Design of a Robust Optimal Decentralized PI Controller Based on Nonlinear Constraint Optimization For Level Regulation: An Experimental Study

This paper presents the development of a new robust optimal decentralized PI controller based on nonlinear optimization for liquid level control in a coupled tank system. The proposed controller maximizes the closed-loop bandwidth for specified gain and phase margins, with constraints on the overshoot ratio to achieve both closed-loop performance and robustness. In the proposed work, a frequency response fitting model reduction technique is initially employed to obtain a first order plus dead time (FOPDT) model of each higher order subsystem. Furthermore, based on the reduced order model, a proposed controller is designed. The stability and performance of the proposed controller are verified by considering multiplicative input and output uncertainties. The performance of the proposed optimal robust decentralized control scheme has been compared with that of a decentralized PI controller. The proposed controller is implemented in real-time on a coupled tank system. From the obtained results, it is shown that the proposed optimal decentralized PI controller exhibits superior control performance to maintain the desired level, for both the nominal as well as the perturbed case as compared to a decentralized PI controller.      

参数不确定机器人分散鲁棒跟踪控制

提出了一种新的参数不确定机器人分散控制器设计方法．首先将关节子系统的动力学模型分解为人工标称模型和非线性时变不确定模型两部分；然后分别设计相应的标称控制器和鲁棒补偿器．标称控制器使得标称闭环系统具有理想的跟踪性能；鲁棒补偿器可以抑制参数不确定和关节间非线性耦合等因素的影响，实现鲁棒跟踪．所设计的控制器只需要局部关节的位置反馈，具有易于实现和可在线调整的优点．仿真结果说明了该方法的有效性．     

An LMI approach to dencentralized H8 control

We consider the design of a decentralized controller for a linear time invariant (LTI) system. This system is modelled as an interconnection of subsystems. For every subsystem, a linear time invariant controller is sought such that the overall closed loop system is stable and achieves a given H performance level. The main idea is to design every local controller such that the corresponding closed loop subsystem has a certain input-output (dissipative) property. This local property is constrained to be consistent with the overall objective of stability and performance. The local controllers are designed simultaneously, avoiding the traditional iterative process: both objectives (the local one and the global one) are achieved in one shot. Applying this idea leads us to solving the following new problem: given an LTI system, parameterize all the dissipative properties which can be achieved by feedback. The proposed approach leads to solving convex optimization problems that involve linear matrix inequality constraints.     

Robust adaptive fault tolerant control for a process with actuator faults

This paper studies design and implementation of an enhanced multivariable adaptive control scheme for an uncertain nonlinear process exposed to actuator faults. For adaptive fault compensation, a model reference adaptive control (MRAC) strategy is utilized as main controller. A new adaptation algorithm making possible to improve transient performance of adaptive control is integrated to the controller. With the help of further modifications, some restrictive conditions on multivariable adaptive design are relaxed so that the system requires less plant information. The resulting controller has a simpler structure than the other matrix factorization based controllers. At the final stage of design, a robust adaptive control scheme is obtained with consideration of practical implementation problems such as sensor noises, external disturbances and unmodeled​ system dynamics. It is proved that the controller guarantees closed-loop signal boundedness and asymptotic output tracking. Real-time experiment results acquired from quadruple tank benchmark system are presented in order to exhibit the effectiveness of the proposed scheme.     

Robust model-following controller design for LTI systems affected by parametric uncertainties: a design example for aircraft motion

This article addresses the design problem of a robust model-following controller (MFC) which minimises the error between plant controlled output and model output for a linear time-invariant (LTI) plant system affected by parametric uncertainties and an LTI target model. To design such an MFC, a previously proposed MFC scheme, whose applicability has already been demonstrated with flight controller design, is adopted in this article. Our design procedure is as follows: first, a basic MFC is designed using the nominal LTI plant model and the LTI target model while a structured free matrix in the MFC is not assigned; second, model-following performance of the MFC for appropriately defined disturbance input and model input for the parametric uncertain plant model and the LTI target model is minimised using the structured free matrix; and finally, a robust MFC is obtained using the basic MFC and the optimal structured matrix. In the second step, an iterative design method for robust H ₂ controllers for LTI parameter-dependent (LTIPD) systems using parameter-dependent Lyapunov functions (PDLFs), which is also proposed in this article, is applied. Two MFCs for the lateral-directional (L/D) motions of a research aircraft, which has been developed for an in-flight simulator, for two different real aircraft models, i.e. a Boeing 747 model and a Lockheed Jetstar model, are designed and their performance is confirmed via numerical simulations and flight tests.     

