Youla-Kucera Parametrization Research Articles

Adaptive compound control of laser beam jitter in deep-space optical communication systems.

In deep-space optical communication systems, precise pointing and aiming of the laser beam is essential to ensure the stability of the laser link. In this paper, an adaptive compound control system based on adaptive feedforward and Proportional-Integral-Differentiation (PID) feedback is proposed. The feedforward controller is stabilized using Youla-Kucera (YK) parameterization. In the YK parameterized structure, the free parameter Q(z) consists of an adaptive filter. The proposed method constitutes an adaptive feedforward control algorithm through the adaptive filter Q(z). The problem of suppressing laser jitter is transformed into a problem of minimizing a sensitivity function containing the adaptive filter. The stability of the compound control system is ensured by configuring the individual parameters of the YK parameterized feedforward controller and the PID controller, and the adaptive regulation of the controller is realized on the premise of system stability. To verify the effectiveness of the compound control system, we established an experimental platform for laser beam stabilization control. We experimentally compare the effectiveness of the proposed control method with the classical method. The experimental results show that the method proposed in this paper can effectively suppress the complex laser beam jitter consisting of narrow-band sinusoidal and broad-band continuous vibrations.

High-frequency line-of-sight jitter rejection via an extended Youla-Kucera parameterization controller in segmented diffractive telescope—Theory and experiment

Line-of-sight jitter caused by mechanical vibrations and disturbances in the transmission medium seriously damages the imaging performance in telescope systems. This paper investigates the problem of high-frequency line-of-sight jitter rejection up to Nyquist frequency in bandwidth-limited control systems due to time delays. Although the piezoelectric ceramic-driven tip-tilt mirror has a wide bandwidth, Large time delays caused by the image sensor for high-quality imaging severely restrict the control system’s closed-loop bandwidth. The disturbance cannot be sufficiently rejected, especially outside the bandwidth. Based on the Small Gain Theorem, the gain factor and time-delay factor as an extra flexible budget in the Youla-Kucera (Y-K) parameterization are derived from decreasing the waterbed effect, improving the closed-loop system stability. Thus, this proposed Y-K method accommodates disturbance rejection frequency inside and outside control bandwidth, which can be extended to the Nyquist frequency. Simulation analyses and Experimental results have been effectively verified in the line-of-sight stabilization control of the segmented lightweight large-scaled diffractive telescope (SLLDT) system.

On Symmetric Gauss–Seidel ADMM Algorithm for H∞ Guaranteed Cost Control With Convex Parameterization

This article involves the innovative development of a symmetric Gauss–Seidel ADMM algorithm to solve the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}_{\infty }$ </tex-math></inline-formula> guaranteed cost control problem. In the presence of parametric uncertainties, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}_{\infty }$ </tex-math></inline-formula> guaranteed cost control problem generally leads to the large-scale optimization. This is due to the exponential growth of the number of the extreme systems involved with respect to the number of parametric uncertainties. In this work, through a variant of the Youla–Kucera parameterization, the stabilizing controllers are parameterized in a convex set; yielding the outcome that the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}_{\infty }$ </tex-math></inline-formula> guaranteed cost control problem is converted to a convex optimization problem. Based on an appropriate reformulation using the Schur complement, it then renders possible the use of the ADMM algorithm with symmetric Gauss–Seidel backward and forward sweeps. Significantly, this approach alleviates the often-times prohibitively heavy computational burden typical in many <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal H_{\infty }$ </tex-math></inline-formula> optimization problems while exhibiting good convergence guarantees, which is particularly essential for the related large-scale optimization procedures involved. With this approach, the desired robust stability is ensured, and the disturbance attenuation is maintained at the minimum level in the presence of parametric uncertainties. Rather importantly too, with the attained effectiveness, the methodology thus evidently possesses extensive applicability in various important controller synthesis problems, such as decentralized control, sparse control, and output feedback control problems.

Image and Kernel Representations for Variational Systems*

The Youla-Kucera parametrization, a method to parametrize all stabilizing controllers, is developed for linear and nonlinear systems based on their stable image and kernel representations. As a stepping stone of parametrizing nonlinear controllers for contraction, we investigate in this paper stable image and kernel representations for variational systems. In particular, we construct stable inner image (resp. co-inner kernel) representations having stable left (resp. right) inverses based on differential Riccati equations for contraction analysis.

