Youla Parameterization Research Articles

On-line and real-time controller tuning architecture based on Youla–Kucera controller parameterization

This paper presents an on-line and real-time controller tuning architecture based on Youla–Kucera controller parameterization. First, a coarse controller is designed to satisfy nominal performance of closed-loop system. Second, Youla parameter is used to construct an on-line and real-time fine tuning mechanism including a group of controller candidates under arbitrary switching strategy. The mechanism can adjust the control performance on-line to achieve the balance between dynamic and steady-state performance without resulting in any closed-loop stability problems.

Closed-loop identification of stabilized models using dual input–output parameterization

This paper introduces a dual input–output parameterization (dual IOP) for the identification of linear time-invariant systems from closed-loop data. It draws inspiration from the recent input–output parameterization developed to synthesize a stabilizing controller. The controller is parameterized in terms of closed-loop transfer functions, from the external disturbances to the input and output of the system, constrained to lie in a given subspace. Analogously, the dual IOP method parameterizes the unknown plant with analogous closed-loop transfer functions, also referred to as dual parameters. In this case, these closed-loop transfer functions are constrained to lie in an affine subspace guaranteeing that the identified plant is stabilized by the known controller. Compared with existing closed-loop identification techniques guaranteeing closed-loop stability, such as the dual Youla parameterization, the dual IOP requires neither a doubly-coprime factorization of the controller nor a nominal plant that is stabilized by the controller. The dual IOP does not depend on the order and the state-space realization of the controller either, as in the dual system-level parameterization. Simulation shows that the dual IOP outperforms the existing benchmark methods.

Youla Parameterized Adaptive Hybrid Control for Active Vibration Control Platform

Abstract To increase the vibration attenuation of the damped platforms, an adaptive hybrid vibration control algorithm based on Youla (Q) parameterization is proposed, where the vehicle suspension platform is considered as an application example. First, an inner controller is designed to keep the hybrid control system stable. Then, the controller is extended to the Youla parameterized controller set. Finally, the Q-parameters are adjusted online by using a recursive least squares (RLS) adaptive algorithm to eliminate vibration disturbances. Simulation results demonstrate that the hybrid algorithm is capable of effectively suppressing the vibration signals.

A dynamic controller synthesis methodology for negative imaginary systems using the internal model control principle

This paper proposes a new controller design methodology for stable and minimum-phase Negative Imaginary (NI) systems relying on the classical Internal Model Control (IMC) principle. The closed-loop stability of the proposed scheme depends only on the DC loop gain, which is theoretically justified by the feedback stability results of the NI theory. The main objective is to design the Youla parameter of an IMC scheme, which has been cast as a Negative Imaginary (NI) controller synthesis problem. Two different methodologies have been proposed. A frequency-domain IMC design approach is first presented, which depends on solving a constrained, linear, least-square estimation problem. Then, an LMI-based methodology is developed, which can be solved by the commercially available SDP solver packages. An in-depth simulation case study on the vibration attenuation problem of a lightweight cantilever beam (a potential application of the NI theory) was carried out to demonstrate the usefulness of the NI-based IMC design methodology. Finally, the simulation results were experimentally validated on a custom-made vibration suppressor to confirm the feasibility of the proposed scheme.

Tracking Performance of Feedback Systems Over a Fading Channel With Limited Bandwidth.

In this study, we investigated the optimal tracking performance (OTP) of feedback control systems with limited bandwidth and colored noise in a fading channel. For the steady state of the feedback control systems, an equivalent average channel (EAC) model was developed by retaining the effects of the first and second moments of the multiplicative channel output, and on the basis of the coprime decomposition, all-pass factorization, and Youla parameterization of controllers, exact expressions for the OTP were derived by designing two compensators. The expressions quantitatively show the relationship between the OTP and inherent features of the plant. Specifically, the directions and locations of unstable poles (UPs) and nonminimum phase (NMP) zeros adversely affect the tracking performance. Furthermore, the bandwidth limitation and the presence of colored noise also degrade the tracking performance. Finally, our conclusions were verified by considering a numerical arithmetic example.

