Generation of QFT bounds for robust tracking specifications for plants with affinely dependent uncertainties

This paper presents an efficient algorithm for the generation of QFT bounds for robust tracking specifications for plants with affinely dependent uncertainties. For a plant with m affinely dependent uncertainties, it is shown that whether a point in the Nichols chart lies in the QFT bound for a robust tracking specification at a given frequency can be easily tested by computing the maxima and minima of m2^m?1 univariate functions corresponding to the edges of the parameter domain box. This test procedure is then utilized along with a pivoting procedure to trace out the boundary of the QFT bound with a prescribed accuracy or resolution. The developed algorithm has the advantages that (1) it is efficient in the sense that it requires less floating point operations than other existing algorithms in the literature; (2) it can avoid the unfavorable trade‐off between the computational burden and the accuracy of the computed QFT bounds that has arisen in the application of many existing QFT‐bound generation algorithms; (3) the maximum allowable error of the computed QFT bound can be prespecified; and (4) it can compute QFT bounds with multi‐valued boundaries. Numerical examples are given to illustrate the proposed algorithm and its computational superiority. Copyright © 2010 John Wiley & Sons, Ltd.     

Efficient algorithm for computing QFT bounds

This article presents an efficient algorithm for computing quantitative feedback theory (QFT) bounds for frequency-domain specifications from plant templates which are approximated by a finite number of points. To develop the algorithm, an efficient procedure is developed for testing, at a given frequency, whether or not a complex point lies in the QFT bound. This test procedure is then utilised along with a pivoting procedure to trace out, with a prescribed accuracy or resolution, the boundary of the QFT bound. The developed algorithm for computing QFT bounds has the advantages that it is efficient and can compute QFT bounds with multi-valued boundaries. A numerical example is given to show the computational superiority of the proposed algorithm.     

基于QFT和ZPETC的高精度鲁棒跟踪控制器设计

阐述了定量反馈理论(QFT)和零相差跟踪控制器(ZOETC)的基本原理及设计方法,并给出了设计实例。在QFT和ZPETC的基础上,提出了一种是实现高精度鲁棒跟踪控制的方案,采用QFT控制保证系统的鲁棒性,通过ZPETC提高系统的跟踪精度。仿真表明,这种方法实现了QFT和ZPETC的完美结合,很适合高精度跟踪系统的鲁棒控制。     

GENERATION OF EXACT QFT BOUNDS FOR PLANTS WITH AFFINELY DEPENDENT UNCERTAINTIES

This paper presents an efficient method for the generation of exact QFT bounds for robust sensitivity reduction and gain‐phase margin specifications for plants with affinely dependent uncertainties. It is shown that, for a plant with m affinely dependent uncertainties, the exact QFT bounds for robust sensitivity reduction and gain‐phase margin specifications at a given frequency and controller phase can be computed by solving m^2m‐1 bivariate polynomial inequalities corresponding to the edges of the parameter domain box. Moreover, the solution set for each bivariate polynomial inequality can be computed by solving for the real roots of one fourth‐order and six second‐order polynomials. This avoids the unfavorable trade‐off between the computational burden and the accuracy of QFT bounds that has arisen in the application of many existing QFT bound generation algorithms. Numerical examples are given to illustrate the proposed method and its computational superiority.     

The input amplitude saturation problem in QFT: A survey

In this work the input amplitude saturation problem is analysed in the Quantitative Feedback Theory (QFT) framework. This paper reviews previous works in the literature dealing with the input amplitude saturation problem in the presence of an uncertain plant in the frequency domain using QFT. The objective of this paper is to compare the different available approaches and summarize the design process for each case so that this paper can be used as a tutorial; there are six main approaches to this problem. Two of these approaches use the classical two degrees of freedom control scheme for QFT; in both of these, the design constraints of a linear QFT compensator are added in the loop shaping stage: they are added in the first approach to avoid excitation of the actuator saturation and in the second one to guarantee global stability. The other three techniques are considered as anti-windup (AW) approaches. Starting from a base design in QFT with two degrees of freedom, the first AW approach introduces a third degree of freedom that guarantees the stability of the system, allowing for base designs for high performance. The other two AW approaches also introduce a third degree of freedom, but they take simple stability considerations into account and focus on the performance of the system. The last solution consists of using a reference governor technique, which guarantees the computation of a reference signal for an inner control loop that is shaped using QFT in such a way that robust stability will be guaranteed. The reference governor technique is a time domain approach that implies the resolution of an optimization problem. The rest of the approaches are frequency domain techniques based on a loop shaping method in the traditional QFT sense.     