Adaptive Damping Control Scheme for Wind Grid-Connected Power Systems With Virtual Inertia Control

With the large-scale wind power integration into the power system, the inertia and damping characteristics of the system have been weakened, which is not conducive to fulfill the grid-friendly operation of wind power. Aiming at this, an adaptive control scheme combining virtual inertia control (VIC) and supplementary damping controller (SDC) is proposed in this paper. Firstly, the mathematical model of wind grid-connected power system with VIC is established. Secondly, the polytopic linear parameter varying (LPV) system is built to describe the uncertainty of system operating points, and the gap metric-based nonlinear evaluation method is used for polytope vertex configuration. Next, Youla-Kucera parametrization are extended to polytopic LPV system to design an adaptive damping control, in which VIC and SDC are coordinated to provide damping and virtual inertia simultaneously. Finally, the proposed adaptive control scheme is compared with several existing control techniques to validate its effectiveness and advantages in suppressing system oscillation in the modified IEEE 39-bus system integrated with 2 wind turbines.

Line of sight control of an image-based tracking system using Youla–Kucera parameterization

For an optical tracking system, due to the limited sampling rate and time delays in the image-based tracking loop, control bandwidth is usually restricted. An optimized controller based on Youla–Kucera parameterization is proposed to improve both vibration rejection and target tracking performance. This optimized controller combined the position error signal and the control output to compensate for the original feedback loop. The performance in low frequency was enhanced using an optimized Q31-filter, although the close-loop bandwidth of the tip-tilt mirror was not improved. The stability and robustness of this control configuration were analyzed by gain margin and phase margin of the open-loop transfer function. Because of relying on a simple and low-frequency model of the tip-tilt mirror control system, this new controller did not lead to a compromise between vibration rejection and noise propagation in the loop. Simulations and experiments were used to testify to the effectiveness of the new controller.

Smooth Switching of Multi-LPV Control Systems Based on Youla-Kucera Parameterization

This paper presents a smooth switching between a set of Linear Parameter-Varying (LPV) controllers that have been designed separately. The switching control strategy is based on Youla-Kucera (YK) parameterization. A generalized interpolation scheme of various LPV controllers is shown and proved for the LPV-YK concept. Such kind of parameterization is beneficial to switch or interpolate between multiple controllers without adding any constraints to the design of the local controllers and the switching signals. The proposed method is applied to an Active Magnetic Bearing (AMB) system and compared to a switched LPV controller.

A Youla–Kucera formulation of the controller design from data problem

The Youla–Kucera parametrization is a fundamental result in system theory, very useful when designing model-based controllers. In this paper, this formulation is employed to solve the controller design from data problem, without requiring a process model. It is shown that, given a set of input–output data generated by the plant and a desired closed-loop reference model, it is possible to estimate an stable filter that parametrizes the controller that minimizes the norm between the closed-loop dynamics and the requested behavior. The employed parametrization gives more degrees of freedom in the controller design than previous works in literature, allowing to achieve more stringent closed-loop performances. The proposed design methodology does not imply a plant identification step and it provides an estimate of the model-matching error between the requested and the resulting model as indicator of stability and performance of the derived control loop. The proposed solution is evaluated in regulation problems for non-minimum phase systems through Monte Carlo simulations and in experimental conditions for the regulation of temperature in an ohmic assisted hydrodistillation process.

Interpolation of multi-LPV control systems based on Youla–Kucera parameterization

This paper presents a methodology which considers an interpolation between Linear Parameter-Varying (LPV) controllers that were designed separately for different objectives. The quadratic stability of the closed-loop system is proved under arbitrary interpolation in terms of a set of Linear Matrix Inequalities (LMIs). The interpolation strategy is based on Youla–Kucera (YK) parameterization. The proposed method can help multi-variable and multi-objective systems, to achieve high performances at different critical situations regardless of the interpolation rate.

