Robust Performance Analysis of Magnetic Bearings

Identification of linear models in view of robust control design requires the identification of a control‐relevant nominal model, and a quantification of model uncertainty. In this paper a procedure is presented to quantify the model uncertainty of any prespecified nominal model, from a sequence of measurement data of input and output signals from a plant. By employing a nonparametric empirical transfer function estimate (ETFE), we are able to split the model uncertainty into three parts: the inherent uncertainty in the data due to data imperfections, the unmodelled dynamics in the nominal model, and the uncertainty due to interpolation. A frequency‐dependent hard error bound is constructed, and results are given for tightening the bound through appropriate input design.

Most control techniques require the use of a plant model during the design phase in order to tune the controller parameters.The mathematical models are an approximation of real systems and contain imperfections by several reasons: use of low-order descriptions, unmodelled dynamics, obtaining linear models for a specific operating point (working with poor performance outside of this working point), etc.Therefore, control techniques that work without taking into account these modelling errors, use a fixed-structure model and known parameters (nominal model ) supposing that the model exactly represents the real process, and the imperfections will be removed by means of feedback.However, there exist other control methods called robust control techniques which use these imperfections implicity during the design phase.In the robust control field such imperfections are called uncertainties, and instead of working only with one model (nominal model), a family of models is used forming the nominal model + uncertainties.The uncertainties can be classified in parametric or structured and non-parametric or non-structured.The first ones allow representing the uncertainties into the model coefficients (e.g. the value of a pole placed between maximum and minimum limits).The second ones represent uncertainties as unmodelled dynamics (e.g.differences in the orders of the model and the real system) (Morari and Zafiriou, 1989).The robust control technique which considers more exactly the uncertainties is the Quantitative Feedback Theory (QFT).It is a methodology to design robust controllers based on frequency domain, and was developed by Prof. Isaac Horowitz (Horowitz, 1982;Horowitz and Sidi, 1972;Horowitz, 1993).This technique allows designing robust controllers which fulfil some minimum quantitative specifications considering the presence of uncertainty in the plant model and the existence of perturbations.With this theory, Horowitz showed that the final aim of any control design must be to obtain an open-loop transfer function with the suitable bandwidth (cost of feedback) in order to sensitize the plant and reduce the perturbations.The Nichols plane is used to achieve a desired robust design over the specified region of plant uncertainty where the aim is to design a compensator C(s) and a prefilter F(s) (if it is necessary) (see Figure 1), so that performance and stability specifications are achieved for the family of plants.

Given a nominal statistical model, we consider the minimax estimation problem consisting of finding the best least-squares estimator for the least favorable statistical model within a neighborhood of the nominal model. The neighborhood is formed by placing a bound on the Kullback-Leibler (KL) divergence between the actual and nominal models. For a Gaussian nominal model and a finite observations interval, or for a stationary Gaussian process over an infinite interval, the usual noncausal Wiener filter remains optimal. However, the worst case performance of the filter is affected by the size of the neighborhood representing the model uncertainty. On the other hand, standard causal least-squares estimators are not optimal, and a characterization is provided for the causal estimator and the corresponding least favorable model. The causal estimator takes the form of a risk-sensitive estimator with an appropriately selected risk sensitivity coefficient.

This paper deals with control method for chemical multivariable systems with time delays and interactions between loops, which is a significant problem of uncertain linear control systems. The distillation column model is required to satisfy certain robustness conditions. The design of robust H∞ controller for this system provides new and important results. The distillation column was tested with a nominal model and various uncertainties. Within uncertainties in the process will be modeled variations of gains alone, and gains and delays simultaneously for different set point changes, disturbance rejection. The simulation results of the distillation model ensure a robust stability and performance. An excellent decoupled response with zero tracking error is done in all simulations using Matlab/Simulink software.

In the present paper, it will be reported original results concerning the application of Neural Networks (NN) in mobile robot in trajectory tracking control. This work combines a feedback linearization based on a nominal model and an NN adaptive dynamic compensation. In mobile robot with uncertain dynamic parameters, two controllers are implemented separately: a kinematic controller and an inverse dynamic controller. The uncertainty in the nominal dynamic model is compensated by a neural adaptive feedback controller. The resulting adaptive controller is efficient and robust in the sense that it succeeds to achieve a good tracking performance with a small computational effort. The learning laws were deduced by Lyapunov's stability analysis. Finally, the performance of the control system is verified through experiments.

Robust control of Cassette Multi-functional Mover for ITER remote handling tasks

Robust modal vibration suppression of a flexible rotor

Given a nominal model, an integrated uncertainty model identification and mu-synthesis algorithm is presented for linear time-invariant (LTI) systems. The goal is 1) to construct an uncertainty model set characterized by parameterized weighting functions of dynamic perturbations and disturbances in the general linear fractional transformation (LFT) form - customary representation in modern robust control and 2) to select from this set according to closed-loop control objectives. The motivation is the simultaneous model validation and model optimization with respect to closed-loop requirements. The algorithm works on sampled, bounded-energy experimental data on the frequency-domain and integrates nominal model invalidation, uncertainty model construction and control synthesis in order to achieve robust performance. Standard D-K iteration steps are combined with an optimization step on a group of selected data. The method is demonstrated on a simple numerical example, where the results are comparable with analytic computations

Robust tracking control for vehicle electronic throttle using adaptive dynamic sliding mode and extended state observer

