A quantitative feedback solution to the multivariable tracking error problem

This paper introduces a novel solution for the multi‐input multi‐output (MIMO) quantitative feedback theory control design problem with tracking error specifications. Looking for a minimum controller overdesign, the technique finds new controller quantitative feedback theory bounds based on necessary and sufficient conditions for the existence of suitable associated prefilter matrix elements. It improves previous approaches to the subject and includes (i) the possibility of a free selection of the nominal plant, (ii) a less conservative application of the Schwartz inequality to decisively reduce the potential controller overdesign, (iii) a methodology to design independently the elements of the prefilter matrix, and (iv) a scope of application to both sequential and nonsequential MIMO controller design methods. The benefits of the new control design technique are illustrated by means of two examples. The first one, a standard 2 × 2 MIMO problem, is provided for comparison purposes with previous approaches. The second example, included as a major control challenge, deals with a well‐known demanding distillation column benchmark problem. Copyright © 2013 John Wiley & Sons, Ltd.     

基于控制参数化的注塑工业过程最优反馈控制方法

本文针对一类典型的注塑工业过程系统, 研究了注塑填充过程中产生的熔体流动速度最优跟踪控制问题, 提出了一种基于控制参数化的计算最优反馈控制器设计方法以实现注塑过程中熔融聚合物流动前沿位移的最优跟 踪控制, 进而达到改善注塑零件性能的高效生产目标. 首先, 面向注塑工艺复杂生产过程建立了动态过程系统数学 模型, 提出了注塑机内部熔融聚合物流动前沿位置的动态最优跟踪控制问题; 其次, 设计了一种多级反馈控制律, 通 过控制参数化方法将控制反馈核进行了参数化表示, 将控制器设计问题转化为一序列最优参数决策问题; 然后, 通 过状态灵敏度方程分析方法, 求解出了目标函数及约束条件关于决策变量参数梯度信息的显式表达式, 并基于所提 供的梯度信息结合序列二次规划算法进行了高效优化迭代求解; 最后, 通过实验仿真验证了本文所提出的最优反 馈控制器设计方法的可行性和有效性.     

Quantitative feedback control for multivariable model matching and disturbance rejection

This article extends two recent contributions in the field of quantitative feedback theory to the multivariable case. They concern the model matching and the measured disturbance rejection problems. The model matching problem is a tracking control problem with specifications given as acceptable deviations from an ideal response. The measured disturbance rejection problem balances feedback and feedforward actions to reject disturbances. Both perspectives present advantages over classical quantitative feedback theory techniques in certain situations. This paper develops the necessary tools to solve both control problems in the case of multi‐input multi‐output plants. In particular, it shows how to derive nonconservative controller bounds for each of the single‐input single‐output control problems in which the overall multivariable problem is divided. The result is a systematic controller design methodology for multi‐input multi‐output plants with structured uncertainty. The application of the technique to the well‐known quadruple‐tank process illustrates the benefits of the method. Copyright © 2016 John Wiley & Sons, Ltd.     

基于ADP的导引控制一体化全状态受限反演控制

针对导引控制一体化设计中状态受限及非线性最优问题，提出了一种结合反演控制与自适应动态规划（ADP）技术，考虑全状态受限的新型导引控制一体化设计方法.首先，将状态受限的严格反馈系统通过坐标变换转化为非状态受限系统.然后，采用前馈反演控制与反馈最优控制相结合的设计思路，利用ADP技术在线求解非线性HJB方程得到最优解.最后通过李亚普诺夫理论证明了系统的闭环稳定性与所有信号的一致有界性.与传统方法的对比仿真验证了该设计方法的可行性与优越性.     

Prescribed performance adaptive neural output feedback dynamic surface control for a class of strict‐feedback uncertain nonlinear systems with full state constraints and unmodeled dynamics

This paper studies the output feedback tracking control problem for a class of strict‐feedback uncertain nonlinear systems with full state constraints and unmodeled dynamics using a prescribed performance adaptive neural dynamic surface control design approach. A nonlinear mapping technique is employed to address the state constraints. Radial basis function neural networks are utilized to approximate the unknown nonlinear functions. The unmodeled dynamics is addressed by introducing an available dynamic signal. Subsequently, we construct the controller and parameter adaptive laws using a backstepping technique. Based on Lyapunov stability theory, it is shown that all signals in the closed‐loop system are semiglobally uniformly ultimately bounded and that the tracking error always remains within the prescribed performance bound. Simulation results are presented to demonstrate the effectiveness of the proposed control scheme.     