Decentralized robust output feedback control for control affine nonlinear interconnected systems

In this paper, a scheme for decentralized robust control for control affine nonlinear interconnected systems using linear matrix inequalities (LMIs) is presented. Based on the Lyapunov theory, sufficient conditions for closed-loop stability of a nonlinear system, reference input tracking, and disturbance attenuation over its operating-range are obtained. Then, achieving these sufficient conditions are formulated as local LMI optimization problems. By solving the appropriately defined local problems, provided the obtained sufficient conditions are satisfied, the closed-loop stability, input tracking, and disturbance attenuation over the operating-range of the system are guaranteed. The designed controller is linear whose implementation is straightforward. An example is given to illustrate the proposed methodology.     

Quantizer design for interconnected feedback control systems

In this paper, we consider the design of interconnected H-infinity feedback control systems with quantized signals. We assume that a decentralized static output feedback has been designed for an interconnected continuous-time LTI system so that the closed-loop system is stable and a desired H-infinity disturbance attenuation level is achieved, and that the subsystems’ measurement outputs are quantized before they are passed to the local controller. We propose a localoutput- dependent strategy for updating the quantizers’ parameters, so that the overall closed-loop system is asymptotically stable and achieves the same H-infinity disturbance attenuation level. Both the pre-designed controllers and the quantizers’ parameters are constructed in a decentralized manner, depending on local information.     

Robust guaranteed cost control of uncertain fuzzy systems under time-varying sampling

In practice, the system is often modeled as a continuous-time fuzzy system, while the control input is applied only at discrete instants. This system is called a sampled-data control system. In this paper, robust guaranteed cost control for uncertain sampled-data fuzzy systems is discussed. A guaranteed cost control where a quadratic cost function is bounded by a certain scalar, not only stabilizes a system but also considers a control performance. A typical sampled-data control is the zero-order input, which can be represented as a piecewise-continuous delay. Here we take a delay system approach to the sampled-data guaranteed cost control problem. The closed-loop system with a sampled-data state feedback controller becomes a system with time-varying delay. First, guaranteed cost control performance conditions for the closed-loop system are given in terms of linear matrix inequalities (LMIs). Such conditions are derived by using Leibniz–Newton formula and free weighting matrix method for fuzzy systems under the assumption that sampling time is not greater than some prescribed scalar. Then, a design method of robust guaranteed cost state feedback controller for uncertain sampled-data fuzzy systems is proposed. Examples are given to illustrate our robust sampled-data guaranteed cost control design.     

Decentralized robust H<Subscript>∞</Subscript> output feedback control for value bounded uncertain large-scale interconnected systems

In this paper, decentralized robust H_∞ output feedback control problem for large-scale interconnected system with value bounded uncertainties in the state, control input and interconnection matrices is investigated. A new bounded real lemma for the large-scale interconnected systems is derived by Lyapunov stability theory and linear matrix inequality method. Based on the new bounded real lemma, a sufficient condition expressed as matrix inequalities for the existence of a decentralized robust H_∞ output feedback controller is obtained. The controller which enables the closed-loop large-scale system robust stable and satisfies the given H_∞ performance is designed through a homotopy iterative method. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.     

PI tracking control for nonlinear time-varying delay Markov jump systems

This paper considers robust stochastic stability and PI tracking control problem for Markov jump systems with both input delay and an unknown nonlinear function. Based on the traditional PI control strategy, a new controller design scheme is proposed for nonlinear time-delay Markov jump systems which can realize multiple control objectives including robust stochastic stability and tracking performance. By using the Lyapunov stability theory and LMI algorithms, a sufficient condition for the solution to robust stochastic stability and tracking control problem is obtained. Then, the desired controller with PI structure is designed, which ensures the resulting closed-loop system is robust stochastically stable and the system state has favorable tracking performance. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.     

Design of decentralized robust load-frequency controller based on SVD method

A decentralized robust control scheme is presented for the load-frequency control of interconnected power systems with uncertain parameters. A singular value decomposition (SVD) technique and Lyapunov stability theory are adopted to implement a decentralized robust controller. The stability analysis of the closed-loop interconnected systems for all admissible uncertainties is discussed. The performance robustness of the proposed decentralized robust control scheme has been verified through simulation studies on a two-area power system model. The effectiveness of the decentralized control algorithm is compared to that of a centralized robust one. It has been found that both control schemes have almost the same performance with integral control action in the presence of parametric uncertainty in the plant.     

