Automatic tuning of decentralized PID controllers for MIMO processes

An automatic tuning algorithm for decentralized PID control in multiple-input multiple-output (MIMO) plants is presented. This algorithm generalizes the authors' recent auto-tuner for two-input two-output systems to any number of inputs and outputs. The algorithm consists of two stages. In the first, the desired critical point, which consists of the critical gains of all the loops and a critical frequency, is identified. The auto-tuner identifies the desired critical point with almost no a priori information about the process. During the identification phase all controllers are replaced by relays, thus generating limit cycles with the same period in all loops. It is shown that each limit cycle corresponds to a single critical point of the process. By varying the relays parameters different points can be determined. The auto-tuner contains a procedure which converges rapidly to the desired critical point while maintaining the amplitudes of the process variables as well as of the manipulated variables within prespecified ranges. In the second stage, the data of the desired critical point is used to tune the PID controllers by the Ziegler-Nichols rules or their modifications. This paper focuses on the first stage. The steady-state process gains, which are required for the appropriate choice of the desired critical point, are determined by the auto-tuner in closed-loop fashion simultaneously with the identification of the critical point. The identification of the process gains is achieved at no extra plant time. Based upon a large number of simulated cases, the proposed auto-tuner seems to be efficient and robust. The paper discusses the underlying principles of the auto-tuner and its properties and capabilities are demonstrated via examples.     

Design of decentralized reliable controllers for large-scale systems

A methodology is developed in this paper for the design of decentralized reliable controllers for large-scale systems. The overall system is decomposed into a group of interconnected subsystems for which local decentralized controllers are designed to ensure the reliability of the overall system, taking into consideration the effect of changes in the system components characteristics and the system structure. The design procedure allows us to find a lower limit for the degree of stability of the subsystems under a wide range of environmental conditions. Finally, the developed methodology is illustrated through a case study.     

Reliable decentralized PID controller synthesis for two-channel MIMO processes

Reliable stabilization and regulation of two-channel decentralized multi-input multi-output (MIMO) control systems is considered. The system has integral-action due to using proportional + integral + derivative (PID) controllers. Closed-loop stability and asymptotic tracking of step-input references are achieved at each output channel when all controllers are operational. Stability is maintained when one of the controllers fails completely and is set to zero. Controller synthesis procedures are proposed for stable MIMO plants and for several unstable MIMO plant classes that admit PID controllers. These synthesis procedures are applied to various examples of process systems to illustrate the design methodology.     

Design of stable decentralized adaptive model-following controllers for large-scale systems

A decentralized model reference adaptive control for a class of large-scale inter-connected systems is developed. The proposed scheme does not require identification of the system parameters, or satisfaction of perfect model-following conditions (PMFC). The boundedness of the output error and the controller parameters is guaranteed using Lyapunov stability theory. The effectiveness of the developed algorithm is demonstrated using a numerical example.     

Improved identification and autotuning of PI controllers for MIMO processes by relay techniques

A technique for on-line identification and tuning is proposed to be used in the framework of a MIMO autotuning procedure. The proposed technique does not suffer from the risks of instability and the lack in performance of common tuning techniques in MIMO autotuning. Identification is accomplished through an extension of the well known ATV autotune identification method and requires only few additional tests in order to obtain some more knowledge about the process. The resulting model, which describes with good precision the process in a region of frequencies around the critical point, is then used for tuning: the integral time is found as a function of the model time constants and delay, while the gain is computed in order to give a desired value of the closed-loop resonance peak. Examples of application show that advantages over other proposed techniques can be retained for processes having different dynamic characteristics.     

Comments on ‘Design of decentralized reliable controllers for large-scale systems’

It is pointed out that the design algorithm given by Darwish and Soliman (1988) in the title paper is improper.     

On decentralized controllers for interconnected power systems

In this paper a scheme for a decentralized controller based on the modelling of interaction in large interconnected power systems is proposed. An example of a two-area power system is presented to illustrate the application of the proposed design procedure in both the continuous-time and discrete-time case. The computer simulation results revealed that the performance of the proposed decentralized controller is comparable to that of a centralized controller.     

