Youla Parameterization Research Articles

Robustified GPC controller based on H ∞ robust control for an hydraulic actuator

This paper proposes the robustification method of primary generalized predictive control GPC for a hydraulic actuator, which is previously modeled by an uncertain plant. Three-step procedures should be followed for robustification: First, the primary GPC controller based on nominal plant is designed to ensure a better tracking dynamic of the closed-loop system. Second, the Q-parameter transfer function is determined from solving the weighted-mixed sensitivity problem using the two Riccati equations where the uncertainty plant and neglected dynamics are taken into account. Finally, the Youla parameterization combines the primary GPC controller and Q-parameter to design the robustified GPC controller which enhances the trade-off robustness of primary GPC controller without changing its better tracking dynamic. To validate the effectiveness of the proposed robustification, the hydraulic actuator, which presents a realistic process, is controlled by both primary and robustified GPC controllers where their simulation results are compared in time and frequency domains by those given by the H∞ controller.

A variable selection aided residual generator design approach for process control and monitoring

This paper investigates the design of residual generator based on data-driven techniques, which is optimized by variable selection and can be applied to control and monitoring in industrial process to satisfy the high performance requirements of systems. The basic idea is designing the residual generator based on the foundation of the Luenberger equations as well as the relationship between diagnosis observer (DO) and the parity vector. The crucial and innovative part of the scheme is to acquire the parity space by the Subspace Identification Method (SIM) and obtain the simplified and optimized data from a new variable selection system according to partial least squares (PLS) method during the procedure of SIM. The design and optimization of the residual generator make it independent of model and effective to deal with big data, and avoid the challenges of handling bulk data. After the realization of the Youla parameterization, the proposed approach of residual generator can not only be applied to control purposes, but also monitoring objective of practical industrial systems. A numerical example is used to demonstrate the performance and effectiveness of the proposed scheme.

Data‐driven design of two‐degree‐of‐freedom controllers using reinforcement learning techniques

Motivated by the successful application for feedback control, this study extends the study of reinforcement learning techniques to the design of two-degree-of-freedom controllers in the data-driven environment. Based on the residual generator based form of Youla parameterisation, all stabilising controllers are first interpreted in the feedback–feedforward situation with a Kalman filter-based residual generator acting as the core part. For the reference tracking problem, further discussions are conducted from the regulatory perspective and using the Q learning, recursive least squares methods and the policy iteration algorithm. The entire design is carried out as a two-stage process that separately achieves the optimal feedback and feedforward controllers. Finally, the effectiveness of the proposed approach is demonstrated with its application in the laboratory continuous stirred tank heater process.

Improved Robustness of Generalized Predictive Control for Uncertain Systems

Abstract An off-line methodology has been developed to improve the robustness of an initial generalized predictive control (GPC) through convex optimization of the Youla parameter. However, this method is restricted with the case of the systems affected only by unstructured uncertainties. This paper proposes an extension of this method to the systems subjected to both unstructured and polytopic uncertainties. The basic idea consists in adding supplementary constraints to the optimization problem which validates the Lipatov stability condition at each vertex of the polytope. These polytopic uncertainties impose a non convex quadratically constrained quadratic programming (QCQP) problem. Based on semidefinite programming (SDP), this problem is relaxed and solved. Therefore, the robustification provides stability robustness towards unstructured uncertainties for the nominal system, while guaranteeing stability properties over a specified polytopic domain of uncertainties. Finally, we present a numerical example to demonstrate the proposed method.