不确定奇异大系统分散鲁棒预测控制

针对一类不确定奇异关联大系统,讨论了当系统状态不可测时,基于输出反馈的分散鲁棒预测控制问题.通过构造Lyapunov函数以及应用线性矩阵不等式方法,将"min-max"优化问题转化为凸优化问题求解,从而得到了输出反馈分散控制器存在的充分条件和显示表达式.证明了优化问题在初始时刻的可行解能保证奇异闭环大系统渐近稳定且正则无脉冲.仿真结果验证了算法的有效性.     

Robust synthesis of a PID controller by uncertain multimodel approach

This paper presents an effective method to design a PID (or PI) controller for nonlinear systems where desirable robustness and performance properties must be maintained across a large range of operating conditions. For this purpose, an uncertain multimodel of the original nonlinear system is used. The uncertainties affecting the system are treated as stochastic matrices. Based on this multimodel representation a robust PID controller can be designed in order to obtain acceptable performance for all operating conditions. Numerical examples show the practical applicability of the proposed method.     

具有测量数据丢失的大系统鲁棒H∞控制

研究一类具有测量数据丢失的大系统分散H∞控制器设计问题.针对由个子系统构成的线性离散大系统,假设测量数据丢失满足已知概率的Bernoulli分布,采用线性矩阵不等式方法给出了分散H∞控制器存在的充分条件,所设计的控制器使得闭环系统均方指数稳定,且满足指定的H∞性能指标.通过仿真例子验证了该方法的有效性.     

基于Vinnicombe距离的迭代辨识与控制设计

迭代辨识与控制设计的主要问题在于保证控制设计的稳定性和闭环性能的不断改善. 针对该问题, 本文提出一种基于Vinnicombe距离的迭代辨识与控制设计方法. 每次迭代辨识使用上次设计的控制器, 通过闭环辨识得到包含真实系统的不确定模型集合, 设计镇定这个集合的控制器; 同时提出迭代辨识过程闭环性能改善条件, 以及控制器的设计方法. 仿真结果显示了该方法的有效性.     

具有扇形执行器的多机电力系统气门开度的时滞无关镇定

本文研究了具有扇形执行器的多机电力系统气门开度的时滞无关分散控制器和鲁棒分散控制器的设计问题.首先利用三角变换把非线性关联函数变换为子系统状态变量的二次有界不等式形式,然后基于Lyapunov稳定性理论,推导出闭环多机电力系统及其参数不确定系统渐近稳定的线性矩阵不等式(LMI)充分条件,最后以两机无穷大母线系统为例进行了仿真分析,验证了所提方法的有效性.     

A model reference quantitative feedback design theory with application to turbomachinery

A new decentralized robust control design framework, model reference quantitative feedback design (MRQFD), is developed for the design of the MIMO parametric uncertain control systems. An internal model reference loop is proposed to obtain the achievement of generalized diagonal dominance (GDD) and the reduction of uncertainty in the resultant compensated internal loop system. Based on nonnegative matrix theory, a useful design guide is derived to achieve the GDD condition for the internal model reference loop. Then a sensitivity-based quantitative feedback design (QFD) method is developed and used to solve the resulting series of single-loop QFD problems. The MIMO quantitative specifications are guaranteed to be satisfied by the proposed design framework for largely uncertain systems. A successful application to the design of a robust multivariable controller for the Allison PD-514 aircraft turbine engine is presented to demonstrate the effectiveness of the methodology developed here.     

High-performance decentralized control design for general interconnected systems with applications in cooperative control

This paper deals with the decentralized control of an interconnected system, where each subsystem has models of all other subsystems (subject to uncertainty). A decentralized controller is constructed based on a reference centralized controller. It is shown that when a priori knowledge of each subsystem about the other subsystems’ models is exact, then the decentralized closed-loop system can perform exactly the same as its centralized counterpart. An easy-to-check necessary and sufficient condition for the internal stability of the decentralized closed-loop system is obtained. Moreover, the stability of the closed-loop system in the presence of the perturbation in the parameters of the system is investigated, and it is shown that the decentralized control system is probably more robust than its centralized counterpart. A proper cost function is then defined to evaluate the closeness of the decentralized closed-loop system to the corresponding centralized control system. This enables the designer to obtain the maximum allowable standard deviation for the modelling errors of the subsystems to achieve a satisfactorily small relative performance deviation with a sufficiently high probability. Finally, the proposed method is exploited to design a near-optimal decentralized control law with respect to a quadratic cost function, whose performance can, under certain conditions, be equal to the minimum achievable performance index corresponding to the centralized LQR control law. The effectiveness of the proposed method is demonstrated in three numerical examples.