Observer‐based residual‐driven dynamic compensation strategy for performance improvement of grid‐forming inverter

SummaryGrid‐forming (GFM) inverters offer stable frequency support for microgrid systems, even in the absence of synchronous generators. However, the GFM inverters have low inertia and vulnerability to system uncertainties and external disturbances. The conventional dual‐loop proportional integral (PI) control strategy, while widely used for its simplicity and robustness, suffers from poor dynamic performance. Motivated by this, this paper presents an observer‐based residual‐driven dynamic compensation (RDDC) strategy based on the coprime factorization technic and the Youla parameterization theory to achieve the primary control of the GFM inverter. The observer‐based RDDC strategy comprises four components: a PI controller for tracking control, a linear quadratic regulator (LQR) controller for dynamic adjustment, a residual generator based on the Kalman filter for state estimation and residual generation, and a residual compensation controller designed using model matching theory and solved through linear matrix inequality (LMI) methods for disturbance suppression. Simulation and experiment results consistently demonstrate that the observer‐based RDDC strategy ensures system robustness, enhances the dynamic and steady‐state performance of the GFM inverter system, and strengthens the ability of the GFM inverter to suppress disturbances.

LQG/LTR based robust youla parameterized adaptive vibration control for the supporting platform of rotating liquid mirror

In mechatronic systems, the vibrations which commonly consist of band-limited random signals mixed with large multiple narrow-band deterministic signals may negatively impact the system performance. For example, due to the incomplete matching of the mechanism and the rotation of the motor, random and deterministic vibration disturbance may occur in the supporting platform of the rotating liquid mirror. In this paper, a robust Youla ( Q) parameterized adaptive regulation approach has been proposed to minimize such kind of vibration signals for the rotating platform system with model uncertainties. Firstly, the inner-loop robust controller with linear quadratic Gaussian with loop transfer recovery ( LQG/LTR) is optimally designed by choosing the suitable weighting functions to achieve the trade-off between robust stability and control performance to deal with random vibration signals. Then the Youla parameter is augmented to construct a set of Q-parameterized stabilizing controllers, and the robust stability of the system is analyzed through dual-Youla parameterization of the uncertain model. The recursive least squares (RLS) adaptive algorithm is developed to tune the Q parameter online to construct a desired adaptive controller for further residual vibration elimination. An experimental evaluation of the controller in reducing the vibration of the supporting platform of a rotating liquid mirror has been carried out, and the results illustrate that the proposed adaptive robust vibration regulation approach can effectively suppress the band-limited random and narrow-band deterministic vibration signals.

Achievable dynamic responses of general damped mass-chain systems

The problem of achievable dynamic responses of general damped mass-chain systems with controllers installed between the first two masses are investigated in this paper. Achievable dynamic response of a system is the sets of functions that system transfer functions can achieve with all linear time-invariant (LTI) stabilizing controllers. The problem arises in the disturbance control of damped multi-degree-of-freedom (MDOF) vibration systems, such as vehicle suspension systems subject to road and load disturbances and multi-storey building systems subject to seismic and wind disturbances. The sets of functions that system transfer functions can achieve with stabilizing controllers and different system measurements are obtained by the Youla parametrization. By analysing achievable functions of system transfer functions, necessary and sufficient conditions (or complete sets of constraints) of system transfer functions are derived. It can be shown that compared with our previous work on achievable dynamic responses of an undamped mass-chain system, the necessary and sufficient conditions of transfer functions of a damped mass-chain system distribute only in the low-frequency range and the high-frequency range. This work generalizes the results of achievable dynamic responses of two-degree-of-freedom (2-DOF) vibration systems into MDOF vibration systems. The results obtained in this work present the boundaries of the transfer functions of damped MDOF vibration systems, and determine frequency-domain constraints of system transfer functions regardless what stabilizing controllers are used.

Optimal tracking performance of network time‐delay systems with multiple constraints

AbstractThis paper investigates the optimal tracking performance based on the codec, colored noise, and bandwidth constraints in the network time‐delay systems. Choosing the optimal two‐degree‐of‐freedom compensator and the dominant expression of the system optimal tracking performance is obtained after Youla parameterization by using the coprime factorizations method and spectral decomposition technology. The result shows that the tracking performance of the system is determined by the nonminimum phase zero and unstable pole of the controlled plant. Moreover, codec, colored noise, and bandwidth constraints can also significantly impact the performance. Finally, two simulation examples prove the accuracy of the theory.

Tracking and Vibration Control with a Parallel Structure Controller Based on a Flexible Ball Screw Drive System

In this paper, we present a parallel structure controller for flexible ball screw drive systems with dynamic variations mainly caused by variations in table position and workpiece mass. The controller consists of two parts: a linear quadratic regulator (LQR) controller with the aim of tracking reference trajectories with high response and accuracy and an interpolated gain-scheduled controller used to restrain system vibration. To damp out the varied resonant modes, the controller is obtained by a set of μ-synthesis linear time-invariant (LTI) controllers interpolated via Youla parameterization. Comparison experiments are conducted to confirm the performance of the proposed controller with a ball screw drive experimental setup. We demonstrate that the parallel structure controller achieves high performance in tracking, vibration suppression and disturbance rejection.

