Limiting interactions in decentralized control of MIMO systems

Despite the closed-loop performance advantages of centralized multivariable controllers, the great majority of industrial process control applications is still based on decentralized controllers. Because of their single loop structure, decentralized controllers cannot suppress the interactions of the plant, which are only taken into account in the controller tuning phase. Therefore, it would be useful in many cases to delimit in some way the undesirable effects of the coupling between inputs and outputs of the closed loop system. A control algorithm to achieve this goal is developed in the paper. The proposal is applicable even to processes with non-minimum phase transmission zeros (provided their off-diagonal transfer functions have their zeros in the left-half-plane). Based on sliding mode attributes, the proposed scheme can be easily added to a previously designed decentralized control system.     

线性离散时间大系统次优分散控制器设计

在大系统分散控制器设计中,如果完全忽略各子系统之间的联系,控制性能往往较差,有 时甚至整个系统都不能稳定;如果完全考虑各子系统之间的联系,则通常需要求解一个高维问 题(其维数等于系统总阶数).为此,本文提出了一种简化设计方法,在求解某个子系统控制器 时,将该子系统以外的系统其余部分降阶,得到一个低阶近似系统,再求解由它们构成的分散 控制器设计问题,从而得到该子系统的控制器.该方法可以大大降低分散控制器设计问题的 复杂性,且控制性能甚好.     

多通道约束下的网络控制系统的最优跟踪性能

本文针对双通道约束下的线性时不变网络控制系统的随机信号跟踪性能极限问题进行了研究.网络通信包含通信噪声和通信带宽两种信道因素.被控系统考虑是非最小相位和不稳定系统,并且系统包含多个不同的非最小相位零点和多个不同的不稳定极点.对上行通道和下行通道都存在通信带宽约束及高斯白噪声影响的情形,从频域角度,通过采用双自由度控制器和尤拉参数化方法,获得了此类网络控制系统的最优可达的跟踪性能.研究结果表明网络控制系统的跟踪性能极限完全由被控对象的结构特征(非最小相位零点、不稳定极点以及被控对象的系统增益),参考输入信号和网络特性(高斯白噪声的统计特征、通信信道带宽)所决定.最后,仿真结果检证了所得结果的正确性.     

Fractional-order unstable pole-zero cancellation in linear feedback systems

As a very well-known classical fact, non-minimum phase zeros of the process put some limitations on the performance of the feedback system. The source of these limitations is that non-minimum phase zeros cannot be cancelled by unstable poles of the controller since such a cancellation leads to internal instability. The aim of this paper is to propose a method for fractional-order cancellation of non-minimum phase zeros of the process and studying its properties. It is specially shown that the proposed cancellation strategy increases the phase and gain margin without leading to internal instability. Since the systems with higher gain and phase margin are easier to control, the proposed method can be used to arrive at more effective controls, which is also verified by the simulation results.     

Adaptive minimum-variance and model-reference control for non-minimum phase systems

The well known minimum-variance adaptive controller and model-reference controller have been extended to include non-minimum phase systems. The simplicity of the original controllers is maintained. By allowing the intersample control signal to have two values, rather than one, the system zeros can be allocated to some prespecified locations. The stability issue related to both controllers for non-minimum phase systems is thus resolved.     

Suboptimal decentralized control over noisy communication channels

In this paper we present a technique for the design of decentralized controllers for mean square stability of a large scale system with cascaded clusters of subsystems. Each subsystem is linear and time-invariant and both system and measurement are subject to Gaussian noise. For stability analysis of this system we consider the effects of Additive White Gaussian Noise (AWGN) channels used for exchanging information between subsystems.     

互联大系统动态输出反馈多重叠鲁棒分散关联镇定

针对一类具有网型拓扑结构的互联大系统,提出一种动态输出反馈多重叠鲁棒分散关联镇定方法.该方法将系统状态空间加以扩展,在扩展空间中将其分解为按循环逆序排列的一系列两两子系统对,并为每个子系统对分别设计使其关联稳定的鲁棒分散动态输出反馈控制器,将这些多重叠设计的控制器再收缩回原空间,实现控制律的协调.将该方法应用到一个四区域网型电力系统控制设计中,仿真结果验证了所提出方法的可行性和优越性.     

