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.     

Low order integral-action controller synthesis

A simple controller synthesis method is developed for certain classes of linear, time-invariant, multi-input multi-output plants. The number of poles in each entry of these controllers depends on the number of right-half plane plant zeros, and is independent of the number of poles of the plant to be stabilized. Furthermore, these controllers have integral-action so that they achieve asymptotic tracking of step input references with zero steady-state error. The designed controller’s poles and zeros are all in the stable region with the exception of one pole at the origin for the integral-action design requirement. The freedom available in the design parameters may be used for additional performance objectives, although the only goal here is stabilization and tracking of constant references.     

MIMO controller synthesis with integral-action integrity

A controller synthesis method is presented for closed-loop stability and asymptotic tracking of step input references with zero steady-state error. Integral-action is achieved in two design steps starting with any stabilizing controller and adding a PID-controller in a configuration that guarantees robust stability and tracking. The proposed design has integral-action integrity, where closed-loop stability is maintained even when any of the proportional, integral, or derivative terms are removed or the entire PID-controller is limited by a constant gain matrix. The integral constant can be switched off when integral-action is not wanted.     

Simultaneous stabilization of MIMO systems with integral action controllers

Simultaneous stabilization with asymptotic tracking of step-input references is explored for linear, time-invariant, multi-input multi-output stable plants. Necessary conditions are presented for existence of simultaneous integral-action controllers and existence of simultaneous PID-controllers. A systematic simultaneous PID-controller synthesis method is proposed under a sufficient condition.     

Reliable stabilization with integral action in decentralized control systems

Reliable stabilization with integral action is studied in a linear, time-invariant, multi-input, multi-output, two-channel decentralized control system, where the plant is stable. The objective is to achieve closed-loop stability when both controllers act together and when each controller acts alone. Necessary and sufficient conditions are obtained for existence of block-diagonal decentralized controllers that ensure reliable stabilization, and integral action and all such decentralized controllers are parametrized. Explicit controller design approaches are discussed for the case of square channels.     

Designing fuzzy controllers from a variable structures standpoint

A procedure is presented for designing fuzzy controllers based upon variable structures techniques. Three such controllers are presented: the fuzzy equivalents of sliding-mode controllers, saturating controllers, and tanh controllers. By using an approach based upon variables structures (VSS) techniques, the stability of each of these controllers is assured. By using a sliding surface, the order of the rule base is reduced to size r×m, where r is the number of inputs and m is the number of fuzzification levels. This combination makes the proposed design procedure able to generate simple controllers with guaranteed stability properties. To illustrate the proposed design procedure, fuzzy controllers are designed for a ball-and-beam system. It is demonstrated that in spite of this system being a fourth-order unstable system, the proposed design procedure results in simple stable fuzzy controllers     

A novel design approach for switched LPV controllers

A novel design procedure for switched linear parameter-varying (LPV) controller is proposed. The new procedure, based on the Youla parameterisation ideas, decomposes the controller design into two steps. One focuses on ensuring global stability and the other on fulfilling the local performance specifications. This scheme allows the design of each local controller independently of each other, which may achieve higher performance without compromising the global stability and also simplifies the synthesis and the implementation of the local controllers. Any standard LPV synthesis procedure can be used to design these controllers. On the other hand, the stability during switching is ensured with convex constraints and no restrictions are imposed on the switching among controllers. The use of the proposed procedure is illustrated with an active magnetic bearing example.     

Design of feedforward controllers for multivariable plants

Simple methods for the design of feedforward controllers to achieve steady-state disturbance rejection and command tracking in stable multivariable plants are developed in this paper. The controllers are represented by simple and low-order transfer functions and are not based on reconstruction of the states of the commands and disturbances. For unstable plants, it is shown that the present method can be applied directly when an additional feedback controller is employed to stabilize the plant. The feedback and feedforward controllers do not affect each other and can be designed independently based on the open-loop plant to achieve stability, disturbance rejection and command tracking, respectively. Numerical examples are given for illustration.     

