Integrated identification and robust control

A framework for integrated identification and control is presented. As part of this framework, frequency domain uncertainty bounds are derived for robust stability tests, a robust stability test for elliptical bounds is developed for SISO systems, a methodology for estimating controller performance is derived, and an optimal experiment design methodology for control-relevant identification is outlined. An example is presented to illustrate how the tools of the framework fit together.     

Robustness optimization in LQG multivariable systems with time-varying non-linear perturbations

This paper presents an algorithm to synthesize a controller in order to treat the problem of robustness optimization in LQG (linear-quadratic-gaussian) multi-variable systems subjected to time-varying non-linear perturbations. The controller not only minimizes the cost functional in LQG problems but also maximizes the excess robustness with respect to the Hardy H^∞-norm criterion by selecting two frequency-dependent weighting matrices Q(s) and R(s). Our approach is based on the Wiener-Hopf technique (frequency domain approach) and two weighting matrices in the cost functional are shaped by the inverse LQG method to achieve the robustness optimization. Furthermore, the plant of the system has no stable, proper, square, and minimum phase constraints. An example is given to illustrate our result.     

Control-relevant model reduction problems for SISO H2, H∞, and μ-controller synthesis

The problem of model reduction in the context of control system design is investigated. Starting from closed-loop objectives (H₂,H_∞, and μ), equivalent weighted open-loop plant and controller reduction problems are developed. The control-relevant weight function incorporates explicitly all the important characteristics of the control problem, such as the setpoint/disturbance spectrum and the designer requirements for the sensitivity/complementary sensitivity functions, Furthermore, these control-relevant reduction problems are complemented with validation procedures that indicate rigorously the effects of the reduction problem on the desired performance objectives. A simple algorithm that uses standard regression routines is presented to solve these problems.     

Stable LQG controllers

The optimal LQG controller is known to stabilize the closed loop if certain mild conditions are satisfied. The controller itself, however, may be unstable. The paper presents a method of selecting the weighting and covariance matrices such that the optimal controller is internally asymptotically stable. The method is very easy to apply and for stable open-loop system involves the solution of a single Lyapunov equation     

Wind turbine mechanical stresses reduction and contribution to frequency regulation

The aim of the present research work has been to design an optimal MIMO LQG controller to reduce the drive-train, blades and tower mechanical stresses of a wind turbine (WT), and at the same time, to involve the WT in the grid primary frequency regulation when it is operating in full load (FL) zone. To verify the effectiveness of the proposed controller, the achieved results are compared to those obtained by a base-line controller based on a PI regulator.Simulation results show that thanks to these controllers, WT can effectively contribute to the grid frequency regulation, tracking tightly the generator power reference which depends on that frequency. Compared with the base-line controller, the LQG controller significantly reduces the mechanical stresses of the WT׳s most costly components.     

Fuzzy bang–bang relay control of a single-axis active magnetic bearing system

Active magnetic bearings (AMB) are presently being utilized in various classes of rotating machinery. Although the rotor-AMB systems are open loop unstable, they are easily stabilized using feedback control schemes of which the PID controller is the most commonly used. The PID controller is however only effective at the vicinity of the rotor’s equilibrium position where the dynamics of the rotor-AMB system is linearized. Significant deviation of the rotor’s motion from this equilibrium position may occur due to large imbalance forces. In this situation, the nonlinearity in AMBs, which arises from the relationship between the electromagnetic force, coil current and air gap, may render the PID controller ineffective. For the control of nonlinear systems, artificial intelligence techniques such as fuzzy and hybrid techniques are effective. In this paper, a new fuzzy controller is proposed for the control of a single-axis AMB system. This controller is based on the bang–bang scheme, which is an old but effective technique to control nonlinear systems in optimal time. The performance of the proposed integrated fuzzy bang–bang relay controller (FBBRC) was found to be superior to that of the optimized PD controller and the conventional fuzzy logic controller. Comparison of the FBBRC with the fuzzy logic controller cascaded with a hard limiter (FBBC) relay revealed almost equal performance. High frequency chattering was however observed in the steady-state response of the FBBC. Such chattering is known to cause instability and distortion in the amplifiers that are used to supply current to the magnetic bearing actuators.     

Supervisory control using a new control-relevant switching

This paper presents a new supervisory control scheme, which is based on a control-relevant switching logic. Unlike most of the existing switching methods considering only estimator performance, the proposed scheme takes both estimator and controller performance into account. As an index to the controller performance, an iISS (integral-input-to-state stability) Lyapunov function is employed; it is ensured that the Lyapunov function satisfies a certain inequality. This Lyapunov-based switching is then coupled to the state-dependent dwell-time switching developed recently, and the state of the uncertain plant is shown to converge asymptotically. The proposed supervisory control scheme is applied to an input-constrained neurally stable linear plant.     