In order to improve the performances of air conditioning systems, it is desirable to track time-varying trajectories generated by optimization algorithms, which H∞ synthesis techniques have been proved to successfully solve. However, the control-oriented models of vapor compressor cycles used for algorithm development, even if built from first-principles, suffer from model uncertainties introduced by modeling assumptions, calibration inaccuracies, and linearization errors. The differences between the actual plant and the control-oriented model, mainly in the form of unmodeled dynamics and parameter uncertainty, undermine the stable margin as well as the performance of the closed-loop system with H∞ controllers. In order to solve the problem, the concept of the structured singular value μ is used to analyze the influences of model uncertainties on robust stability and robust performance. Based on μ analysis results, μ synthesis techniques compared to H∞ methods achieve better stability and performance margins over the same set of uncertainties. Furthermore, simulation results show that the μ controller achieves better performances of output tracking and disturbance rejection than the H∞ controller for the automotive air conditioning system studied.

Optimisation of fed batch fermenters can substantially increase the profitability of these processes. Optimal control of a fed batch fermenter is usually based on a nominal process model. Parameter uncertainties are not taken into account. Simulation studies show that results obtained with fixed nominal model parameters can be quite sensitive to the uncertainty in parameter values. This paper presents a method for obtaining robust optimal control profiles in the presence of uncertainty in the model parameters. The proposed approach is illustrated with a case study. It is also shown that feedback controllers can reduce the effect of the uncertainties.

The three-tank (3-tank) liquid-level control system commonly exists in industries under the proportional-integral-derivative (PID) control loop. However, the proportional-integral-derivative-accelerated (PIDA) can yield better responses than the PID for higher order plant. In this paper, the robust PIDA controller design by the cuckoo search (CS) for the 3-tank liquid-level control system is proposed. Results obtained will be compared with the PID controller designed by the CS. As results, the responses of the 3-tank liquid-level controlled system with the robust PIDA controller optimally designed by the CS are better than the PID controller designed by the CS. Due to model uncertainty within ±10% of each parameter of the nominal plant model, the robust PIDA controller optimized by the CS can provide the very satisfactory responses in both time and frequency domains with robust performance and robust stability.

In l/sub 1/-robust control design, model uncertainty can be handled if an upper bound on the l/sub 1/-norm of the model error is known. A procedure is developed which yields such an upper bound for a given nominal model, using measurement data and a priori information consisting of a time-domain bound on the noise and information about the decay rate of the pulse response of the model error. The upper bound is calculated by solving a set of linear programming problems. Moreover, a procedure is presented for obtaining a new nominal model which is optimal in an l/sub 1/-sense, i.e., has a minimal upper bound on the l/sub 1/-norm of the model error. This is performed in two steps: in the first step the central estimate is computed, and in the second step model reduction in the l/sub 1/-norm is performed. For the latter problem, a solution is given for the case when the reduced-order model is linear in the parameters. >

Some robust control methods have been developed in the past in order to increase tracking performance in the presence of parametric uncertainties. In the presence of parametric uncertainty, unmodelled dynamics and other sources of uncertainties, robust control laws are used. Corless-Leitmann [1] approach is a popular approach used for designing robust controllers for robot manipulators. In early application of Corless-Leitmann [1] approach to robot manipulators [2, 3], it is difficult to compute uncertainty bound precisely. Because, uncertainty bound on parameters depends on the inertia parameters, the reference trajectory and manipulator state vector. Spong [4] proposed a new robust controller for robot manipulators using the Lyapunov theory that guaranties stability of uncertain systems. In this approach, Leithmann [5] or Corless-Leithman [1] approach is used for designing the robust controller. One of the advantage of Spong’s approach [4] is that uncertainty on parameter is needed to derive robust controller and uncertainty bound parameters depends only on the inertia parameters of the robots. Yaz [6] proposed a robust control law based on Spong’s study [4] and global exponential stability of uncertain system is guaranteed. However, disturbance and unmodelled dynamics are not considered in algorithm of [4, 6]. Danesh at al [7] develop Spong’s approach [4] in such a manner that control scheme is made robust not only to uncertain inertia parameters but also to robust unmodelled dynamics and disturbances. Koo and Kim [8] introduce adaptive scheme of uncertainty bound on parameters for robust control of robot manipulators. In [8], upper uncertainty bound is not known as would be in robust controller [4] and uncertainty bound is estimated with estimation law in order to control the uncertain system. A new robust control approach is proposed by Liu and Goldenerg [9] for robot manipulators based on a decomposition of model uncertainty. Parameterized uncertainty is distinguished from unparameterized uncertainty and a compensator is designed for parameterized and unparameterized uncertainty. A decomposition-based control design framework for mechanical systems with model uncertainties is proposed by Liu [10]. In order to increases tracking performance of uncertain systems, design of uncertainty bound estimation functions are considered. For this purpose, some uncertainty bound estimation functions are developed [11-15] based on a Lyapunov function, thus, stability of

The aim of the paper is to obtain suitable state-space models of continuous biotechnological processes (CBTP) in the framework of Linear Fractional Transformation (LFT). The LFT models are starting point in most of the advanced robust control design and analysis methods. Therefore, a linearized process model in the state-space is used whose elements are supposed to vary within certain bounds to represent the nonlinear behaviour of the real plant. The performance specifications are defined in the frequency domain through weighting functions. Two LFT models of CBTP are obtained ready for controller design aimed to optimize robust stability margins and robust performance, respectively.