An Analytical Study on Structure, Stability and Design of General Nonlinear Takagi–Sugeno Fuzzy Control Systems

In this paper, we first study analytical structure of general nonlinear Takagi-Sugeno (TS, for short) fuzzy controllers, then establish a condition for analytically determining asymptotic stability of the fuzzy control systems at the equilibrium point, and finally use the stability condition in design of the control systems that are at least locally stable. The general TS fuzzy controllers use arbitrary input fuzzy sets, any types of fuzzy logic AND, TS fuzzy rules with linear consequent and the generalized defuzzifier which contains the popular centroid defuzzifier as a special case. We have mathematically proved that the general TS fuzzy controllers are nonlinear controllers with variable gains continuously changing with controllers’ input variables. Using Lyapunov’s linearization method, we have established a necessary and sufficient condition for analytically determining local asymptotic stability of TS fuzzy control systems, each of which is made up of a fuzzy controller of the general class and a nonlinear plant. We show that the condition can be used in practice even when the plant model is not explicitly known. We have utilized the stability condition to design, with or without plant model, general TS fuzzy control systems that are at least locally stable. Three numerical examples are given to illustrate in detail how to use our new results. Our results offer four important practical advantages: (1) our stability condition, being a necessary and sufficient one, is the tightest possible stability condition, (2) the condition is simple and easy to use partially because it only needs the fuzzy controller structure around the equilibrium point, (3) the condition can be used for determining system local stability and designing fuzzy control systems that are stable at least around the equilibrium point even when the explicit plant models are unavailable, and (4) the condition covers a very broad range of nonlinear TS fuzzy control systems, for which a meaningful global stability condition seems impossible to establish.     

A robust fractional-order PID controller design based on active queue management for TCP network

In this paper, a robust fractional-order controller is designed to control the congestion in transmission control protocol (TCP) networks with time-varying parameters. Fractional controllers can increase the stability and robustness. Regardless of advantages of fractional controllers, they are still not common in congestion control in TCP networks. The network parameters are time-varying, so the robust stability is important in congestion controller design. Therefore, we focused on the robust controller design. The fractional PID controller is developed based on active queue management (AQM). D-partition technique is used. The most important property of designed controller is the robustness to the time-varying parameters of the TCP network. The vertex quasi-polynomials of the closed-loop characteristic equation are obtained, and the stability boundaries are calculated for each vertex quasi-polynomial. The intersection of all stability regions is insensitive to network parameter variations, and results in robust stability of TCP/AQM system. NS-2 simulations show that the proposed algorithm provides a stable queue length. Moreover, simulations show smaller oscillations of the queue length and less packet drop probability for FPID compared to PI and PID controllers. We can conclude from NS-2 simulations that the average packet loss probability variations are negligible when the network parameters change.     

Synthesis of non-rational controllers for linear delay systems

This paper addresses the control of linear delay systems using non-rational controllers. The structure of the controller is chosen so as to copy the structure of the plant, reproducing the delays in the state and in the output. The resulting stabilization and performance design problems are entirely expressed as linear matrix inequalities. Although the design inequalities are based on delay independent stability conditions, the overall design is delay dependent, in the sense that the controller makes use of the delay parameter of the plant. This parameter is assumed to be constant yet arbitrary. Using non-rational controllers we overcome the main difficulty faced when designing rational controllers for linear delay systems, which is to incorporate in the design problem the matrix multiplier used to prove stability with respect to the delayed part of the system. We illustrate the paper with several examples and provide extensive comparisons with existent results.     

非线性相似组合系统的渐近稳定

本文对一类具有相似性的不确定非线性组合系统设计了鲁棒控制器．对不确定性只要 求一个已知的可能函数界,互联的强度由非减函数限制,减弱了对互联项的要求．我们利用系 统本身的相似性,简化了设计过程．所得控制器保证系统的渐近稳定性．     

Truncated adaptation design for decentralised neural dynamic surface control of interconnected nonlinear systems under input saturation

This paper studies decentralised neural adaptive control of a class of interconnected nonlinear systems, each subsystem is in the presence of input saturation and external disturbance and has independent system order. Using a novel truncated adaptation design, dynamic surface control technique and minimal-learning-parameters algorithm, the proposed method circumvents the problems of ‘explosion of complexity’ and ‘dimension curse’ that exist in the traditional backstepping design. Comparing to the methodology that neural weights are online updated in the controllers, only one scalar needs to be updated in the controllers of each subsystem when dealing with unknown systematic dynamics. Radial basis function neural networks (NNs) are used in the online approximation of unknown systematic dynamics. It is proved using Lyapunov stability theory that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded. The tracking errors of each subsystems, the amplitude of NN approximation residuals and external disturbances can be attenuated to arbitrarily small by tuning proper design parameters. Simulation results are given to demonstrate the effectiveness of the proposed method.     

