Multivariable State Feedback Research Articles

A Control Method to Reduce Overshoots in High-Frequency Link Current and Voltages at Load Transients of a Dual-Active-Bridge Series-Resonant Converter

Dual Active Bridge Series Resonant Converter (DABSRC) is well researched in the literature to find out a suitable pulse width modulation (PWM) technique that can achieve voltage regulation, zero voltage switching (ZVS), and minimum rms current in high frequency (HF) link. Although the advanced PWM techniques achieve desired performance at steady state, the HF link current and voltages suffer from huge overshoots during the load transients, which can damage the semiconductor devices and can cause the saturation of the high frequency transformer. Therefore, in this paper, a relationship is derived between the pole positions and the percentage overshoot, so that any design with the trade-off between the fast dynamics and overshoot can be done analytically. As the system involves multiple state and input variables, which are also closely coupled, a multivariable state feedback controller design is proposed to control the dynamics of all the HF link state variables simultaneously. In any DAB-based topology, the peak volt-ampere (VA) rating of the passive components can increase by 80% due to these overshoots. The proposed control successfully restricts the overshoots below 25% with a settling time of 5 ms for the output voltage. The experimental verification is carried out in a 2.25 kW hardware prototype.

Multivariable State-Feedback Controller Design for PV Inverter Connected to a Weak Grid

This paper presents a robust multi-input multi-output (MIMO) state-feedback control scheme for a photovoltaic (PV) inverter connected to a weak grid. For a weak grid, the point of common coupling (PCC) voltage is very sensitive to the power disturbances and it is dynamically coupled to the PLL dynamics. So far, most of the control methods do not take into accounts these couplings. Therefore, in this paper, the MIMO controller was designed taking into account the dynamics of the phase-locked loop (PLL) and coupling effects between PCC voltage and the active power to enhance the system’s robustness. As result, the robust performance of the PV inverter interfaced to a weak grid was yielded. In addition, the sensitivity of the system to PLL was eliminated, allowing the use of larger PLL bandwidth even in a very weak grid. Based on the eigenvalues analysis method, a comparative study between the proposed control method and the conventional vector control method was performed. The proposed method is verified with simulations in PLECS and real-time simulations in the RT Box. The results show that the proposed MIMO control method preserves the system stability robustness against any change of grid strength, generated power and PLL bandwidth.

Optimal state feedback controller for three tank cylindrical interacting system using Grey Wolf Algorithm

This article presents, optimal state feedback controller for three tank cylindrical interacting system was proposed to maintain set point in the tank. Grey Wolf Optimization Algorithm used to describe the optimal tuning of state feedback controller. Generally, optimal state feedback controller reduces fluctuation state with lowest control energy. Gain of the optimal state feedback controller used to reduce the fluctuation state to minimum value. By adding integrator, the measured value of the tank moves towards set point. Linear quadratic regulator is a multivariable state feedback control and it depends on the state of the system. The controller performance enhanced by suitable range of Q and R value. The proposed technique uses heuristic algorithm for tuning the state feedback gain directly. The results show that the developed control technique given better performance.

Dynamic Control of a DFIG Wind Power Generation System to Mitigate Unbalanced Grid Voltage

This paper presents an improved control strategy for a doubly-fed induction generator (DFIG) during unbalanced grid voltage conditions. The proposed strategy was applied in both synchronization and grid-connected conditions. The synchronization process is carried by controlling the extracted positive and negative sequence components of the stator q-axis voltage to follow the grid q-axis voltage. This strategy can be accomplished by controlling the positive and negative sequence components of the rotor d-axis current. By perturbing the rotor d-axis current, the stator EMF builds up and follows the grid voltage accurately. The stator frequency and the phase difference between the stator and grid voltage are compensated by adjusting the stator d-axis positive and negative voltage components to zero. After synchronization, the proposed control strategy focuses on regulating the average stator active and reactive power control by controlling the positive components of q and d-axis currents, respectively. The second target is to minimize the generator torque ripple by controlling the rotor negative sequence components. At the same time, the grid side converter is controlled to minimize the grid power pulsations to reduce the impact of the unbalanced grid voltage. This study focuses on enhancing the dynamics of DFIG during the unbalanced grid voltage by using Multivariable State Feedback (MSF) current controllers. Experiments are carried out to validate the performance improvement by using the proposed method. The simulation and experimental results showed superior performance of the proposed control strategy.