Generalized internal model robust control for active front steering intervention

Because of the tire nonlinearity and vehicle’s parameters’ uncertainties, robust control methods based on the worst cases, such as H ∞, µ synthesis, have been widely used in active front steering control, however, in order to guarantee the stability of active front steering system (AFS) controller, the robust control is at the cost of performance so that the robust controller is a little conservative and has low performance for AFS control. In this paper, a generalized internal model robust control (GIMC) that can overcome the contradiction between performance and stability is used in the AFS control. In GIMC, the Youla parameterization is used in an improved way. And GIMC controller includes two sections: a high performance controller designed for the nominal vehicle model and a robust controller compensating the vehicle parameters’ uncertainties and some external disturbances. Simulations of double lane change (DLC) maneuver and that of braking on split-µ road are conducted to compare the performance and stability of the GIMC control, the nominal performance PID controller and the H ∞ controller. Simulation results show that the high nominal performance PID controller will be unstable under some extreme situations because of large vehicle’s parameters variations, H ∞ controller is conservative so that the performance is a little low, and only the GIMC controller overcomes the contradiction between performance and robustness, which can both ensure the stability of the AFS controller and guarantee the high performance of the AFS controller. Therefore, the GIMC method proposed for AFS can overcome some disadvantages of control methods used by current AFS system, that is, can solve the instability of PID or LQP control methods and the low performance of the standard H ∞ controller.

Blending for H∞ performance: a group theoretic approach

In order to design efficient algorithms that work on the set of controllers that fulfill a given property, e.g., stability or a norm bound, it is important to have an operation that preserves that property, i.e., a suitable blending method. Concerning stability, a traditional approach is to use the Youla parametrization and the corresponding parameters as a starting point. While this method guarantees stabilizability as the invariant property for the fairly large class of strictly proper plants, there are also other solutions to the problem. The authors already provide a detailed analysis for feedback stability placing the controller blending problem in a general setting by pointing to the basic global geometric structures that are related to well-posedness and feedback stability. In this paper these efforts are continued and the group structure corresponding to performance problems, e.g., those related to a suboptimal H∞ design, is presented. Besides its educative value the presentation provides a possible tool for the algorithmic development.

Off-line robustification of Generalized Predictive Control for uncertain systems

Abstract An off-line methodology was proposed for enhancing the robustness of an initial Generalized Predictive Control (GPC) by convex optimization of the Youla parameter. However, this procedure of robustification is restricted with the case of the systems affected only by unstructured uncertainties. This paper proposes an extension of this method to the systems subjected to both unstructured and structured polytopic uncertainties. The main idea consists in adding supplementary constraints to the optimization problem which validates the Lipatov stability condition at each vertex of the polytope. These polytopic uncertainties impose a set of non convex quadratic constraints. The globally optimal solution is found by means of the GloptiPoly3 software. Therefore, this robustification provides stability robustness towards unstructured uncertainties for the nominal system, while guaranteeing stability properties over a specified polytopic domain of uncertainties. Finally, an illustrative example is given

Data-Driven Design and Optimization of Feedback Control Systems for Industrial Applications

In this paper, regarding the observer form of the well-known Youla parameterization, the controller design and optimization are exhibited with an integrated residual access. To better reveal this philosophy, the feedback control loop is interpreted on the basis of the observer-based residual generator. The next main attention is drawn to the generation of residuals, the design of a deadbeat controller for system stabilization both in the data-driven environment, and later the optimal adaptive realization of a dynamic system that translates residuals into compensatory control inputs to meet certain performance specifications. Towards these goals, numerical algorithms are summarized, and for the issues of controller optimization, the reinforcement learning algorithm is introduced using only measured input-output and residual signals. In addition, the effectiveness of developed schemes for industrial applications is also illustrated by experimental studies on a laboratory continuous stirred tank heater (CSTH) process.

Stable controller design for mixed sensitivity reduction of infinite-dimensional systems

In this paper we study the design of stable controllers for mixed sensitivity reduction for systems that have input/output delays and infinitely many unstable zeros. The proposed method is based on interpolation with a unit in H∞, which gives a necessary and sufficient condition for stabilization by stable controllers. Using the Youla parameterization, we introduce a two-block problem for the stable H∞ controller design. The two-block problem is then transformed to a one-block problem solvable by the skew Toeplitz approach.