Simultaneous Design of Parallel Distributed Output Feedback and Anti‐windup Compensators for Constrained Takagi‐Sugeno Fuzzy Systems

This paper is devoted to developing a novel approach to deal with constrained continuous‐time nonlinear systems in the form of Takagi‐Sugeno fuzzy models. Here, the disturbed systems are subject to both input and state constraints. The one‐step design method is used to simultaneously synthesize the dynamic output feedback controller and its anti‐windup strategy. A parameter‐dependent version of the generalized sector condition is used together with Lyapunov stability theory to derive linear matrix inequality design conditions. Based on this result and for different design specifications, the synthesis of an anti‐windup based dynamic output feedback controller is expressed on the form of convex optimization problems. A physically motivated example is given to illustrate the effectiveness of the proposed method.     

A combined QFT/H ∞ design technique for TDOF uncertain feedback systems

A new way of incorporating QFT principles into H X -control design techniques for solving the two-degrees of freedom feedback problem with highly uncertain plants is developed. The proposed practical design approach consists of two stages. In the first stage, the robustness problem, due to plant uncertainties, is solved by H X -norm optimization. In this stage, the controller inside the loop (the first degree of freedom) is designed, with the ultimate goal of minimizing the cost of feedback. Minimization of the sensor white noise amplification at the input to the plant is also performed using QFT principles. In the second stage of the design, the prefilter outside the loop (the second degree of freedom), is used to achieve the tracking specifications by conventional classical control theory, as practiced by the QFT design procedure. The combined QFT/H X design procedure for single input-single output (SISO) feedback systems is directly applicable to multi input-multi output (MIMO) feedback uncertain systems. The efficiency of the proposed technique is demonstrated with SISO and MIMO design examples for higly uncertain plants.     

Frequency‐based nonlinear controller design for regulating systems subjected to time‐domain constraints

Presented is a nonlinear controller design methodology for a class of linear regulating systems subjected to quantitative time‐domain constraints. The design objective is to satisfy an output time‐domain tolerance given an actuator saturation constraint despite an external step disturbance. The goal is to increase the allowable magnitude of the external disturbance beyond that achievable via linear control subject to the time‐domain specifications. The controller design process is comprised of two phases. In the first phase, a linear controller is designed that balances the trade‐off between output regulation and required actuation. To realize the linear design, the time‐domain performance specifications are mapped into amplitude and phase constraints which are in turn imposed on the frequency response of the linear open‐loop transfer function. In the second phase, the linear controller is then augmented with an odd nonlinearity. The coefficient for the nonlinear term is designed such that the gain and phase distortions (in the sense of describing functions) meet the frequency‐domain constraints. The describing function calculation is automated by a recursive Volterra Series relationship. The nonlinear controller design methodology is experimentally verified on the idle speed control of a Ford 4.6L V‐8 fuel injected engine. Copyright © 2000 John Wiley & Sons, Ltd.     

Short-time parameter optimization with flight control application

A design approach is presented for systems operating over a relatively short period of time about various operating points with state variable constraints. This class of problems is especially relevant to certain flight control problems. The design approach is applied to a simplified model of longitudinal dynamics of the F-4 aircraft operating in three widely separated flight conditions. A linear model is assumed about each operating point. Control is achieved via constrained state feedback. The basic problem is then to minimize a suitable integral quadratic performance measure subject to state variable constraints. The main theoretical result is theorem 1 which supplies the inequality constraints required to guarantee short-time stability. The short-time optimization problem is ultimately reduced to a nonlinear programming problem with inequality constraints.     

Finite‐time boundedness of large‐scale systems with actuator faults and gain fluctuations

This paper addresses the issue of finite‐time boundedness of large‐scale interconnected systems with the use of a distributed nonfragile fault‐tolerant controller. The objective of this paper is to design a state‐feedback controller consisting of a time‐varying delay such that the resulting closed‐loop system is finite‐time bounded under a prescribed extended passivity performance level even in the presence of all admissible uncertainties and possible actuator faults. More precisely, based on the Lyapunov‐Krasovskii stability theory, a new set of sufficient conditions is obtained in the framework of linear matrix inequality constraints that ensures finite‐time boundedness and satisfies the prescribed extended passivity performance index of the considered system. Finally, two numerical examples, including the interconnected inverted pendulum, are given to show the effectiveness of the proposed controller design technique.     

