload parameters and bounded disturbances. The dynamic equations of a free-flying space manipulator with two flexible revolute joints were derived by the momentum conservation law and the Lagrange equations. A flexibility compensator was introduced to make the equivalent joint stiffness large enough, which made traditional singular perturbation approach applicable. Then, a singular perturbation model was formulated and a reduced-order controller is proposed. This controller consisted of a slow sub-controller and a fast flexible-joint sub-controller. To the slow subsystem, a sliding observer based robust slow sub-controller was proposed. By optimal linear quadratic regulator method, the fast sub-controller was designed with the estimated velocity by linear observer. This fast sub-controller could stabilize the fast subsystem around the equilibrium trajectory created by the slow subsystem under the effect of the slow control. Finally the numerical simulations were carried out, which showed that elastic joint vibrations had been stabilized effectively and good tracking performances had been achieved.

A Reduced-Order Controller Considering High-Order Modal Information of High-Rise Buildings for AMD Control System with Time-Delay

Time-delays of control force calculation, data acquisition, and actuator response will degrade the performance of Active Mass Damper (AMD) control systems. To reduce the influence, model reduction method is used to deal with the original controlled structure. However, during the procedure, the related hierarchy information of small eigenvalues will be directly discorded. As a result, the reduced-order model ignores the information of high-order mode, which will reduce the design accuracy of an AMD control system. In this paper, a new reduced-order controller based on the improved Balanced Truncation (BT) method is designed to reduce the calculation time and to retain the abandoned high-order modal information. It includes high-order natural frequency, damping ratio, and vibration modal information of the original structure. Then, a control gain design method based on Guaranteed Cost Control (GCC) algorithm is presented to eliminate the adverse effects of data acquisition and actuator response time-delays in the design process of the reduced-order controller. To verify its effectiveness, the proposed methodology is applied to a numerical example of a ten-storey frame and an experiment of a single-span four-storey steel frame. Both numerical and experimental results demonstrate that the reduced-order controller with GCC algorithm has an excellent control effect; meanwhile it can compensate time-delays effectively.

New Designs of Reduced-Order Observer-Based Controllers for Singularly Perturbed Linear Systems

The slow and fast reduced-order observers and reduced-order observer-based controllers are designed by using the two-stage feedback design technique for slow and fast subsystems. The new designs produce an arbitrary order of accuracy, while the previously known designs produce the accuracy of O(ϵ) only where ϵ is a small singular perturbation parameter. Several cases of reduced-order observer designs are considered depending on the measured state space variables: only all slow variables are measured, only all fast variables are measured, and some combinations of the slow and fast variables are measured. Since the two-stage methods have been used to overcome the numerical ill-conditioning problem for Cases (III)–(V), they have similar procedures. The numerical ill-conditioning problem is avoided so that independent feedback controllers can be applied to each subsystem. The design allows complete time-scale separation for both the reduced-order observer and controller through the complete and exact decomposition into slow and fast time scales. This method reduces both offline and online computations.

Reduced-Order Modeling, Testing, and Control of Nonlinear Mechanical and Structural Systems

Reduced-Order Modeling, Testing, and Control of Nonlinear Mechanical and Structural Systems

天井クレーン液体容器搬送制御システムの設計

In the steel/casting industries, a liquid container transport is carried out by an overhead traveling crane or a trolley. The operation of the overhead traveling crane is carried out both operation by the experience operator and operation by automated transportation in order to prevent quality deterioration due to the overflow and involvement in a hostile environment. In particular, the overhead crane transportation by the operator, which is allowed to select freely pathway, is needed from the point of freedoms of the operation. This paper presents a design of a liquid container transport control system with an overhead traveling crane, which is allowed to operate by an inexperienced operator easily. The presented control system is designed as to suppress both the rod vibration and the sloshing (liquid vibration) without measuring the sloshing. The presented control system is two DOFs controller, the feed-forward controller is based on two notch filter, and the feedback controller is based on the H2/H∞ controller design method using LMI. The derived controller is performed a controller order reduction in consideration with practical use. Some experiments are presented to show the effectiveness of the proposed design of control system.