Performance issues in the individual channel design of 2-input 2-output systems. Part 2. Robustness issues

In this second part of a three part series of papers examining the performance issues raised by the introductory paper (O'Reilly and Leithead 1991) on individual channel design for multivariable control, attention is focused on robustness: that is, on the meeting of performance specifications—in particular closed-loop system stability—in the face of plant uncertainty. The main results are that the use of phase margins and gain margins to assess robustness of 2-input 2-output multi-variable systems is justified. Further, it is shown that controllers for uncertain 2-input 2-output multivariable systems can be designed by classical SISO Nyquist-Bode local loop shaping using stable minimum phase controllers. Several additional results are also described in the paper.     

Tuning of multi-loop PI controllers based on gain and phase margin specifications

In this paper, a single-iteration strategy is proposed for the design of a multi-loop PI controller to achieve the desired gain and phase margins for two-input and two-output (TITO) processes. To handle loop interactions, a TITO system is converted into two equivalent single loops with uncertainties drawn from interactions. The maximum uncertainty is estimated for the initial controller design in one loop and single-input and single-output (SISO) controller design is applied. This controller is substituted to other equivalent loop for design, and finally, the first loop controller is refined on knowledge of other loop controller. For SISO controller tuning, a new method is presented to determine the achievable gain and phase margins as well as the relevant controller parameters. Examples are given for illustration and comparison.     

Multi-loop design of multi-scale controllers for multivariable processes

Based on the recently proposed (SISO) multi-scale control scheme, a new approach is introduced to design multi-loop controllers for multivariable processes. The basic feature of the multi-scale control scheme is to decompose a given plant into a sum of basic modes. To achieve good nominal control performance and performance robustness, a set of sub-controllers are designed based on the plant modes in such a way that they are mutually enhanced with each other so as to optimize the overall control objective. It is shown that the designed multi-scale controller is equivalent to a conventional PID controller augmented with a filter. The multi-scale control scheme offers a systematic approach to designing multi-loop PID controllers augmented with filters. Numerical studies show that the proposed multi-loop multi-scale controllers provide improved nominal performance and performance robustness over some well-established multi-loop PID controller schemes.     

EFFECTIVE DECENTRALIZED TITO PROCESS IDENTIFICATION FROM CLOSED‐LOOP STEP RESPONSES

In this paper, a new identification method performed in the time domain based on the decentralized step‐test is proposed for two inputs and two outputs (TITO) processes with significant interactions. In terms of parameter identification, the coupled closed‐loop TITO system is decoupled to obtain four individual single open‐loop systems with the same input signal. As in the SISO case, new linear regression equations are derived, from which the parameters of a first‐ or second‐order plus dead‐time model can be obtained directly. The proposed method outperforms the existing estimation methods for multivariable control systems that use step‐test responses. Furthermore, the method is robust in the presence of high levels of measurement noise. Simulation examples are given to show both effectiveness and practicality of the identification method for a wide range of multivariable processes. The usefulness of the identified method in multivariable process modeling and controller design is demonstrated.     

Autotuning process controller with improved load disturbance rejection

This paper presents an autotuning process controller aimed at providing efficient rejection of load disturbances in a class of situations that are quite typical in process control, and not easy to treat with most standard autotuning controllers, especially when not only the duration of the load disturbance response, but also the peak deviation of the controlled variable is an issue. The regulator structure is not fixed a priori; this is a peculiarity with respect to the main research stream on autotuning regulators, that refers essentially to fixed-structure (PID) regulators. Both simulation and laboratory examples are reported, to show the advantages of the proposed autotuning controller.     