Multivariable quantitative feedback design for tracking error specifications

The use of tracking error specifications in quantitative feedback theory (QFT) design is discussed for multi-input, multi-output (MIMO) systems. These specifications bound the closed loop transfer function within a disk around some nominal (model) performance while preserving the QFT approach that allows treatment of highly structured (and unstructured) uncertainty. Because the specifications capture phase information, the level of over-design in certain MIMO QFT designs is reduced. The method presented allows independent, two-degree-of-freedom design.     

Robust neural network tracking controller using simultaneous perturbation stochastic approximation

This paper considers the design of robust neural network tracking controllers for nonlinear systems. The neural network is used in the closed-loop system to estimate the nonlinear system function. We introduce the conic sector theory to establish a robust neural control system, with guaranteed boundedness for both the input/output (I/O) signals and the weights of the neural network. The neural network is trained by the simultaneous perturbation stochastic approximation (SPSA) method instead of the standard backpropagation (BP) algorithm. The proposed neural control system guarantees closed-loop stability of the estimation system, and a good tracking performance. The performance improvement of the proposed system over existing systems can be quantified in terms of preventing weight shifts, fast convergence, and robustness against system disturbance.     

Robust adaptive speed regulator with self-tuning law for surfaced-mounted permanent magnet synchronous motor

This study exhibits a self-tuning speed control scheme for the surface-mounted permanent magnet synchronous motor (SPMSM) against the parameter variations through the multivariable approach. The proposed method has two novelties. The first one is to combine the adaptive controller with the self-tuning algorithm so as to make the decay ratio of the tracking errors higher in the transient period. The second one is to provide a systematical way to find a robust stabilizing control gain corresponding the speed and current tracking errors by solving an optimization problem. The efficacy of the proposed method was experimentally investigated using a 3-kW SPMSM.     

Observer-based adaptive sliding mode control for robust tracking and model following

This paper presents a methodological approach to design an observer-based adaptive sliding mode control to realize the problem of robust tracking and modeling following for a class of uncertain linear systems. Only partial information of the system states is known. Based on Lyapunov stability theorem, it will be shown that the proposed scheme guarantees the stability of closed-loop system and achieves zero-tracking error in the presence of parameter uncertainties and external disturbances. The proposed observer-based adaptive sliding mode control scheme can be implemented without requiring a priori knowledge of upper bounds on the norm of the uncertainties and external disturbances. This scheme assures robustness against system uncertainties and disturbances. Both the theoretical analysis and illustrative example demonstrate the validity of the proposed scheme.     

Automated synthesis of multivariable QFT controller using interval constraint satisfaction technique

Robust controller synthesis of Multi-Input–Multi-Output (MIMO) systems is of great practical interest and their automation is a key concern in control system design. The synthesis problem consists of obtaining a controller that ensures stability and meets a given set of performance specifications, in spite of the disturbance and model uncertainties. In addition to perform the above tasks, a MIMO controller also has to perform the difficult task of minimizing the interaction between the various control loops.Unlike existing manual or convex optimization based Quantitative Feedback Theory (QFT) design approaches, the proposed method gives a controller which meets all performance requirements in QFT, without going through the conservative and sequential design stages for each of the multivariable sub-systems. In this paper, a new, simple, and reliable automated MIMO QFT controllers design methodology is proposed. A fixed structure MIMO QFT controller has been synthesized by solving QFT quadratic inequalities of robust stability and tracking specifications. The quadratic inequalities (constraints) are posed as Interval Constraint Satisfaction Problem (ICSP). The constraints are solved by constraint solver — RealPaver. The main feature of this method is that the algorithm finds all the solutions to within the user-specified accuracy. The designed MIMO QFT controllers are tested on the experimental setup designed by Educational Control Product (ECP) Magnetic Levitation Setup ECP 730. From the experimental results presented, it is observed that, the designed controller satisfies the desired performance specifications. It is also observed that, the interactions between the loops are within the specified limits. The robustness of the designed controllers are verified by putting extra weights on the magnets.     