Design of decentralized constant-volume controllers for open-channels by solving a least squares problem

In this paper we consider a mathematical model for open-channels that expresses the dynamic relationships, in terms of transcendental functions, between the gate opening sections and the corresponding stored water volume variations in the different canal reaches with respect to an initial reference configuration of uniform flow. Series expansion around s = 0 gives a state variable linear and time invariant model as well as the corresponding rational transfer matrix. Both a proportional and a proportional integral decentralized constant-volume control law are designed by solving a linear least squares problem. Such a procedure enables us to impose the desired structure on the feedback gain matrix by means of the optimization of the controller parameters. It makes the closed loop transfer function approach a target function as closely as possible over a specified frequency range. In this paper, the target closed loop functions are designed by means of an LQR technique applied to the linear time-invariant model obtained by means of the Taylor series expansion.     

Design of robust gain-scheduled PI controllers for nonlinear processes

Gain-scheduling has proven to be a successful design methodology in many engineering applications. However, in the absence of a sound theoretical analysis, these designs come with no guarantees of robust stability, performance or even nominal stability of the overall gain-scheduled deign.This paper presents such an analysis for one type of nonlinear gain-scheduled control system based on the process input for nonlinear chemical processes. A methodology is also proposed for the design and optimization of the robust gain-scheduled PI controller. Conditions which guarantee robust stability and performance are formulated as a finite set of linear matrix inequalities (LMIs) and hence, the resulting problem is numerically tractable. Issues of modeling error and input-saturation are explicitly incorporated into the analysis. A simulation study of a nonlinear continuous stirred tank reactor (CSTR) process indicates that this approach can produce efficient sub-optimal robust gain-scheduled controllers.     

Design of dynamic output feedback decentralized controllers via a separation procedure

This paper investigates the well-known separation properties that hold in the design of unconstrained output feedback controllers and tries to generalize them to cope with the design of structurally constrained decentralized controls. This problem, which until now has been open, presents additional constraints which destroy the useful properties that lead to separation. Necessary and sufficient conditions for decentralized stability and H₂ norm minimization are given, providing a framework in which a suitable ad hoc separation procedure is developed. A numerical algorithm based on crossdecomposition is presented and applied in two situations: first, when separation fails to provide a feasible solution; and then, to improve the obtained controller. An example and a comprehensive benchmark illustrate and validate the method.     

Discrete-time decentralized optimal controllers for multimachine power systems

Decentralized compensation of large-scale power systems has the appealing feature that local substations may be controlled by a small subset of state or output variables. In this paper, the problem of decentralized control by discrete-time compensation is addressed. By formulating the dynamics of each subsystem and including the interaction terms with other subsystems, a performance measure is constructed, based upon local desired system performance. This resulting controller is optimal, even if the subsystems are strongly coupled. An example using a 10-machine power system is provided to illustrate the improvement of the system response to faults when compared to classical excitation control.     

离散模糊大系统的分散化PDC 控制器设计: LM I 方法

考虑了由N个相互关联的T—S子模糊系统组成的离散模糊大系统的分散镇定问题，给出了保证该模糊大系统闭环渐近稳定的分散化并行分布补偿(DPDC)控制器的设计方法，这些DPDC控制器的存在条件均以LMI的形式出现，LMI可通过MATLAB的LMI工具箱求解，因此提供了一条综合离散模糊大系统分散化PDC控制器的有效途径，仿真例子说明了所提出方法的有效性。     

Interconnection-based performance analysis for a class of decentralized controllers

This paper is concerned with decentralized controller design for large-scale interconnected systems of pseudo-hierarchical structure. Given such a system, one can use existing techniques to design a decentralized controller for the reference hierarchical model, obtained by eliminating certain weak interconnections of the original system. Although this indirect controller design is appealing as far as the computational complexity is concerned, it does not necessarily result in satisfactory performance for the original pseudo-hierarchical system. An LQ cost function is defined in order to evaluate the performance discrepancy between the pseudo-hierarchical system and its reference hierarchical model under the designed decentralized controller. A discrete Lyapunov equation is then solved to compute this performance index. However, due to the large-scale nature of the system, this equation cannot be handled efficiently in many real-world systems. Thus, attaining an upper bound on this cost function can be more desirable than finding its exact value, in practice. For this purpose, a novel technique is proposed which only requires solving a simple LMI optimization problem with three variables. The problem is then reduced to a scalar optimization problem, for which an explicit solution is provided. It is also shown that when the original model is exactly hierarchical, then the upper bounds obtained from the LMI and scalar optimization problems will both be equal to zero.     