Distributed model predictive control over network information exchange for large-scale systems

A class of large scale systems, which is naturally divided into many smaller interacting subsystems, are usually controlled by a distributed or decentralized control framework. In this paper, a novel distributed model predictive control (MPC) is proposed for improving the performance of entire system. In which each subsystem is controlled by a local MPC and these controllers exchange a reduced set of information with each other by network. The optimization index of each local MPC considers not only the performance of the corresponding subsystem but also that of its neighbours. The proposed architecture guarantees satisfactory performance under strong interactions among subsystems. A stability analysis is presented for the unconstrained distributed MPC and the provided stability results can be employed for tuning the controller. Experiment of the application to accelerated cooling process in a test rig is provided for validating the efficiency of the proposed method.     

Decentralized risk-sensitive controller design for strict-feedback systems

This paper studies decentralized control of uncertain systems. The class of systems focused on is a set of stochastic strict-feedback systems which interact through their outputs, and performance is measured with respect to a risk sensitive cost criterion. The unknown nonlinear interconnection terms are assumed to be bounded by some known functions of the outputs of the subsystems, multiplied by some unknown parameters. The controllers designed for each subsystem have access only to the information available with regard to the respective subsystem, and they achieve an arbitrarily small value for the risk-sensitive cost for the overall system. Under this completely decentralized control scheme, all closed-loop signals remain bounded in probability.     

A robust two degree-of-freedom controller for systems with both model and measurement uncertainty

This paper presents a design method for robust two degree-of-freedom (DOF) controllers that optimize the control performance with respect to both model uncertainty and signal measurement uncertainty. In many situations, non-causal feedforward is a welcome control addition when closed loop feedback bandwidth limitations exist due to plant dynamics such as: delays, non-minimum phase zeros, poorly placed zeros and poles (Xie, Alleyne, Greer, and Deneault (2013); Xie (2013), etc. However, feedforward control is sensitive to both model uncertainty and signal measurement uncertainty. The latter is particularly true when the feedforward is responding to pre-measured disturbance signals. The combined sensitivity will deteriorate the feedforward controller performance if care is not taken in design. In this paper a two DOF design is introduced which optimizes the performance based on a given estimate of uncertainties. The controller design uses H_∞ tools to balance the controlled system bandwidth with increased sensitivity to signal measurement uncertainties. A successful case study on an experimental header height control system for a combine harvester is shown as an example of the approach.     

Overlapping decentralized approach to automation generation control of multi-area power systems

An overlapping decentralized control scheme is presented and applied to automatic generation control (AGC) for multi-area power systems. Based on the inclusion principle, the system is first decomposed in the expanded space as a group of pair-wise subsystems (areas). Then, the decentralized controllers designed, by standard linear quadratic (LQ) control laws are implemented in each pair-wise subsystem. Finally, the overlapping decentralized controller is obtained by coordinating and contracting the pair-wise decentralized controllers from the expanded space to the original space, preserving the inclusion conditions. When applied to AGC of a four-area power system, the proposed methodology not only guarantees AGC qualities, but also increases the system reliability with respect to a wide variety of structured perturbations. Simulation results illustrate the effectiveness of the presented approach both in the general case of information structure constraints and in the cases when some pairs of subsystems are disconnected by unpredicted faults.     

Decentralized control of sequentially minimum phase systems

Fundamental limitations in decentralized control of systems with multivariable zeros are considered. It is shown that arbitrary bandwidth can be obtained with a stable block-diagonal controller, if certain subsystems of the open-loop system fail to have zeros in the right half-plane and a high-frequency condition holds. Implications on control structure design and sequential loop-closuring methods are discussed     

Plug-and-play model predictive control based on robust control invariant sets

We consider the problem of designing decentralized controllers for large-scale linear constrained systems composed by a number of interacting subsystems. As in Riverso et al. (2013b), (i) the design of local controllers requires limited transmission of information from other subsystems and (ii) the addition/removal of a subsystem triggers the design of local controllers for child subsystems only. These properties enable Plug-and-Play (PnP) operations, and we show how to perform them while preserving global stability of the origin and constraint satisfaction. We improve several aspects of the PnP design procedure proposed in Riverso et al. (2013b) and, using recent results in the computation of Robust Control Invariant (RCI) sets, we show that all critical steps in the design of a local controller can be solved through Linear Programming (LP). Finally, an application of the proposed design procedure to a large-scale mechanical system is presented.     