Force Reflecting Bilateral Control of Master–Slave Systems in Teleoperation

In this paper, a simple structure design with arbitrary motion/force scaling to control teleoperation systems, with model mismatches is presented. The goal of this paper is to achieve transparency in presence of uncertainties. The master–slave systems are approximated by linear dynamic models with perturbed parameters, which is called the model mismatch. Moreover, the time delay in communication channel with uncertainties is considered. The stability analysis will be considered for two cases: (1) stability under time delay uncertainties and (2) stability under model mismatches. For the first case, two local controllers are designed. The first controller is responsible for tracking the master commands, while the second controller is in charge of force tracking as well as guaranteeing stability of the overall closed-loop system. In the second case, an additional term will be added to the control law to provide robustness to the closed-loop system. Moreover, in this case, the local slave controller guarantees the position tracking and the local master controller guarantees stability of the inner closed-loop system. The advantages of the proposed method are two folds: (1) robust stability of the system against model mismatches is guaranteed and (2) structured system uncertainties are well compensated by applying independent controllers to the master and the slave sites. Simulation results show good performance of the proposed method in motion tracking as well force tracking in presence of model mismatches and time delay uncertainties.     

Robust Bounding Ellipsoidal Adaptive Constrained least-squares algorithm and its performance analysis

In this paper, the robust Bounding Ellipsoidal Adaptive Constrained least-squares (BEACON) algorithm based on new set-membership error bounds is proposed to improve robustness and steady-state misalignment in impulsive noise environments. The expressions for the steady-state excess mean square error (EMSE) of the proposed robust BEACON are obtained. Simulations on system identification and double-talk scenarios show that the robust BEACON algorithm considerably outperforms the traditional BEACON algorithm in the presence of impulsive noise and the theoretical predictions are in good agreement with simulation results.     

On quantitative feedback design for robust position control of hydraulic actuators

This paper discusses several practical issues related to the design of robust position controllers for hydraulic actuators by quantitative feedback theory (QFT). Important properties of the hydraulic actuator behavior, for control system design, are identified by calculating a family of equivalent frequency responses from acceptable nonlinear input–output data. The role of this modeling approach towards reducing over-design by decreasing the sizes of the QFT plant templates is described. The relationship between the geometry of the QFT bounds and the complexity of the robust feedback law is examined through the development of two low-order controllers having characteristics suitable for different applications. Experimental test results demonstrate the extent that each QFT controller is able to maintain robustness against variations in the hydraulic system dynamics that occur due to changing load conditions as well as uncertainties in the hydraulic supply pressure, valve spool gain, and actuator damping.     

Open-loop worst-case identification of nonSchur plants

This paper presents an LMI based algorithm for deterministic worst-case identification of nonSchur plants in an open-loop setting. Contrary to other approaches dealing with this problem, the proposed technique does not require prior knowledge of a stabilizing controller. The main result of the paper shows that, as the information is completed, the identified model converges, in the ?₂-induced topology, to the actual plant. Additional results include upper bounds on the worst-case identification error on the finite horizon. The usefulness of the proposed approach is illustrated with a practical example arising in the context of robust visual tracking.     

含有驱动器模型的移动机器人自适应跟踪控制

本文针对包含驱动器模型的移动机器人, 考虑到其在粗糙表面上运动过程中所受的摩擦力以及不可建模的动态的影响, 使用反步设计法(Backstepping)给出了一种自适应跟踪控制策略.其中对于不可建模的动态, 本文使用一种非线性函数对其影响进行抵消,使得机器人的路径跟踪对不确定具有鲁棒性; 对于摩擦力项, 使用径向基神经网络(RBFNN)对其进行逼近, 在控制器中能够根据逼近值给予相应的摩擦力补偿量, 从而使移动机器人比较适合在粗糙度大的路面(如沙地)上进行路径跟踪. 仿真结果验证了该控制方法的有效性.     

