Loop-shaping Approach Research Articles

Road profile estimation based on the second generation CRONE control

The objective of this paper is to present a new design method for an unknown input estimator with a closed-loop structure. A frequency domain approach is carried out using a model-based design method and a loop-shaping technique. The loop-shaping approach used to the estimator design is usually applied in the context of control system design. More precisely, it is the second generation CRONE system design methodology that is used. This method is applied to the estimation of a speed bump by using one of the sensors initially intended for suspension control. Note that the noise measurement used in the simulation is recorded from on-board sensors used to control the piloted suspension of a DS7 Crossback. The time responses of the estimator, obtained with a non-linear quarter-car simulator, illustrate the very good results obtained.

A Supplementary Control Design for Multi-Vendor Realization of Parallel VSCs: A Loop Shaping Approach

The formation of hybrid alternating current (AC)-(DC) direct current systems from converters built by different manufacturers has attracted considerable attention in recent years. In multi-vendor AC-DC systems, the converter stations and their controllers are designed independently due to confidentiality requirements. If the converters have a physical connection at their AC side, unforeseen interactions among adjacent converters may disrupt stability and alter the dynamic performance of the converters from that intended by their designers. This paper contributes to seamlessly integrating converters with independently designed controllers into a multi-VSC (voltage-sourced converter) system. An <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> control problem is defined to design two supplementary filters (SFs) per converter, one for the direct (d)-axis and one for the quadrature (q)-axis control loop, to simultaneously stabilize the multi-VSC system and minimize the perturbation of the dynamic response of the interconnected converters from the vendors' designed dynamic behavior. Adding the SFs to the control system of converters will not cause new disruptive interactions, because the coupling dynamics among the converters are considered in designing the SFs. It is also analytically shown that employing the proposed SFs increases the robust stability margin of the multi-VSC system. Various studies based on the nonlinear model of a 2-VSC system verify the effectiveness of the presented method in integrating independently designed converters into a multi-VSC system.

A two-degree-of-freedom controller for a high-precision air temperature control system with multiple disturbances

The key equipment to prevent precision machinery such as lithography from being influenced by air temperature fluctuation is a high-precision air temperature control (ATC) system. The ATC system developed for a lithography immersion testing platform suffers from the difficulties of multiple disturbances, large inertia and time delay. However, seldom have control methods can solve these problems systematically. A two-degree-of-freedom (2DOF) controller is proposed in this paper for this system, where model predictive control (MPC) is developed to overcome large inertia and time delay in the main control loop, and the measurable disturbance from the inlet air is compensated; based on the loop shaping approach, the controller in the disturbance rejection control loop is designed to attenuate the load disturbance; a Kalman filter is designed to reduce the influence of noise having no stable frequency characteristic. The experimental results show that the MPC controller and Kalman filter can effectively avoid the system oscillation, and the disturbance rejection control loop can significantly attenuate the load disturbance in the frequency range from 0.01 to 0.02 rad/s. Therefore, the 1σ precision is increased by 3.3 mK to 8.7 mK by the 2DOF controller when the system is influenced by the load disturbance with different fluctuation amplitudes.

Decoupled $dq$ Current Control of Grid-Tied Packed E-Cell Inverters in Vehicle-to-Grid Technologies

This article investigates a decoupled vector current control strategy for grid-tied single-phase nine-level Packed E-Cell (PEC) inverters for vehicle-to-grid (V2G) technologies. The control design is based on a loop shaping approach, where performance specifications such as desired closed-loop bandwidth, closed-loop stability, robustness to pure time-delays in control loops/process, and decoupling between direct ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$d$</tex-math></inline-formula> ) and quadrature ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$q$</tex-math></inline-formula> ) axis of control signals are specified in the frequency domain. The control design problem is formulated as a convex optimization problem whose solution results in a multivariable controller in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$dq$</tex-math></inline-formula> framework. The effectiveness of the proposed control strategy in terms of robust stability, current tracking, and improved total harmonic distortion is evaluated by experimental and simulation results under several case studies. The results also show that the designed controller provides the desired transient response as well as decoupling between the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$dq$</tex-math></inline-formula> output currents.