Adaptive Robust Active Vibration Control for Vehicle Seat Suspension with Unknown Passenger Mass

The vibration of the car seat can affect the comfort of passengers and can even cause some health hazards to them. In this paper, a vehicle seat control system is built to reduce the hazards of vehicle seat vibration. Firstly, the dynamic of the vehicle seat suspension is modelled. Then, an adaptive robust vibration control method is introduced: a base controller with an enhanced Youla parameterization is designed to turn it into a global stable controller set, followed by online tuning of the Q-parameters using an adaptive algorithm. The results of the vehicle seat vibration control were simulated in MATLAB/Simulink.

Two-stage control algorithm for magnetic fluid deformation mirror with dual-layer actuators

To increase the correction effectiveness of full-order aberration, a control system based on a magnetic fluid flexible mirror with dual-layer actuators is presented. The combined magnetic field created by the Maxwell coil and the double-layer driving coils controls the geometry of the magnetic fluid surface. A model-based optical sensorless control approach for lower layer coils is developed and aimed to enable high magnitude restoration of lower-order aberrations. An adaptive important factor that causes on Youla parameterization, on the other hand, is developed for the upper coils to rectify higher-order residual aberrations. Matlab is used to simulate the algorithm in order to test its performance in full-order aberration correction, and the results reveal that the approach has good correction performance.

A convex optimization approach to multi-objective design of two-stage compensators for MIMO linear systems

The previous design of two-stage compensators with multi-objectives concerns the closed-loop stability, the low-sensitivity, and the satisfactory time-domain performance. However, the design only considers the single-input single-output system. This paper aims to present the design of two-stage compensators for multi-input multi-output (MIMO) linear systems which contain dynamical interaction between inputs and outputs. When Youla parameterization is applied to the MIMO linear system, the design criteria can be cast as a nonlinear optimization. In addition, the infinite dimension optimization problem is approximated to a finite dimension problem with Ritz approximation. The suitable form of design parameters is proposed to ensure the low sensitivity of the MIMO system. The two-stage compensator design is formulated as convex optimization which is efficiently solved using available solvers. Finally, the two-stage compensators are designed for Wood and Berry’s model of binary distillation column. The numerical results indicate that all design objectives of frequency domain and time domain can be achieved by the two-stage compensators.

Enhanced Observer-Based Repetitive Control for Tip-Tilt Disturbance Rejections Beyond Control Bandwidth in Optical-Stabilized Systems

The stabilization and tracking performance of an image-based tip-tilt system is usually deteriorated by tip-tilt vibrations and beam jitter in optical links due to a limited tip-tilt correction bandwidth. This paper proposes an enhanced observer-based repetitive control (OBRC) method to break the bandwidth limitation of the time delay tip-tilt stabilized loop, which achieves high-frequency disturbance rejections beyond control bandwidth even up to Nyquist frequency. The enhanced repetitive controller is fused with the optimized observer based on Youla parameterization, which improves the stability of the closed-loop and reduces the waterbed effect in non-repetitive frequency. Furthermore, the time delay of the closed-loop system could be compensated by the OBRC. Therefore, disturbance suppressions can be transformed into the design of a repetitive controller, which is effective and easy to be used for tip-tilt vibrations and beam jitter suppression. Finally, simulation and experimental results show that the OBRC effectively suppresses the high-frequency disturbance beyond the control bandwidth of the optical-stabilized system.

Learning Over All Stabilizing Nonlinear Controllers for a Partially-Observed Linear System

This letter proposes a nonlinear policy architecture for control of partially-observed linear dynamical systems providing built-in closed-loop stability guarantees. The policy is based on a nonlinear version of the Youla parameterization, and augments a known stabilizing linear controller with a nonlinear operator from a recently developed class of dynamic neural network models called the recurrent equilibrium network (REN). We prove that RENs are universal approximators of contracting and Lipschitz nonlinear systems, and subsequently show that the proposed Youla-REN architecture is a universal approximator of stabilizing nonlinear controllers. The REN architecture simplifies learning since unconstrained optimization can be applied, and we consider both a model-based case where exact gradients are available and reinforcement learning using random search with zeroth-order oracles. In simulation examples our method converges faster to better controllers and is more scalable than existing methods, while guaranteeing stability during learning transients.