A data‐driven bilinear predictive controller design based on subspace method

In this paper, a new data‐driven model predictive control (MPC), based on bilinear subspace identification, is considered. The system's nonlinear behavior is described with a bilinear subspace predictor structure in an MPC framework. Thus, the MPC formulation results in a fixed structure objective function with constraints regardless of the underlying nonlinearity. For unconstrained systems, the identified subspace predictor matrices can be directly used as controller parameters. Therefore, we design optimization algorithms that exploit this feature. The open‐loop optimization problem of MPC that is nonlinear in nature is solved with series quadratic programming (SQP) without any approximations. The computational efficiency already demonstrated with the current formulation presents further opportunities to enable online control of nonlinear systems. These improvements and close integration of modeling and control also eliminate the intermediate design step, which provides a means for data‐driven controller design in generalized predictive controller (GPC) framework. Finally, the proposed control approach is illustrated with a verification study of a nonlinear continuously stirred tank reactor (CSTR) system. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust Stability and Stabilization of Positive Interval Systems Subject to Actuator Saturation

This paper addresses the stabilization problem for a class of uncertain positive linear systems (PLSs) in the presence of saturating actuators. The objective is to obtain sufficient conditions for the robust stability of PLSs and to design robust state feedback control laws such that the closed‐loop uncertain system is asymptotically stable and positive at the origin with a large domain of attraction. Several sufficient conditions for robust stabilization and positivity are derived via the Lyapunov function approach and convex analysis method for both the discrete‐time and the continuous‐time cases, respectively. The state feedback controller design and the estimation of the domain of attraction are presented by solving a convex optimization problem with linear matrix inequalities (LMIs) constraints. A numerical example is given to show the effectiveness of the proposed methods.     

Mixed‐Objective Robust Dynamic Output Feedback Controller Synthesis for Continuous‐Time Polytopic Lpv Systems

A robust dynamic output feedback controller synthesis algorithm considering H_∞/H₂ performance and regional pole placement is addressed for a nonlinear system with parameter uncertainties and external disturbance. First, the formulation of a gain‐scheduled mixed‐objective robust dynamic output feedback controller for continuous‐time polytopic linear parameter varying (LPV) systems is presented. To reduce conservativeness, some auxiliary slack variables and parameter‐dependent Lyapunov functions are employed in addition to well‐established performance conditions. Then, sufficient conditions for the desired gain‐scheduled mixed‐objective robust dynamic output feedback controllers are cast into an efficiently tractable finite‐dimensional convex optimization problem in terms of linear matrix inequalities (LMIs). Finally, numerical simulation shows the validity of the proposed controller, which has good stability, strong robustness, satisfied disturbance attenuation ability, and smooth dynamic properties.     

Multi-objective constraint optimizing IOL control of distillation column with nonlinear observer

Performance of input–output linearizing (IOL) controllers suffers due to constraints on input and output variables. This problem is successfully tackled by augmenting IOL controllers with quadratic dynamic matrix controller (QDMC). However, this has created a constraint-mapping problem for coupled MIMO systems like distillation column. A multi-objective optimization problem needs to be solved to map the constraints on inputs. A suitable transformation technique is proposed to convert this multi-objective optimization problem to a single objective one. This makes the controller less computationally intensive and easy to implement. This controller (IOL-QDMC) along with nonlinear observer is implemented on a binary distillation column for dual composition control. Its performance is evaluated against a quadratic dynamic matrix controller (QDMC) and input–output linearization with PI controller (IOL-PI).     

Two-degree-of-freedom H∞-optimization ofmultivariable feedback systems

A solution to the two-degree-of-freedom H_∞ -minimization problem that arises in the design of multivariable optimal continuous-time stochastic control systems is derived. A decoupling approach that enables a partially independent design of the prefilter and the feedback controller and yields a simple solution to the optimization problem is applied. This solution is obtained by transforming the optimization problem into two standard form (four-block) problems     

Suboptimal design of intentionally nonlinear controllers

A method of designing nonlinear controls for stationary plants is presented in the paper. The objective of the design is to produce soft-saturation-type constraints on certain state variables, such as velocity or acceleration. This is accomplished by formulating the problem as an optimization of a nonquadratic performance index. A sequence of suboptimal controls is then obtained. Although this sequence converges to the exact optimum solution, the procedure is stopped when the complexity of the resulting non-linear controller exceeds the design considerations of cost, size, and/or reliability. Experimental results of an actual design clearly indicate the desired velocity saturation effects.     