Youla Parameterization Robust Control Strategy Considering Power System Uncertainties

In view of the reduced low-frequency oscillation damping effect caused by inaccurate modeling of the power system due to various uncertainties, a Youla parameterization robust control strategy considering system uncertainties is proposed in this article. First, the uncertainties of the measurement error and parameter estimation are described by the perturbation matrix, and the convex polytopic model is utilized to describe uncertainties caused by variation of the operating point. Then, by solving the H2/H∞ inequalities, the Youla parameterization matrix is gained. Finally, the output error of the actual system to the nominal system is introduced to the output feedback control link via the Youla parameterization matrix. Thus, tracking control of the output error can be realized, as well as H2/H∞ robust control of the system. Simulation results show that the proposed method is immune to internal and external uncertainties. Compared with control methods without considering uncertainties, the proposed method is capable of damping low-frequency oscillation faster and more effectively with better robust performance.

Orthonormal basis functions applied to optimal control design with closed-loop pole location constraints

This article proposes an optimal control design technique to ensure that the closed-loop poles are assigned to prescribed locations in the complex plane. A key element in this approach is the usage of orthonormal basis functions to parametrise the main design parameter. This goal is achieved by using a quadratic cost based optimisation approach, considering control effort penalisation as well as cheap control. Youla parametrisation is used, subject to a set of constraints which guarantee stability, zero steady error to constant references and disturbances, and yielding the prescribed set of closed-loop poles.

Application of Dual Youla Parameterization Based Adaptive Wide-Area Damping Control for Power System Oscillations

An adaptive damping control scheme based on the dual Youla parameterization is proposed in this paper for inter-area low frequency oscillations. First, a set of observer-based feedback controllers are pre-designed using ${\rm H}_{2} /{\rm H}_{\infty}$ robust control method for a set of nominal operating conditions. Second, the power system and controllers are parameterized using Youla method, respectively. Finally, online measurements are utilized to identify the changing dynamics and adjust the parameterized controllers to adapt to changing operating conditions through the updated Youla parameters. A 127-bus equivalent of the Western Electricity Coordinating Council (WECC) system with three additional controllers of energy storage system is employed as a test system. The results of frequency domain and time domain of different contingences demonstrate the effectiveness and robustness of the Youla based adaptive control scheme.

On the control of a single flexible arm robot via Youla-Kucera parameterization

SUMMARYIn this paper, based on the Youla-Kucera (Y-K) parameterization, the control of a flexible beam acting as a flexible robotic manipulator is investigated. The method of Youla parameterization is the simple solution and proper method for describing the collection of all controllers that stabilize the closed-loop system. This collection comprises function of the Youla parameter which can be any proper transfer function that is stable. The main challenge in this approach is to obtain a Youla parameter with infinite dimension. This parameter is approximated by a subspace with finite dimensions, which makes the problem tractable. It is required to be generated from a finite number of bases within that space and the considered system can be approximated by an expansion of the orthonormal bases such as FIR, Laguerre, Kautz and generalized bases. To calculate the coefficients for each basis, it is necessary to define the problem in the form of an optimization problem that is solved by optimization techniques. The Linear Quadratic Regulator (LQR) optimization tool is employed in order to optimize the controller gains. The main aim in controller design is to merge the closed-loop system and the second order system with the desirable time response characteristic. The results of the Youla stabilizing controller for a planar flexible manipulator with lumped tip mass indicate that the proposed method is very efficient and robust for the time-continuous instances.

Robust generalized predictive control of the Orthoglide robot

Purpose – The purpose of this paper is to address the synthesis and experimental application of a generalized predictive control (GPC) technique on an Orthoglide robot. Design/methodology/approach – The control strategy is composed of two control loops. The inner loop aims at linearizing the nonlinear robot dynamics using feedback linearization. The outer loop tracks the desired trajectory based on GPC strategy, which is robustified against measurement noise and neglected dynamics using Youla parameterization. Findings – The experimental results show the benefits of the robustified predictive control strategy on the dynamical performance of the Orthoglide robot in terms of tracking accuracy, disturbance rejection, attenuation of noise acting on the control signal and parameter variation without increasing the computational complexity. Originality/value – The paper shows the implementation of the robustified predictive control strategy in real time with low computational complexity on the Orthoglide robot.