Enhanced Observer Control of a Cubic Stewart Platform With Image Sensor Measurement

A cubic Stewart platform with an image sensor meausring is proposed for a line-of-sight (LOS) pointing and stabilization. The charge couple device (CCD) as a image sensor mounted on the Stewart platform can provide the LOS error only in the azimuth and elevation directions, so a decoupled control strategy through the transformation of the Jacobian matrix is introduced to transform a Multiple-Input Multiple-Output (MIMO) control into Single-Input Single-Output (SISO) control. Due to the low bandwidth of the Stewart platform and the finite sampling rate of the CCD, the closed-loop performance is greatly restricted. An optimal observer control based on Youla parameterization is proposed to improve the tracking performance in the CCD-based Stewart platform control system. This improved controller relies on the LOS error combined with the controller output to produce high gain, plugging into the tradditional closed-loop structure, which results in minimizing the error attenuation function by designing an appropriate Q-filter. Both the simulations and experiments are carried out to prove the effectiveness of the proposed observer compared with the classical feedback controller.

Tracking performance for NCSs with multi-communication constraints

In this paper, the tracking performance of multiple input multiple output (MIMO) networked control systems (NCSs) with multiple communication constraints is studied. The effects of network induced factors (packet loss and network delay) and basic communication constraints (bandwidth, encoding–decoding and different noise) are considered. By inner–outer factorization and Youla parameterization, the mathematical expressions of the performance of the one-degree of freedom (1DOF) controller and two-degree of freedom (2DOF) controller are obtained, respectively. It shows that internal characteristics and network constraints have different effects on the tracking performance of the plant, and the performance of the 2DOF controller is better than that of the 1DOF controller. Finally, several simulation examples are provided to verify the influence of each constraint.

A novel feedback controller design with robust fault isolation ability

This paper proposes a novel feedback controller design scheme which can achieve fault isolation based on the control signal or its embedded signal, i.e., with the self-fault-isolation ability. First of all, according to the well-known Youla parameterization, a controller structure consisting of state and residual joint feedback is developed. Then, the residual feedback gain and observer gain are designed to make the cooperative structured residual feedback signal have fault isolation ability. Some free design parameters in the two gains are further utilized for robust self-fault-isolation. Moreover, the state feedback gain is designed, in the framework of switched system, to realize the self-fault-diagnosis and isolation, based on the control signal directly. The proposed control structure also has the advantage of cooperative fault tolerance. Finally, the simulation of HVAC (Heating, Ventilation and Air Conditioning) system, composed of four rooms in one story building scenario, is carried out to demonstrate the effectiveness and superiority of the proposed feedback controller design approach.

A Residual-Generator-Based Plug-and-Play Control Scheme Toward Enhancing Power Quality in AC Microgrids

In this article, an active power quality control scheme centered on an observer-based residual generator is proposed for power quality improvement in ac microgrids. The active power quality controller is realized by a plug-and-play (PnP) configuration and consists of three parts: the control of the power electronic converter, the flexible structure, and the optimization algorithm. By means of the observer-based realization of the Youla parameterization of a stabilizing controller, the active power quality controller with the PnP flexible structure is designed. The proposed active controller has the advantage of improving power quality without changing the structure or parameters of the original controller. The optimization of the controller is implemented by tuning the Youla parameterization system in the PnP flexible structure. Here, a gradient descent optimizing algorithm is applied to estimate the optimal tuning/control parameters online. Finally, extensive hardware-in-the-loop experiments and simulations are given to demonstrate the effectiveness of the proposed power quality controller.

Microgrid inverter control strategy based on augmented state feedback and dynamic feedforward compensation

In order to improve the rapidity and immunity of microgrid inverter response, an inverter control structure with augmented state feedback plus dynamic feedforward is designed. The control structure is based on the augmented state feedback, robust mutual mass decomposition and Youla parameterisation theory, which can get the augmented state feedback control parameters and feedforward control structure, and the specific expression of feedforward controller is obtained by model matching theory, after which the Current loop compensation structure is added by combining the inverter and controller structures. The load switching and three-phase unbalance experiments are designed by Matlab/Simulink. The results show that without changing the structural parameters of the original system, the new controller can quickly stabilise the voltage fluctuation within 20 ms, change the fluctuation from 15 V to 2 V, and reduce the unbalance degree from 4% to less than 1%, effectively improving the response speed and anti-interference performance of the whole system, The speed and robustness of the inverter are improved.