Youla–Kucera based multi-objective car following controller

This paper presents the design and implementation of a novel multi-objective Adaptive Cruise Controller (ACC). The proposed control strategy is based on Youla–Kucera parametrization to interpolate two ACC controllers with conflicting objectives: (1) a performant controller with fast preceding tracking capabilities; and (2) a robust controller with perception noise attenuation capabilities within the system bandwidth. The proposed multi-controller structure uses tools of both performance and robust control in order to adapt car-following behavior to perception system status. The solution is implemented in an automated Renault ZOE, and compared to H∞ controller, providing encouraging results.

Adaptive rejection of narrow-band disturbances in the presence of plant uncertainties—A dual Youla–Kucera approach

The stability of adaptive disturbance rejection schemes using Youla–Kucera (YK) parametrization and the internal model principle (IMP) in the presence of plant model uncertainties is investigated. The problem is approached by using the dual Youla–Kucera parametrization for the description of the plant model uncertainties. The known disturbance case is discussed first, emphasizing the need of over parametrization of the Youla–Kucera filter used for control in order to both solving the IMP and the stability problems. Then this solution is extended for the case of unknown disturbances leading to the use of a parameter adaptation algorithm with projection. A stability analysis of the adaptive scheme is provided. Simulation results on relevant examples and experimental evaluation on an active noise attenuation system illustrate the possibilities of this approach for handling significant plant-model mismatch.

A Youla-Kucera Parametrization for Data-Driven Controllers Tuning

Abstract The Youla-Kucera parametrization is a fundamental result in system theory, very useful when designing model-based controllers. In this paper, this parametrization is employed to solve the controller design from data problem, without requiring a process model. It is shown that employing the proposed controller structure it is possible to achieve more stringent closed-loop performances than previous works in literature, maintaining a criterion to estimate the closed-loop stability. The developed design methodology does not imply a plant identification step and the solution can be obtained by least-squares algorithms in the case of stochastic additive noise. The designed solution is evaluated through Monte Carlo simulations for the regulation problem of an under-damped system.

A Design Method of Optimal PID-Based Repetitive Control Systems

This paper is concerned with the design of a PID-based repetitive control strategy for a strictly proper plant with requirements of high-precision tracking performance for periodic signals and good rejecting performance for an external disturbance with a finite frequency range. The PID-based controller consists of a PID controller and a repetitive controller connected in series, and its control parameters are optimized to meet the performance requirements. First, utilizing Youla–Kucera Parameterization, the necessary and sufficient conditions for the existence of the PID-based repetitive controller are derived. Second, from the requirements of the control performance and the analysis of the sensitivity function, the description of the PID-based repetitive controller is deduced. Third, the design of PID control parameters depends on the stability of closed-loop system and the attenuation performance. By introducing an arbitrarily small relaxation variable and applying the $H_\infty $ control method, the design problem is transformed into a generalized eigenvalue minimization problem (GVEP) under linear matrix inequality (LMI) constraints. In addition, the largest cutoff frequency in the repetitive controller is also achieved by solving a GVEP. Finally, simulations are applied to examine the validity and efficacy of the proposed method.

Feedback stabilization: the algebraic view

Based on an abstract algebraic setting we provide an elementary derivation of the Youla-Kucera parametrization of stabilizing controllers and also an alternative, coordinate free, approach of the problem. For this latter case, in contrast to the Youla-Kucera approach, the parameter set is not universal but its elements can be generated by a universal algorithm. We also emphasise the natural continuity property of this parametrization compared to the Youla-Kucera case. Extending the framework to the LFT loops we show by using elementary tools that every controller which stabilizes the interior loop of the generalized plant also stabilizes the LFT loop.

A pedagogical path from the internal model principle to Youla-Kučera parametrization

We propose a sequence of pedagogical steps for introducing the Youla-Kucera parametrization, starting from the internal model principle, and introducing the control structures of disturbance observ ...