Current controller design for DFIG‐based wind turbines using state feedback control

Doubly-fed induction generators (DFIGs) are widely used in wind energy conversion systems. The dynamic features of DFIGs make it important to focus on designing high-performance control schemes. However, the dynamic characteristics of such generators depend on nonlinear parameters, such as stator flux, stator current, and rotor current, which increase overall system complexity. Therefore, robust controllers must be implemented with the ability to support the dynamic frequencies of wind energy to ensure system stability. Conventional vector control configurations that use proportional-integral controllers have various drawbacks, such as parameter tuning difficulties, mediocre dynamic performance, and reduced robustness. In this study, improving DFIG dynamics by applying a multivariable state feedback current controller with a feedforward component to improve the steady-state and transient characteristics of the controller has been introduced and discussed. Multivariable state feedback controllers are proposed to replace the proportional-integral controllers on both the rotor and grid sides. The proposed controller is designed using a multivariable system and feedforward control for input reference and incorporating disturbances into the control equations for fast transient responses. To demonstrate the advantages of this controller, experimental studies are presented for both the transient and steady states.

Multivariable state feedback control as a foundation for lithium-ion battery pack charge and capacity balancing

Multivariable state feedback control as a foundation for lithium-ion battery pack charge and capacity balancing

Multivariable State Feedback Control as a Foundation for Lithium-Ion Battery Pack Charge and Capacity Balancing

This article presents a framework for examining the impact of different balancing strategies on cell-to-cell variations in state of charge (SOC), maximum capacity, and resistance within a lithium-ion battery pack. The literature motivates this work by showing that imbalance in both SOC and maximum capacity places limitations on pack-level charge and discharge capabilities. The use of equalization circuits to mitigate differences in SOC and voltage between cells in a battery pack is well-established. The goal of this article, in contrast, is to make the case for the use of state feedback control as a tool for balancing both SOC and maximum charge capacity. Specifically, the article draws on the electrochemical modeling and control theory literature to examine two balancing strategies: voltage balancing and a proposed novel multivariable SOC/capacity balancing strategy. The latter strategy navigates the implicit short-term trade-offs between SOC and capacity balancing by inducing a temporary SOC imbalance between cells to increase the dissipation rate of capacity imbalance. Results indicate that voltage balancing fails to eliminate capacity and resistance imbalance between cells. In contrast, the proposed method is able to eliminate charge, capacity and resistance imbalance within the lifespan of the pack, and extends pack lifespan by 9.2%.

An Improved Internal Model Principle Based Multivariable Nonlinear Control Method with Multiclass Nonharmonic Disturbances and Its Application to Speed Control of a Motor Drive System

We study the global disturbance rejection problem for a class of general multivariable nonlinear systems with multiclass nonharmonic disturbances. The paper first introduces the importance and state of the art for disturbance rejection problem and describes the control problem in the form of mathematical expressions. It stresses the multiclass disturbances produced by the exosystem satisfying certain characteristic conditions. Then, the nonlinear internal models are designed in accordance with different characteristics of multiclass external disturbances. On the basis of introduction of the control law for disturbance-free system, a multivariable state feedback controller is devised in terms of the designed internal model equations and corresponding assumptions. A Lyapunov function is constructed to theoretically prove the global uniform boundness of all signals for the multivariable closed-loop system. Finally, the presented method is applied to implement the speed control and reject the multiclass nonharmonic disturbances for a two-input motor drive system. The simulation results testify correctness and effectiveness of the presented algorithm.

Global Harmonic Current Rejection of Nonlinear Backstepping Control with Multivariable Adaptive Internal Model Principle for Grid-Connected Inverter under Distorted Grid Voltage

Based on a brief review on current harmonics generation mechanism for grid-connected inverter under distorted grid voltage, the harmonic disturbances and uncertain items are immersed into the original state-space differential equation of grid-connected inverter. A new algorithm of global current harmonic rejection based on nonlinear backstepping control with multivariable internal model principle is proposed for grid-connected inverter with exogenous disturbances and uncertainties. A type of multivariable internal model for a class of nonlinear harmonic disturbances is constructed. Based on application of backstepping control law of the nominal system, a multivariable adaptive state feedback controller combined with multivariable internal model and adaptive control law is designed to guarantee the closed-loop system globally uniformly bounded, which is proved by a constructed Lyapunov function. The presented algorithm extends rejection of nonlinear single-input systems to multivariable globally defined normal form, the correctness and effectiveness of which are verified by the simulation results.