基于LQG基准的预测控制器经济敏感度分析及调节准则

为考虑控制变量方差变化对控制器经济性能的影响, 提出一种基于线性二次高斯(Linear Quadratic Gaussian, LQG)基准的预测控制器经济敏感度分析方法及调节准则. 首先由子空间辨识算法推导出带输入输出变量加权的LQG基准一般描述形式, 在此基础上, 构造了基于方差调节和基于约束松弛的两个优化问题进行敏感度分析, 最终求解得到敏感变量的方差调节量和约束松弛量以提高控制器的经济效益. Shell塔仿真实验结果表明本文方法的有效性.     

On the assessment of multivariable controllers using closed loop data. Part I: Identification of system models

Controller performance assessment of SISO and MIMO systems requires effective and systematic identification of the associated system models based on closed-loop data. In this work, a new methodology for the identification of the process, controller and disturbance models is presented for the purpose of enabling the evaluation of the performance of MIMO control systems. The methodology is based on subspace identification algorithms for the identification of the controller, process and disturbance models from closed-loop data. However, identification of the process model is enhanced by the estimation of the associated interactor matrix via the Variable Regression Estimation technique, the existence of which is mathematically proved. The proposed identification methodology is applied to two 2 × 2 systems utilizing both step-response and PRBS closed-loop data.     

Least costly closed-loop performance diagnosis and plant re-identification

The inherent time-varying nature of dynamics in chemical processes often limits the lifetime performance of model-based control systems, as the plant and disturbance dynamics change over time. A critical step in the maintenance of model-based controllers is distinguishing control-relevant plant changes from variations in disturbance characteristics. In this paper, prediction error identification is used to evaluate a hypothesis test that detects if the performance drop arises from control-relevant plant changes. The decision rule is assessed by verifying whether an identified model of the true plant lies outside the set of all plant models that lead to adequate closed-loop performance. A unified experiment design framework is presented in the least costly context (i.e., least intrusion of nominal plant operation) to address the problem of input signal design for performance diagnosis and plant re-identification when the performance drop is due to plant changes. The application of the presented performance diagnosis approach to a (nonlinear) chemical reactor demonstrates the effectiveness of the approach in detecting the cause of an observed closed-loop performance drop based on the designed least costly diagnosis experiment.     

A novel on-line OCID method and its application to input-constrained active fault-tolerant tracker design for unknown nonlinear systems

ABSTRACT

The existing off-line observer/controller identification (OCID) method for linear systems is newly extended in this paper for off-line/on-line identification of known/unknown highly nonlinear systems, and a new input-constrained active fault-tolerant tracker is developed, based on the identified linear models. The advantages of the proposed extended on-line OCID method for linear/nonlinear systems are briefly described as follows: (i) Implement novel servo-control-oriented off-line OCID methods in observer and controller canonical forms for highly nonlinear systems; (ii) Is able to overcome the discontinuity induced by the singular value decomposition (SVD) that should be carried out at each sampling instant; (iii) It directly realises the identified parameters in the observer/controller canonical forms; this simplifies the identification process; (iv) Can be practically implemented for the on-line control of an unknown nonlinear system which was constituted by an unknown open-loop plant, an existing but unknown controller and/or an unknown observer; and (v) Can be utilised to develop a new active fault-tolerant controller to compensate the immovable existing controller of the practical operating system. Finally, the servo-control-oriented off-line OCID method for the highly nonlinear PUMA 560 manipulator is shown in the illustrative examples to demonstrate the superiority of the proposed method.     

Adaptive actuator failure compensation control for MIMO systems*

Two adaptive failure compensation control schemes based on MRAC are developed for a class of MIMO LTI systems with unknown actuator failures. An effective controller structure is proposed to achieve the desired plant-model output matching when implemented with matching parameters. Design conditions are specified for such nominal plant-model output matching. Two adaptive versions of the nominal controller are proposed and stable adaptive laws are derived for updating the controller parameters when plant parameters and failure parameters are unknown. All closed-loop signals are bounded and the plant outputs track the given reference outputs asymptotically, despite the uncertainties in actuator failures and plant parameters. Simulation results for an aircraft lateral dynamic model verify the desired adaptive control system performance in the presence of unknown rudder and aileron failures.     