State‐constrained stabilization of beam‐balance systems

We present nonlinear control techniques to stabilize a beam‐balance system with state constraints. We consider two different actuator configurations: the first one is actuated by a cart moving on the beam, while in the second case, the actuation is by a single electromagnet. In the first case, the constrained stabilization problem is solved via an output feedback controller designed using feedback linearization, Luenberger‐like observer and linear matrix inequality based optimization. In the second case, a Lyapunov‐based controller is proposed that takes care of both the input and state constraints. Copyright © 2007 John Wiley & Sons, Ltd.     

Optimal two-degree-of-freedom fuzzy control for locomotion control of a hydraulically actuated hexapod robot

Locomotion control of legged robots is a very challenging task because very accurate foot trajectory tracking control is necessary for stable walking. An electro-hydraulically actuated walking robot has sufficient power to walk on rough terrain and carry a heavier payload. However, electro-hydraulic servo systems suffer from various shortcomings such as a high degree of nonlinearity, uncertainty due to changing hydraulic properties, delay due to oil flow and dead-zone of the proportional electromagnetic control valves. These shortcomings lead to inaccurate analytical system model, therefore, application of classical control techniques result into large tracking error. Fuzzy logic is capable of modeling mathematically complex or ill-defined systems. Therefore, fuzzy logic is becoming popular for synthesis of control systems for complex and nonlinear plants. In this investigation, a two-degree-of-freedom fuzzy controller, consisting of a one-step-ahead fuzzy prefilter in the feed-forward loop and a PI-like fuzzy controller in the feedback loop, has been proposed for foot trajectory tracking control of a hydraulically actuated hexapod robot. The fuzzy prefilter has been designed by a genetic algorithm (GA) based optimization. The prefilter overcomes the flattery delay caused by the hydraulic dead-zone of the electromagnetic proportional control valve and thus helps to achieve better tracking. The feedback fuzzy controller ensures the stability of the overall system in the face of model uncertainty associated with hydraulically actuated robotic mechanisms. Experimental results exhibit that the proposed controller manifests better foot trajectory tracking performance compared to single-degree-of-freedom (SDF) fuzzy controller or optimal classical controller like state feedback LQR controller.     

Adaptive optimal dynamic surface control of strict‐feedback nonlinear systems with output constraints

In this paper, an adaptive optimal control strategy is proposed for a class of strict‐feedback nonlinear systems with output constraints by using dynamic surface control. The controller design procedure is divided into two parts. One is the design of feedforward controller and the other is the design of optimal controller. To guarantee the satisfaction of output constraints in feedforward controller, nonlinear mapping is utilized to transform the constrained system into an unconstrained system. Neural‐network based adaptive dynamic programming algorithm is employed to approximate the optimal cost function and the optimal control law. By theoretical analysis, all the signals in the closed‐loop system are proved to be semi‐globally uniformly ultimately bounded and the output constraints are not violated. A numerical example illustrates the effectiveness of the proposed scheme.     

Robust plant by plant control design using model‐error tracking sets

This paper presents a method for designing a robust two‐degree‐of‐freedom control scheme, capable of satisfying multiple model‐error specifications on a plant by plant basis. Traditional quantitative feedback theory methods generally use a single model‐error or above‐below magnitude tracking specification, which can result in overdesign for plants located away from the bounding conditions. The performance specifications are also generally hand‐tuned, or iteratively adjusted to keep the underlying time‐domain signals within permissible levels. Our method aims to perform a model‐error design on a per‐plant basis, such that each plant's corresponding model tracking has equal weighting given the plant's inherent feedback requirements and capability. The quantitative feedback theory method allows this per‐plant approach to be undertaken with ease. Additionally, sufficiently low‐order model specifications are designed using simple optimisation, which take into account performance limiting effects, such as non‐minimum phase behaviour and signal constraints. A worked example is presented, showing the viability and transparency of the proposed method.