The design of nonovershooting and nonundershooting multivariable state feedback tracking controllers

We consider the use of linear multivariable feedback control to achieve a nonovershooting and nonundershooting step response. Recently, Schmid and Ntogramatzidis (2010) [13] introduced a linear state feedback controller design method to avoid overshoot. In this paper, we describe conditions under which the design method may be modified to avoid undershoot. The method is applicable to square and nonsquare systems, minimum and nonminimum phase systems, and also strictly proper and bi-proper systems.

Nonundershooting linear multivariable tracking controllers

AbstractWe consider the use of linear multivariable state feedback control to achieve a nonundershooting step response. The recently introduced nonovershooting linear state feedback controller design method of Schmid and Ntogramatzidis (2010) is here modified to yield a step response that is nonundershooting. The design method is applicable to square and non-square systems, minimum and nonminimum phase systems, and also strictly proper and bi-proper systems.

Enhancing integrity in multivariable process control under actuator failures

Achieving fault tolerance in process control usually involves supervision and reconfiguration. On the other hand, common robust control approaches achieve a common performance level for a family of plants, which can be unsatisfactory in the nominal case if faulty conditions are not taken into account. This paper discusses the problem of guaranteeing both a nominal performance and a degraded second-class control performance under actuators' permanent faults, by using a time invariant controller. LMI, BMI and other possible solutions are investigated in a multivariable state feedback control framework. Two examples from the literature (reactor and jet bank angle control) illustrate the procedure.

DEVELOPMENT OF FUZZY LOGIC LQR CONTROL INTEGRATION FOR AERIAL REFUELING AUTOPILOT

This paper investigates the performance on the aircraft control system during air refuel purposes of the Linear Quadratic Regulator (LQR) control alone, and the integration between fuzzy control and LQR. LQR is modern linear control that is suitable for multivariable state feedback and is known to yield good performance for linear systems or for nonlinear systems where the nonlinear aspects are presented. The fuzzy control is known to have the ability to deal with nonlinearities without having to use advanced mathematics. The LQR integrated fuzzy control (LQRIFC) simultaneously makes use of the good performance of the LQR in the region close to switching curve, and the effectiveness of the fuzzy control in region away from switching curve. A new analysis of the fuzzy system behavior presented helps to make possible precise integration of LQR features into the fuzzy control. The LQRIFC is verified by simulation to suppress the uncertainty instability more effectively than the LQR besides minimizing the time of the mission proposed.

CONTROL-ORIENTED MODELING OF HYDROSTATIC TRANSMISSIONS CONSIDERING LEAKAGE LOSSES

Hydrostatic Transmissions, also called hydrostatic gears, have been widely used in mobile machines and off-road vehicles such as wheel loaders, graders or tractors. The hydrostatic transmissions are gears with high power density which offer important advantages like continuously variable transmission, maximum tractive force at low speeds and reversing without changing gear. In the industrial practice the transmission output torque, transmission ratio or output speed are usually controlled by model-free PID control methods. This approach results in limited closed-loop bandwidth, limited working efficiency and accuracy due to the high nonlinear characteristic of the plant.This paper presents a control-oriented model of a general hydrostatic transmission as a first step towards a multivariable model-based fuzzy state feedback gain scheduling controller based on parallel distributed compensation scheme (PDC) using Takagi-Sugeno (TS) fuzzy systems. First principles are used to determine the structure of the TS fuzzy system. The relevance of the approach is shown by simulation studies.