Comparison of Fractional-Order and Integer-Order H∞ Control of a Non-Collocated Two-Mass Oscillator

We consider the robust control of a two-mass oscillator with a dominant input delay. Our aim is to compare a fractional-order tuning approach including the partial compensation of non-minimum phase zeros with a classical H∞ loop-shaping design, since both these designs lead to a relatively high controller order. First of all a detailed physical model is derived and validated using measurement data. Based on the line arized model both controllers are designed to be comparable, i.e. they show a similar crossover frequency in the open loop and the final controller order is reduced to the same range for both designs. The major differences between both are the different methods how the feed-forward action is included. The loop-shaping approach with fractional-order elements relies on the plant inverse using a fat output, whereas the H∞ design incorporates a two-degree of freedom control, i.e. the reference signal is included into the known inputs of the generalized plant. Each controller is tested in simulation and experiment. As both open-loops are nearly identical in the frequency range of interest, the results from an input disturbance experiment show no major difference. The different design approaches of the feed forward path are clearly visible in the tracking experiment.

A Frequency-Domain Tuning Method for a Class of Reset Control Systems

Constant in gain Lead in phase (CgLp) compensators, which are a type of reset elements, have shown high potential to overcome limitations of linear control systems. There are few works which investigate the tuning of these compensators. However, there are some significant drawbacks which make those methods unreliable. First, their analyses are performed in the open-loop configuration which do not guarantee the existence of steady-state response of the closed-loop. If it is guaranteed, unlike linear control systems, open-loop analyses cannot precisely predict the closed-loop steady-state performance. In addition, the stability condition could not be assessed during the tuning process. These significant challenges have been separately solved in our recent works by proposing frequency-domain frameworks for analyzing the closed-loop performance and stability of reset control systems. However, they are not formulated and implemented for tuning CgLp compensators. In this paper, based on the loop-shaping approach, the recent frequency-domain framework and the frequency-domain stability method are utilized to provide a reliable frequency-domain tuning method for CgLp compensators. Finally, different performance metrics of a CgLp compensator, tuned by the proposed method, are compared with those of a PID controller on a precision positioning stage. The results show that this method is effective, and the tuned CgLp can achieve more favorable dynamic performance than the PID controller.

Hybrid vibration control of offshore wind turbines under multiple external excitations

Structural control methods are a promising way to improve the dynamic response of offshore wind turbines. In this study, the effectiveness of passive tuned mass damper (TMD) and hybrid mass damper (HMD) control is examined for suppressing the vibration in a monopile offshore wind turbine subjected to a combination of wind, wave, and seismic loads. A high-fidelity wind turbine model is established based on the multi-body dynamics simulation code SIMPACK. A reduced-order model of the wind turbine is, then, extracted from input-output time-domain response data, which is used to design an HMD controller using the H∞ loop shaping approach. The controller is, then, applied in the high-fidelity multi-body model of the wind turbine, and an additional control force is applied using feedback from the displacement acceleration at the tower top. The performance of the passive TMD and HMD control systems is examined and compared in terms of the suppression of tower-top displacements under normal operating and parked conditions. The results revealed that the HMD control system can better reduce the tower-top displacement as compared to the passive TMD system before and during earthquakes, albeit at the expense of high input control power and large TMD displacements. However, the two control systems have a negative impact on the dynamic response of tower after the earthquake. Moreover, the investigation of controller gains indicated that the vibration suppression effect of HMD improves with the increase in control power, leading to larger TMD strokes.