Limitations of integral-action in control systems design

The standard problem of designing a cascade controller with integral-action in unity-feed back configuration is re-examined. It is established that the integral-action has some limitations which prevent ultimate rejection of step disturbances. The limitations are expressed in terms of restrictions on the plant and/or controller parameters.     

Reliable control using redundant controllers

This paper presents a methodology for the design of reliable control systems by using multiple identical controllers to a given plant. The resulting closed-loop control system is reliable in the sense that it provides guaranteed internal stability and H_∞ performance (in terms of disturbance attenuation), not only when all controllers are operational but also when some controller outages (sensor and/or actuator) occur. A numerical example is given to illustrate the proposed design procedures     

Reliable stabilization of linear plants using a two-controller configuration

A reliable controller design method is developed for linear, time-invariant, multi-input multi-output control systems; two controllers are designed to stabilize the closed-loop system when acting together and acting independently if one fails. All reliable controllers which achieve closed-loop stability are characterized for strongly stabilizable plants using a factorization approach.     

A parameter set division and switching gain-scheduling controllers design method for time-varying plants

This paper presents a new technique to design switching gain-scheduling controllers for plants with measurable time-varying parameters. By dividing the parameter set into a sufficient number of subsets, and by designing a robust controller to each subset, the designed switching gain-scheduling controllers achieve a desired L₂-gain performance for each subset, while ensuring stability whenever a controller switching occurs due to the crossing of the time-varying parameters between any two adjacent subsets. Based on integral quadratic constraints theory and Lyapunov stability theory, a switching gain-scheduling controllers design problem amounts to solving optimization problems. Each optimization problem is to be solved by a combination of the bisection search and the numerical nonsmooth optimization method. The main advantage of the proposed technique is that the division of the parameter region is determined automatically, without any prespecified parameter set division which is required in most of previously developed switching gain-scheduling controllers design methods. A numerical example illustrates the validity of the proposed technique.     

Reliable decentralised stabilisation of multi-channel systems: a design method via dilated LMIs and unknown disturbance observers

Reliable decentralised stabilisation is considered for general multi-channel plants, where the objective is to maintain stability of the closed-loop system when all of decentralised controllers work together and when one of the controllers is extracted due to a failure. For this control problem, a design method is presented, where a dilated LMI technique is employed for deriving reliable state feedback design, while a version of unknown disturbance observer is used as a decentralised observer for extending the design to output feedback case. Applicability of the proposed method is demonstrated through a power system example, where a model reduction and a low pass filter are further employed.     

Control system design by using a multi-controller approach with a real-time experimentation for a robot wrist

The idea of the multi-controller approach is to design local controllers, each of them combined with a special environment. One problem of this approach is to select the best local controller or even several controllers in order to design the final control law, which will be applied to the plant. In this paper, a 'switching' algorithm based on a symbolic fuzzy system is used. The main goal is basically to blend the control signals provided by several controllers, which are modelreference output feedback controllers (RST controllers) in our method. Nonetheless, an interesting issue is the stability of the global structure with a reference signal. In this paper, we present research studies on the stability analysis of the proposed multi-controller approach by using Lyapunov theory and linear matrix inequalities (LMIs). The derivative of a candidate quadratic Lyapunov function is calculated thanks to a weighted sum of local derivatives. Finally, a real-time experimentation on a robot wrist shows the effectiveness of the approach.     

Output feedback controller design of Takagi–Sugeno fuzzy systems

This paper presents new systematic design methods of two types of output feedback controllers for Takagi–Sugeno (T–S) fuzzy systems, one of which is constructed with a fuzzy regulator and a fuzzy observer, while the other is an output direct feedback controller. In order to use the structural information in the rule base to decrease the conservatism of the stability analysis, the standard fuzzy partition (SFP) is employed to the premise variables of fuzzy systems. New stability conditions are obtained by relaxing the stability conditions derived in previous papers. The concept of parallel distributed compensation (PDC) is employed to design fuzzy regulators and fuzzy observers from the T–S fuzzy models. New stability analysis and design methods of output direct feedback controllers are also presented. The output feedback controllers design and simulation results for a nonlinear mass-spring-damper mechanical system show that these methods are effective.