A NEW PERFORMANCE EVALUATION STRATEGY FOR DECENTRALIZED MULTIVARIABLE PID CONTROL SYSTEMS

This paper addresses the problem of performance evaluation for decentralized multivariable PID controllers, by comparing the actual performance with that of a benchmark multivariable state-feedback LQR controller. The procedure can be used at a design stage and for closed-loop performance monitoring of industrial plants. An overall measure of controller suboptimality is proposed along with a matrix that quantifies the closed-loop interactions among control loops. The minimum interactions evaluated under the benchmark controller can be regarded as an intrinsic process property. Finally, a retuning procedure for the decentralized controller is proposed with the aim of improving the overall closed-loop performance. Several extensions of the benchmark controller are discussed, such as how to identify a process model from data and how to consider output feedback. The features of the proposed methodology are explained by application to the Shell Control problem.

Gray Balance Control Loop for Digital Color Printing Systems

Four-color process printers generally use gray balance for achieving color balance. Here we describe a novel gray balance control system which uses multivariable state feedback principles. We show that the system performance is greatly improved and the requirements on number of color measurements per calibration initialization are greatly reduced. A synthesis of a state space control model, feedback controller and TRC smoothing techniques are discussed in detail to achieve good prints after gray balance. Experimental results are shown to validate the approach when used for real-time feedback control of color systems.

Bounded robust control of constrained multivariable nonlinear processes

This work focuses on control of multi-input multi-output (MIMO) nonlinear processes with uncertain dynamics and actuator constraints. A Lyapunov-based nonlinear controller design approach that accounts explicitly and simultaneously for process nonlinearities, plant-model mismatch, and input constraints, is proposed. Under the assumption that all process states are accessible for measurement, the approach leads to the explicit synthesis of bounded robust multivariable nonlinear state feedback controllers with well-characterized stability and performance properties. The controllers enforce stability and robust asymptotic reference-input tracking in the constrained uncertain closed-loop system and provide, at the same time, an explicit characterization of the region of guaranteed closed-loop stability. When full state measurements are not available, a combination of the state feedback controllers with high-gain state observes and appropriate saturation filters, is employed to synthesize bounded robust multivariable output feedback controllers that require only measurements of the outputs for practical implementation. The resulting output feedback design is shown to inherit the same closed-loop stability and performance properties of the state feedback controllers and, in addition, recover the closed-loop stability region obtained under state feedback, provided that the observer gain is sufficiently large. The developed state and output feedback controllers are applied successfully to non-isothermal chemical reactor examples with uncertainty, input constraints, and incomplete state measurements. Finally, we conclude the paper with a discussion that attempts to put in perspective the proposed Lyapunov-based control approach with respect to the nonlinear model predictive control (MPC) approach and discuss the implications of our results for the practical implementation of MPC, in control of uncertain nonlinear processes with input constraints.

Modeling Analysis and Control of a Current Source Inverter-Based STATCOM

This article presents a new approach for the dynamic control of a current source inverter (CSI)-based STATCOM. The dq-frame model and the steady-state characteristic of the CSI STATCOM are proposed as a basis for control design. Use of traditional PI controllers leads to a poorly damped high-frequency oscillation between the inductance and capacitance of the CSI output filter. The new approach includes a fast ac current control inner loop and a slower dc current control outer loop. The inner loop, which is a combination of multivariable full state feedback and integral control, allows for rapid nonoscillatory dynamics of the ac current without overshoot or steady-state error. Experimental tests on a 5 kVA laboratory CSI STATCOM setup validate the proposed control design as well as the simulation results.

Multivariable model state feedback: Computationally simple, easy-to-tune alternative to MPC

Methods for the design and tuning of multivariable model state feedback (MMSF) systems for complete and triangular output decoupling of inherently stable processes are presented. MMSF is a method of implementing multivariable IMC controllers that substantially reduces the complexity of the implementation and compensates for control effort saturation. Complexity is reduced because the controls are formed as a linear combination of past and current model states. Saturation-induced directionality problems are avoided by temporarily increasing filter time constants to bring the control vector into the constraint set. The possibility that needed future controls will be inadequate to compensate for past control actions is avoided by setting minimum values for the controller filter time constants. The feedback structure of MMSF facilitates on-line tuning, one process variable at a time. Also, because MMSF is a form of IMC, it can be tuned off-line to accommodate process uncertainty using H∞ methods.

Identification of Multivariable State Feedback Systems Using the Indirect Identification method

Identification of Multivariable State Feedback Systems Using the Indirect Identification method