Decentralized model reference adaptive control without restrictionon subsystem relative degrees

When the direct model reference adaptive control (MRAC) scheme with first-order local estimators is employed to design totally decentralized controllers, the stability result can only be applied to a system with all of its nominal subsystem relative degrees less than or equal to two. In this paper, this restriction is relaxed and it is achieved by employing the parameter projection together with static normalization. To implement the local controllers, no a priori knowledge of the subsystem unmodeled dynamics and no information exchange between subsystems are required. Global stability is established for the closed-loop system and small in the mean tracking error is ensured. With this analysis, the class of interactions and subsystem unmodeled dynamics can be enlarged to include those having infinite memory     

Fundamental limitation on achievable decentralized performance

A commonly accepted fact is that the diagonal structure of the decentralized controller poses fundamental limitations on the achievable performance, but few quantitative results are available for measuring these limitations. This paper provides a lower bound on the achievable quality of disturbance rejection using a decentralized controller for stable discrete time linear systems with time delays, which do not contain any finite zeros on or outside the unit circle. The proposed result is useful for assessing when full multivariable controllers can provide significantly improved performance, as compared to decentralized controllers. The results are also extended to the case, where the individual subcontrollers are restricted to be PID controllers.     

Virtual Reference Feedback Tuning for non-minimum phase plants

Model reference control design methods fail when the plant has one or more non-minimum phase zeros that are not included in the reference model, leading possibly to an unstable closed loop. This is a very serious problem for data-based control design methods, where the plant is typically unknown. In this paper, we extend the Virtual Reference Feedback Tuning method to non-minimum phase plants. This extension is based on the idea proposed in Lecchini and Gevers (2002) for Iterative Feedback Tuning. We present a simple two-step procedure that can cope with the situation where the unknown plant may or may not have non-minimum phase zeros.     

Performance limitations in the robust servomechanism problem for discrete time periodic systems

Fundamental limitations for error tracking/regulation are obtained for the robust servomechanism problem (RSP) for discrete time periodic systems. In studying this problem, the RSP for a multi-input/multi-output discrete time system is considered; application of these results is then made to the “periodic system robust servomechanism problem”, and explicit expressions for the limiting costs for error tracking regulation are obtained. These limitations can be characterized completely by the number and location of the non-minimum phase transmission zeros of the system's associated lifted system, together with a term which depends on the order of the system, the number of inputs, the number of transmission zeros and the system's period.     

Stability of Large Space Structures Preserved Under Failures of Local Controllers

This note considers position and attitude control of large space structures composed of a number of subsystems (substructures) interconnected by flexible links. A decentralized control law of dynamic displacement feedback compatible with subsystems is applied under the assumption that sensors and actuators are collocated. It has been known that the overall closed-loop system is robustly stable against uncertainties in mass, damping, and stiffness, if rigid modes of each subsystem are controllable and observable. The objective of this note is to derive conditions for the overall system to be stable even when some local controllers fail. The conditions are expressed in terms of the stiffness (or damping) matrices and interconnection location matrices of the subsystems whose local controllers fail     

Decentralized adaptive stabilization in the presence of unknown backlash-like hysteresis

Due to the difficulty of handling both hysteresis and interactions between subsystems, there is still no result available on decentralized stabilization of unknown interconnected systems with hysteresis, even though the problem is practical and important. In this paper, we provide solutions to this challenging problem by proposing two new schemes to design decentralized output feedback adaptive controllers using backstepping approach. For each subsystem, a general transfer function with arbitrary relative degree is considered. The interactions between subsystems are allowed to satisfy a nonlinear bound with certain structural conditions. In the first scheme, no knowledge is assumed on the bounds of unknown system parameters. In case that the uncertain parameters are inside known compact sets, we propose an alternative scheme where a projection operation is employed in the adaptive laws. In both schemes, the effects of the hysteresis and the effects due to interactions are taken into consideration in devising local control laws. It is shown that the designed local adaptive controllers can ensure all the signals in the closed-loop system bounded. A root mean square type of bound is obtained for the system states as a function of design parameters. This implies that the transient system performance can be adjusted by choosing suitable design parameters. With Scheme II, the proposed control laws allow arbitrarily strong interactions provided their upper bounds are available. In the absence of hysteresis, perfect stabilization is ensured and the L₂ norm of the system states is also shown to be bounded by a function of design parameters when the second scheme is applied.