Mixing V2V- and non-V2V-equipped vehicles in car following

Cooperative Adaptive Cruise Control (CACC) provides significant traffic flow improvements when a vehicle-to-vehicle (V2V) communication link exists with the preceding vehicle, but it degrades to an Adaptive Cruise Control (ACC) when this communication link is no longer available. This degradation occurs even if the information from another V2V-equipped vehicle ahead (different to the preceding one) is still available. This paper presents a novel car-following control system–Advanced Cooperative Adaptive Cruise Control (ACACC)–that benefits from the existing communication with this vehicle ahead in the string, reducing inter-vehicle gap whereas keeping string stability. The proposed control structure provides a hybrid behaviour between two CACC controllers with different time gaps according to the string position of the vehicle with the V2V communication link available. An stable hybrid behavior between both controllers is ensured through the Youla-Kucera parameterization. Simulation and real experiments show the proper behaviour of the designed control algorithm and a good performance compared to existing ACC/CACC controllers.

Youla–Kucera Parameterization-Based Optimally Closed-Loop Control for Tip–Tilt Compensation

In this paper, we develop a new method based on Youla–Kucera parameterization in frequency domain to reduce tip and tilt vibrations of astronomical telescopes. This proposed method can be implemented in real time and can also achieve optimal correction when frequencies of vibrations are provided. Based on this parameterization, the closed-loop stability is easily assured, which can relax the stability condition to design control parameters. Due to being plugged into an existing feedback control loop, the sensitivity function of the tip–tilt mirror control system can be minimized by optimizing Q-filter for adapting the changes of vibrations. Two types of Q-filter are introduced to deal with low-frequency and large-magnitude narrowband vibrations. Because of not being restricted by an accurate model of tip–tilt mirror, this improved control mode cannot lead to a compromise between vibrations rejection and noise propagation in the control loop. Although on-line identification of disturbances models is not required, finding the vibration frequencies is crucial. Simulations and experiments demonstrate that the Youla–Kucera controller has a clear improvement of the closed-loop performance in comparison with the original method.

Periodic disturbance rejection to the Nyquist frequency and beyond

In this paper, we address periodic disturbance rejection for sampled-data control systems, where the frequency of the disturbance can be beyond the Nyquist frequency of the limited measured plant output sampling rate. The disturbance effect on steady-state response of the fictitious fast-rate plant output including intersample information is obtained using discrete-time Fourier series. A sufficient condition for disturbance rejection together with a sufficient and necessary condition for perfect disturbance elimination are provided by employing the steady-state response. A simple but effective controller design procedure combining H∞ loop shaping, Youla–Kucera parameterization, and gradient methods is provided to achieve the two conditions. The proposed approach is applied on vibration control beyond the Nyquist frequency in a commercial hard disk drive. The effectiveness of the proposed approach is verified by our simulation results showing disturbance rejection of 62% and perfect disturbance elimination, as well as by our experimental results showing disturbance rejection of 54%.

Robust and Adaptive Feedback Noise Attenuation in Ducts

In this brief, the attenuation of sound propagation in an air-handling duct using robust and adaptive feedback active noise control (ANC) strategies is investigated. The case of multiple narrow-band disturbances located in distinct frequency regions and the interference occurring in the presence of disturbances with very close frequencies are considered. The active control uses a loudspeaker as a compensatory system. The objective is to minimize the residual noise at the end of the duct segment considered. The system does not use any additional sensors for receiving real-time information upon the disturbances. This brief illustrates the application of the techniques for active vibration control presented by Landau et al. to this problem. A hierarchical feedback control approach will be used. At the first level, a robust linear controller will be designed taking advantage of the knowledge of the domains of variation of the frequencies of the noise disturbances. To further improve the performance, a direct adaptive control algorithm will be added. Its design is based on the use of the internal model principle combined with the Youla–Kucera parameterization of the controller. Guidelines for the design of the baseline (central) controller are provided. Both robust and adaptive controls require the knowledge of the discrete-time model of the compensation path, which is obtained by identification from experimental data. Experimental results on a relevant duct ANC test bench will illustrate the performance of the proposed methodology.

Compensating for a multisinusoidal disturbance based on Youla–Kucera parametrization

We consider the problem of compensation for a multisinusoidal disturbance for a linear stationary system with a given nominal control law. We consider the general structure of a controller that lets one use arbitrary algorithms for identification of disturbance parameters satisfying certain assumptions. The proposed structure is based on the Youla–Kucera parametrization and lets one compensate for a disturbance while preserving nominal behavior of a control system with respect to the reference.