Implementation of LPV H∞ Loop-Shaping Control for a Variable Stiffness Actuator

Compliant actuators have been increasingly used for active joints in lower-limb exoskeletons or orthoses because they help to guarantee a safe human interaction. One example of such compliant motors is the variable stiffness actuator (VSA). The design of a torque controller for such an actuator is a crucial task in order to provide patients with physical gait assistance and overcome the mechanical limitations of the VSA. Our goal is to implement a torque controller for our mechanical-rotary variable impedance actuator (MeRIA) used in future lower-limb exoskeletons. In the torque control design, we derive a gain-scheduled controller for the polytopic linear parameter-varying (LPV) model of the actuator. This controller is based on the classical H∞ loop-shaping approach. Measurements on the hardware-in-the-loop system in time and frequency domain show that the designed controller provides adequate performance over the whole varying stiffness range. Additionally, the controller provides H∞ robustness with respect to coprime factor uncertainty for the polytopic system. Thus, the torque controller fulfills major safety requirements, and can further be used for human-in-the-loop tests and applications with a lower-limb exoskeleton.

Modeling and Temperature Control of Retinal Laser Therapy

The development of a noninvasive technique to measure tissue temperature during retinal laser treatment allows feedback control approaches to regulate the temperature rise to desired values. The main challenge is to provide fast and consistent good control performance regardless the uncertainty of the dynamics of the temperature increase at the different irradiated spots on the retina, which is due to the large variance of the retinal light absorption. In this paper, we demonstrate a successful experimental application in ex-vivo of robust H∞ PID control to handle such a control problem. The system input is the applied laser power and its output is the temperature increase. Based on measurements of input-output data, we employ system identification to model the range of the system dynamics at different retinal irradiation sites. Then, we use a loop shaping approach to express the performance specifications of the closed-loop system and we synthesize accordingly the controller using efficient robust H∞ synthesis tools for fixed structure controllers. The experimental implementation of the closed-loop system for tracking different reference temperatures demonstrates the achievement of the control objectives consistently at the different irradiation sites.

Improving Wafer Stage Performance With Multiple Hybrid Integrator-Gain Systems

An experimental demonstration is given of a nonlinear feedback controller applied to a short-stroke wafer stage system of an industrial wafer scanner. The controller design adopts a classical linear PID-based configuration in which both the integrator and low-pass filter are replaced with hybrid integrator-gain-based filter elements. The reduced phase lag associated with these filters gives rise to increased design flexibility, and potentially enables a substantial increase in low-frequency disturbance suppression. The nonlinear controller is designed by means of a quasi-linear loop-shaping approach, while stability of the full nonlinear closed-loop system is verified by solving a set of linear matrix inequalities. Performance of the controlled system is discussed on the basis of measurement results obtained from a wafer stage system.

LFT-Structured Uncertainty State-Space Modeling for State Feedback Robust Control of the Ultra-Precision Wafer Stage

This paper presents linear-fractional-trans-formation (LFT)-structured uncertainty state-space modeling for robust control of the multiple-input multiple-output (MIMO) ultra-precision wafer stage with flexible structures to meet the challenges of vibration-dependent model uncertainties. Specifically, based on the modal MIMO state-space model, a parametric uncertainty model related with flexible modes is presented, and the uncertainty parameters are structured to a diagonal matrix with the LFT method. Meanwhile, a multiplicative uncertainty model is employed to express the uncertainty in high frequency with respect to ignored high-order modes. Thus, the final uncertainty model is structured with uncertainty parameters and high-frequency uncertainty. Based on the proposed uncertainty model, a comprehensive robust control scheme is proposed. Specifically, the weighting function matrixes are designed by the loop-shaping approach, and a $\mu$ analysis is employed to achieve a nonconservative solution with respect to the structured uncertainty. A standard stability criterion of a $\bf{M} \boldsymbol{\Delta}$ structure system is then utilized to determine the system stability by the largest structure singular value. Comparative experiments on a developed ultra-precision wafer stage are finally conducted, and the results validate that the proposed method achieves significant improvements on control performance, robustness, and robust stability in all exposure fields.