A methodology for control-relevant nonlinear system identification using restricted complexity models

A broadly-applicable, control-relevant system identification methodology for nonlinear restricted complexity models (RCMs) is presented. Control design based on RCMs often leads to controllers which are easy to interpret and implement in real-time. A control-relevant identification method is developed to minimize the degradation in closed-loop performance as a result of RCM approximation error. A two-stage identification procedure is presented. First, a nonlinear ARX model is estimated from plant data using an orthogonal least squares algorithm; a Volterra series model is then generated from the nonlinear ARX model. In the second stage, a RCM with the desired structure is estimated from the Volterra series model through a model reduction algorithm that takes into account closed-loop performance requirements. The effectiveness of the proposed method is illustrated using two chemical reactor examples.     

Subspace identification using instrumental variable techniques

Subspace-based algorithms for system identification have lately been suggested as alternatives to more traditional techniques. Variants of the MOESP type of subspace algorithms are in addition to open-loop identification applicable to closed-loop and errors-in-variables identification. In this paper, a new instrumental variable approach to subspace identification is presented. It is shown how existing MOESP-algorithms can be derived within the proposed framework, simply by changing instruments and weighting matrices. A noteworthy outcome of the analysis is that an improvement of an existing MOESP method for errors-in-variables identification can be proposed.     

Integrating virtual reference feedback tuning into a unified closed-loop identification framework

This paper compares particular instances of control-relevant identification, closed-loop identification, and controller identification (either in an actual loop or in a virtual reference feedback tuning approach, VRFT) problems. Significant similarities appear between them which allow, in particular, alternative formulations of the VRFT methodology in a differentiable setting.     

Optimization of boiler control to improve the load-following capability of power-plant units

The capability to perform fast load changes has been an important issue in the power market, and will become increasingly more so due to the increasing commercialization of the European power market. An optimizing control system for improving the loadfollowing capability of power-plant units has therefore been developed. The system is implemented as a complement, producing control signals to be added to those of the existing boiler control system, a concept which has various practical advantages in terms of implementation and commissioning. The optimizing control system takes account of the multivariable and load-dependent nonlinear characteristics of the boiler process, as a scheduled LQG controller with feedforward action is utilized. The LQG controller improves the control of critical process variables, making it possible to increase the load-following capability of a specific plant. Field tests on a 265 MW coal-fired power-plant unit reveals that the maximum allowable load gradient that can be imposed on the plant, can be increased from 4 to 8 MW/min.     

Control of a flexible rotor active magnetic bearing test rig: a characteristic model based all-coefficient adaptive control approach

Active magnetic bearings(AMBs) have found a wide range of applications in high-speed rotating machinery industry.The instability and nonlinearity of AMBs make controller designs difficult, and when AMBs are coupled with a flexible rotor, the resulting complex dynamics make the problems of stabilization and disturbance rejection, which are critical for a stable and smooth operation of the rotor AMB system, even more difficult. Proportional-integral-derivative(PID) control dominates the current AMB applications in the field. Even though PID controllers are easy to implement, there are critical performance limitations associated with them that prevent the more advanced applications of AMBs, which usually require stronger robustness and performance offered by modern control methods such as H-infinity control and μ-synthesis. However, these advanced control designs rely heavily on the relatively accurate plant models and uncertainty characterizations, which are sometimes difficult to obtain. In this paper, we explore and report on the use of the characteristic model based all-coefficient adaptive control method to stabilize a flexible rotor AMB test rig. In spite of the simple structure of such a characteristic model based all-coefficient adaptive controller,both simulation and experimental results show its strong performance.     

Duality between the discrete-time Kalman filter and LQ control law

In the context of linear quadratic Gaussian (LQG) controller design for single-input, single-output, discrete-time, linear, time-invariant systems, a duality is demonstrated between the Kalman filter design phase and the linear quadratic (LQ) design phase. Furthermore, an asymptotic recovery design procedure is proposed. Through specific Kalman filter design choices, the LQG open-loop transfer function is forced to approach the LQ open-loop transfer function     

LQG/LTR设计方法中的可变参数选择

LQG/LTR作为一种常见的多变量控制器设计方法,虽然设计步骤简单,但是设计过程中可变参数的选择却没有明确可行的参考原则,这一点使LQG/LTR方法的推广应用受到极大限制。该文以某型航空涡扇发动机LQG/LTR双输入-双输出控制器设计为例,给出LQG/LTR方法设计中可变参数和权矩阵的选择原则,并分析了按照这些原则所设计的发动机控制系统的性能。运用MATLAB仿真的结果证明,依据文中自由参数的选取方法可以获得理想的控制效果。