Constrained doubly coprime factorization for all stabilizing ℋ∞ controllers

The conventional Youla parameterization (equivalently Q-Parameterization) approach to solve ℋ∞ optimal control problems requires solving the well-known matrix dilation optimization as a method for satisfying the ℋ∞-norm constraint of the closed-loop transfer matrix. As an alternative, this paper presents a constrained doubly coprime factorization so that the ℋ∞-norm constraint of the closed-loop transfer matrix can be satisfied without the need for matrix dilation optimization. For a given ℋ∞-norm constraint, a constrained plant is suggested from a state estimator that includes the worst-case disturbance and estimation effects. Then, the constrained doubly coprime factorization is derived from the constrained plant model. All the stabilizing ℋ∞ controllers are expressed by using the constrained coprime factors. Finally, an application example is provided to demonstrate the effectiveness of the proposed method.

Real-Time Implementation of Fault-Tolerant Control Systems With Performance Optimization

In this paper, two online schemes for an integrated design of fault-tolerant control (FTC) systems with application to Tennessee Eastman (TE) benchmark are proposed. Based on the data-driven design of the proposed fault-tolerant architecture whose core is an observer/residual generator based realization of the Youla parameterization of all stabilization controllers, FTC is achieved by an adaptive residual generator for the online identification of the fault diagnosis relevant vectors, and an iterative optimization method for system performance enhancement. The performance and effectiveness of the proposed schemes are demonstrated through the TE benchmark model.

An Observer-Based PID Regulator

An equivalent transfer function representation ( TFR ) is used to study the state-feedback/observer ( SFO ) topologies of control systems. This approach is applied to combine this methodology with Youla-parametrization ( YP ) introducing new classes of regulators. Then this method is used to introduce observer based PID regulators.

Fault‐tolerant control of linear multivariable controllers using iterative feedback tuning

SummaryThis paper introduces the iterative feedback tuning (IFT) into a Youla parameterization scheme for fault‐tolerant control. By off‐line IFT‐experiments of tuning Youla parameters, the proposed algorithm deals with a number of conditional failures that are described by the dual Youla parameter. The main contribution of this paper is to show how Youla scheme‐based IFT can be constructed for multivariable linear time‐invariant systems. Particular attention is given to the issue of the structure of the Youla parameter (filter), in which both finite impulse response and infinite impulse response filters are presented and compared. As an illustration, the method is applied to a simulation model of a continuous stirred tank heater system. Copyright © 2014 John Wiley & Sons, Ltd.

Disturbance attenuation over a first-order moving average Gaussian noise channel

In this paper, the problem of disturbance attenuation has been studied for a linear time-invariant feedback control system with a first-order moving average Gaussian noise channel. By applying the concept of entropy power, a lower bound of signal-to-noise ratio has been achieved which is necessary for stabilisation of a system with the limited channel input power constraint. Moreover, the problem of minimising the influence of a stochastic disturbance on the output has also been investigated, and the controller design method has been obtained by using Youla parameterisation and H2 theory. It is shown that the minimum variance of the system output depends not only on the disturbance variance, noise variance and unstable poles, but also on the non-minimum phase zeros and channel parameter. Finally, the effectiveness of the proposed results is illustrated by a numerical example.

Attenuation of the Model Error in Observer-Based State-Feedback Regulators

An equivalent transfer function representation (TFR) is introduced to study the state-feedback/observer (SFO) topologies of control systems. This approach is used to explain why an observer can radically reduce even large model errors. Then the same principle is combined with Youla-parametrization (YP) introducing a new class of regulators.