Independent design of robust partially decentralized controllers

An independent design method for robust partially decentralized controllers is developed. In the proposed design method, the partially decentralized control system is first expanded to the nonsquare decentralized structure. Using the Internal Model Control parametrization, the independent design procedure for robust nonsquare decentralized controllers can then be applied directly to the expanded system. Two examples, including a nonlinear stirred mixing tank, are used to illustrate the developed design method and a comparison to a decentralized controller is made.     

Design of linear multivariable discrete-time tracking systems incorporating fast-sampling decentralized error-actuated controllers

In this paper, the class of linear multivariable continuous-time plants which are amenable to fast-sampling decentralized error-actuated control is characterized in terms of the relatively prime polynomial matrix factors of the transfer function matrices of such plants. It is shown that this characterization greatly facilitates the design of fast-sampling decentralized error-actuated controllers, and the resulting synthesis technique is illustrated by designing such a controller for a third-order plant. with two inputs and two outputs.     

Optimizing fixed-size stochastic controllers for POMDPs and decentralized POMDPs

POMDPs and their decentralized multiagent counterparts, DEC-POMDPs, offer a rich framework for sequential decision making under uncertainty. Their high computational complexity, however, presents an important research challenge. One way to address the intractable memory requirements of current algorithms is based on representing agent policies as finite-state controllers. Using this representation, we propose a new approach that formulates the problem as a nonlinear program, which defines an optimal policy of a desired size for each agent. This new formulation allows a wide range of powerful nonlinear programming algorithms to be used to solve POMDPs and DEC-POMDPs. Although solving the NLP optimally is often intractable, the results we obtain using an off-the-shelf optimization method are competitive with state-of-the-art POMDP algorithms and outperform state-of-the-art DEC-POMDP algorithms. Our approach is easy to implement and it opens up promising research directions for solving POMDPs and DEC-POMDPs using nonlinear programming methods.     

Stabilization of decentralized control systems via time-varying controllers

In the design of decentralized control systems it is well known that the existence of unstable fixed modes prevents us from stabilizing it via linear time-invariant local controllers. In this note, we show that such systems might be stabilizable via time-varying controllers. In particular, a design method using sample and hold is proposed.     

On the parametrization of all decentralized stabilizing controllers

A novel parametrization of all decentralized stabilizing controllers is provided in terms of a single parameter Q that is constrained to satisfy a finite number of quadratic equations. The results are presented in a general algebraic framework and apply to linear time-invariant systems. Implications of this parametrization for decentralized control system performance are also discussed.     

A constructive procedure for stabilization of large-scale systemsby informationally decentralized controllers

A constructive procedure for the design of an informationally decentralized stabilization scheme for large-scale interconnected systems is presented. The design procedure is based on a stability result that uses the notion of block-diagonal dominance in matrices and considerably improves on the existing results in either enlarging the class of interconnections for which the design of a stabilization scheme can be satisfactorily conducted or yielding lower values of controller gains for a given interconnection pattern. It is demonstrated how the controller gains can be tailored systematically to the existing interconnection pattern within the overall system     

Adaptive fuzzy decentralized control for interconnected MIMO nonlinear subsystems

This paper describes an adaptive fuzzy control strategy for decentralized control for a class of interconnected nonlinear systems with MIMO subsystems. An adaptive robust tracking control schemes based on fuzzy basis function approach is developed such that all the states and signals are bounded. In addition, each subsystem is able to adaptively compensate for disturbances and interconnections with unknown bounds. The resultant adaptive fuzzy decentralized control with multi-controller architecture guarantees stability and convergence of the output errors to zero asymptotically by local output-feedback. An extensive application example of a three-machine power system is discussed in detail to verify the effectiveness of the proposed algorithm.