Robust H∞ loop-shaping controller design for temperature and air flows control of a passive nonlinear air conditioning unit

This paper designs a controller of a passive nonlinear air-conditioning unit based on a loop-shaping approach, with respect of the environmental conditions for micro-climate in growth chambers and greenhouses. The control problem consists in mixing two prescribed air flows and tracking the mixed output set point temperature. Simulations were carried out on the closed-loop formed by connecting the controller to the nonlinear original system. The synthesized controller based on the H∞ loop-shaping technique provides robust stability and performance. Using the v-gap metric, the controller was shown to stabilize a large class of systems with uncertainties in power heating coefficients.

A Fast Piezo Actuated Tip/Tilt Mirror for raster scan applications

This paper presents the system and control design of a novel high performance piezo-actuated fast steering mirror (FSM) for high speed optical scanning which is centered around an easy-to-manufacture membrane-like mechanical flexure and uses an optical sensor system for position measurement. With the membrane flexure the first fundamental resonance mode of the actuator is placed as high as 6.7 kHz, while still enabling an optical angular range of ±4.8 mrad. Using a PI controller together with three notch filters designed in a loop shaping approach for maximizing the system bandwidth and tracking of high resolution raster trajectories, a closed-loop bandwidth as high as 2.7 kHz and a positioning uncertainty of 3.8 µrad rms is obtained. The obtained tracking error when tracking a 250 Hz raster scanning trajectory with a scan amplitude of 2.2 mrad is as small as 73.8 µrad rms (3.6% of scan amplitude).

Multivariable modeling and nonlinear coordination control of nuclear reactor cores with/without xenon oscillation using H∞ loop shaping approach

This investigation is to achieve multivariable modeling for a pressurized water reactor core with/without iodine-xenon dynamics and design nonlinear core multivariable coordination control systems with stability analyses for simultaneous regulations of the core power and axial power difference during load following/transient load maneuvers. A two-point based multivariable model for this nonlinear core with iodine-xenon and that for the core without iodine-xenon are respectively built adopting the power regulating rod and the axial offset regulating rod as inputs and ignoring boron, and are then linearized. The H∞ loop shaping control with robustness is utilized to contrive a coordination controller of each linearized model and this controller is applied to the nonlinear model corresponding to the linear model. The nonlinear model with iodine-xenon and its coordination controller construct the nonlinear core load following coordination control system, and the nonlinear model without iodine-xenon and its coordination controller structure the nonlinear core transient load coordination control system. One stability theorem is deduced to analysis stability of the two nonlinear control systems. Eventually, the two nonlinear coordination control systems are simulated. Simulations show that the systems possess the desired decoupling control ability for coordination regulations of multi-parameter and good dynamic performance, and are effective.

Robust H∞ switching MIMO control for a plasma time-varying parameter model with a variable structure in a tokamak

The paper deals with design and simulation of hierarchical multi-loops feedback magnetic plasma control system on the base of experimental data for the operating Globus-M spherical tokamak in line with the special methodology developed. The components of the system are designed to achieve high-performance operation during short pulses of plasma discharges about 200 ms. The plasma equilibrium reconstruction algorithm with regularization in terms of moving filaments without iterations was developed. The LPV plant model was derived from reconstructed plasma equilibriums as a distributed parameter system with time-varying parameters. A switching plasma shape multivariable controller was designed by the H∞ robust loop-shaping approach for magnetic field at X-point and poloidal fluxes on plasma separatrix (isoflux control). The novelty of the plasma shape control system is the application of robust switching control with a controller state vector matching. The feedback control was applied to the whole discharge with the transition from a limiter phase to a diverter phase when the plasma changed its magnetic topology as a controlled structure.

Robust consensus of linear systems on directed graph with non‐uniform delay

The authors propose a consensus control framework for multiple heterogeneous general single-input single-output linear systems with no zeros at s = 0 on a directed information graph with constant, yet, non-uniform and unknown delays. The proposed consensus control is easy to design via loop-shaping like graphical approach, robust against plant uncertainty and constant delay, and completely decentralisable (i.e. locally synthesisable without consulting other agents). Consensus proof using multi-input multi-output Nyquist theorem and algebraic graph theory is given, with a numerical example to illustrate the theory.