Interval QFT: a mathematical and computational enhancement of QFT

The paper presents an overview of a mathematical and computational enhancement of Horowitz's QFT design procedure. The enhancement uses methods of interval analysis and is called as interval QFT, or IQFT. IQFT addresses and solves some of the fundamental issues in QFT, concerning selection of design frequencies, selection of controller phases in bound generation, approximation of plant templates with finite plant sets, and generation of plant templates and controller bounds with reliability and to a prescribed accuracy. An example is presented to illustrate the key features of IQFT. Copyright © 2002 John Wiley & Sons, Ltd.     

Nonlinear robust H-infinity filtering for a class of uncertain systems via convex optimization

A new approach for robust H-infinity filtering for a class of Lipschitz nonlinear systems with time-varying uncertainties both in the linear and nonlinear parts of the system is proposed in an LMI framework. The admissible Lipschitz constant of the system and the disturbance attenuation level are maximized simultaneously through convex multi-objective optimization. The resulting H-infinity filter guarantees asymptotic stability of the estimation error dynamics with exponential convergence and is robust against nonlinear additive uncertainty and time-varying parametric uncertainties. Explicit bounds on the nonlinear uncertainty are derived based on norm-wise and element-wise robustness analysis.     

The robust knapsack problem with queries

We consider robust knapsack problems where item weights are uncertain. We are allowed to query an item to find its exact weight,where the number of such queries is bounded by a given parameter Q. After these queries are made, we need to pack the items robustly, i.e., so that the choice of items is feasible for every remaining possible scenario of item weights.The central question that we consider is: Which items should be queried in order to gain maximum profit? We introduce the notion of query competitiveness for strict robustness to evaluate the quality of an algorithm for this problem, and obtain lower and upper bounds on this competitiveness for interval-based uncertainty. Similar to the study of online algorithms, we study the competitiveness under different frameworks, namely we analyze the worst-case query competitiveness for deterministic algorithms, the expected query competitiveness for randomized algorithms and the average case competitiveness for known distributions of the uncertain input data. We derive theoretical bounds for these different frameworks and evaluate them experimentally. We also extend this approach to Γ-restricted uncertainties introduced by Bertsimas and Sim.Furthermore, we present heuristic algorithms for the problem. In computational experiments considering both the interval-based and the Γ-restricted uncertainty, we evaluate their empirical performance. While the usage of a Γ-restricted uncertainty improves the nominal performance of a solution (as expected), we find that the query competitiveness gets worse.     

A robust correntropy based subspace tracking algorithm in impulsive noise environments

The maximum correntropy criterion (MCC) demonstrates the inherent robustness to outliers in adaptive filtering. By employing the MCC based cost function in projection approximation subspace tracking (PAST) algorithm, the MCC-PAST algorithm is deduced and utilized for the subspace tracking under impulsive noise environments. To handle the fast varying subspaces circumstances, the variable forgetting factor (VFF) technique is developed and incorporated into the MCC-PAST algorithm. To assess the robustness of the proposed MCC-PAST with VFF algorithm, SαS processes are employed to comprehensively model different scenarios of impulsive noises. The simulation results show the proposed MCC-PAST algorithm with VFF performs better than the other two PAST algorithms developed for subspace tracking in impulsive noise environments, namely, the robust PAST algorithm and the robust Kalman filter based algorithm with variable number of measurements (KFVNM), especially when the noise is extremely impulsive or the GSNR (generalized signal to noise ratio) is relatively low.     

Robust parametric CMAC with self-generating design for uncertain nonlinear systems

In this paper, a robust parametric cerebellar model articulation controller (RP-CMAC) with self-generating design, called RPCSGD, is proposed for uncertain nonlinear systems. The proposed controller consists of two parts: one is the parametric CMAC with self-generating design (PCSGD), which is utilized to approximate the ideal controller and the other is the robust controller, which is designed to achieve a specified H^∞ robust tracking performance of the system. The corresponding memory size of the proposed controller can be suitably constructed via the self-generating design. Thus, the useless or untrained memories will not take possession of the space. Besides, the concept of sliding-mode control (SMC) is adopted so that the proposed controller has more robustness against the approximated error and uncertainties. The stability of the system can be guaranteed surely due to the derivations of the adaptive laws of the proposed RPCSGD based on the Lyapunov function. Finally, the proposed controller is applied to the second-order chaotic system and the one-link rigid robotic manipulator. The tracking performance and effectiveness of the proposed controller are verified by simulations of the computer.