An H&lt;sub&gt;∞&lt;/sub&gt; Design Approach for the Heading Hold Autopilot of a Flying Wing UAV

The paper presents a modified loop shaping approach for the design of the automatic flight control system of an unmanned air vehicle’s lateral-directional dynamics. The design objectives include robust stabilization with respect to modeling uncertainties, heading angle tracking of an ideal model, coordinated turn and reduced sensitivity with respect to low frequency measurement errors. Based on the resulting full order controller one determined a reduced order controller. The numerical results show that both the full order and the reduced order autopilots accomplish the design objectives.

Fixed structure [formula omitted] loop shaping control of switched reluctance motor for electrical vehicle

This paper presents a new control design based on fixed order H∞ loop shaping approach for switched reluctance motor (SRM) drive in electrical vehicle. H∞ control is a powerful technique to design robust controllers for systems with uncertainties and disturbances. However, controllers designed by this technique are complex, with a high order, so it is difficult to implement them on electric vehicles. The purpose of this paper is to overcome this drawback by applying a technique based on fixed structure H∞ loop shaping control for SRM drive. To show the performance of this control approach, a robustness analysis is performed by comparing fixed structure and conventional H∞ loop shaping controllers using the concept of the singular structured value, i.e. the μ-analysis. The main interest of this approach is highlighted by simulation and experiment results.

Robust Sliding-Mode Control Design for a Voltage Regulated Quadratic Boost Converter

A robust controller design to obtain output voltage regulation in a quadratic boost converter with high dc gain is discussed in this paper. The proposed controller has an inner loop based on sliding-mode control whose sliding surface is defined for the input inductor current. The current reference value of the sliding surface is modified by a proportional-integral compensator in an outer loop that operates over the output voltage error. The stability of the two-loop controller is proved by using the Routh-Hurwitz criterion, which determines a region in the K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> -K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> plane, where the closed-loop system is always stable. The analysis of the sliding-mode-based control loop is performed by means of the equivalent control method, while the outer loop compensator is derived by means of the Nyquist-based Robust Loop Shaping approach with the M-constrained Integral Gain Maximization technique. Robustness is analyzed in depth taking into account the parameter variation related with the operation of the converter in different equilibrium points. Simulations and experimental results are presented to validate the approach for a 20-100-W quadratic boost converter stepping-up a low dc voltage (15-25-V dc) to a 400-V dc level.

Modelling for robust feedback control of fluid flows

This paper addresses the problem of designing low-order and linear robust feedback controllers that providea prioriguarantees with respect to stability and performance when applied to a fluid flow. This is challenging, since whilst many flows are governed by a set of nonlinear, partial differential–algebraic equations (the Navier–Stokes equations), the majority of established control system design assumes models of much greater simplicity, in that they are: firstly, linear; secondly, described by ordinary differential equations (ODEs); and thirdly, finite-dimensional. With this in mind, we present a set of techniques that enables the disparity between such models and the underlying flow system to be quantified in a fashion that informs the subsequent design of feedback flow controllers, specifically those based on the$\mathscr{H}_{\infty }$loop-shaping approach. Highlights include the application of a model refinement technique as a means of obtaining low-order models with an associated bound that quantifies the closed-loop degradation incurred by using such finite-dimensional approximations of the underlying flow. In addition, we demonstrate how the influence of the nonlinearity of the flow can be attenuated by a linear feedback controller that employs high loop gain over a select frequency range, and offer an explanation for this in terms of Landahl’s theory of sheared turbulence. To illustrate the application of these techniques, an$\mathscr{H}_{\infty }$loop-shaping controller is designed and applied to the problem of reducing perturbation wall shear stress in plane channel flow. Direct numerical simulation (DNS) results demonstrate robust attenuation of the perturbation shear stresses across a wide range of Reynolds numbers with a single linear controller.