Frequency-interval control configuration selection for multivariable bilinear systems

Control configuration selection is the procedure of choosing the appropriate input and output pairs for the design of decoupled (SISO or block) controllers for multivariable systems. This step is an important prerequisite for a successful industrial control strategy. The focus of this paper is on the problem of control configuration selection for a class of nonlinear systems which is known as bilinear systems. First, new frequency-interval gramians are presented for bilinear systems. These gramians are devised in particular for many applications in which one is interested in analysis and control of a system within a frequency-interval. It is shown that these gramians are the solutions to the so-called frequency-interval generalized Lyapunov equations. These gramians are used in the interaction measure for control configuration selection of MIMO bilinear systems. Most of the results on control configuration selection, which have been proposed so far, can only support linear systems. The proposed gramian-based interaction measure supports bilinear processes, can show the input–output interactions for any frequency-interval of interest, and can be used to propose a richer sparse or block diagonal controller structure.     

A comparative study of recent relay autotuning methods for multivariable systems

A typical procedure for designing multivariable controllers is the following: build a model for the multivariable process, choose the control structure, calculate the control parameters, test the controller (possibly with simulation) and then retune controller parameters as necessary. This procedure is complex and time consuming even for scalar control loops. For multivariable controllers, the procedure is even more daunting. Automation of the design method is and has been a concern of many researchers. There has been a large number of papers on relay autotuning of control systems. The choice of relay feedback to solve the design problem is justified by the possible integration of system identification and control into the same design strategy, giving birth to relay autotuning. In this paper, nine different relay autotuning methods for multivariable systems are compared. Most of these methods have common basics but they may differ in the tuning procedure, convergence, identification method, control structure and performance achievement. The paper summarizes these methods and investigates the advantages and drawback of each algorithm.     

A genetic-multivariable fractional order PID control to multi-input multi-output processes

A multivariable fractional order PID controller is designed and to get suitable coefficients for the controller, a genetic algorithm with a new topology to generate a new population is proposed. The three parts of the genetic algorithm such as reproduction, mutation, and crossover are employed and some variations in the methods are fulfilled so that a better performance is gained. The genetic algorithm is applied to design FOPID controllers for a multivariable process and the results are compared with the responses of a H_∞ based multivariable FOPID controller. The simulation responses show that in all cases, the genetic-multivariable FOPID controller has suitable performance, and the output of the system has a smaller error. Also, in the proposed method, variations in one output have a smaller effect on another output which is shown the ability of the proposed method to overcome the interaction in the multivariable processes.     

Neural network controller for a multivariable model of submarine dynamics

Recently, there have been many attempts to use neural networks as a feedback controller. However, most of the reported cases seek to control Single-Input Single-Output (SISO) systems using some sort of adaptive strategy. In this paper, we demonstrate that neural networks can be used for the control of complex multivariable, rather than simply SISO, systems. A modified direct control scheme using a neural network architecture is used with backpropagation as the adaptive algorithm. The proposed algorithm is designed for Multi-Input Multi-Output (MIMO) systems, and is similar to that proposed by Saerens and Soquet [1] and Goldenthal and Farrell [2] for (SISO) systems, and differs only in the form of the gradient approximation. As an example of the application of this approach, we investigate the control of the dynamics of a submarine vehicle with four inputs and four outputs, in which the differential stern, bow and rudder control surfaces are dynamically coordinated to cause the submarine to follow commanded changes in roll, yaw rate, depth rate and pitch attitude. Results obtained using this scheme are compared with those obtained using optimal linear quadratic control.     

Fuzzy‐Neuron Intelligent Coordination Control Fora Unit Power Plant

A novel fuzzy‐neuron intelligent coordination control method for a unit power plant is proposed in this paper. Based on the complementarity between a fuzzy controller and a neuron model‐free controller, a fuzzy‐neuron compound control method for Single‐In‐Single‐Out (SISO) systems is presented to enhance the robustness and precision of the control system. In this new intelligent control system, the fuzzy logic controller is used to speed up the transient response, and the adaptive neuron controller is used to eliminate the steady state error of the system. For the multivariable control system, the multivariable controlled plant is decoupled statically, and then the fuzzy‐neuron intelligent controller is used in each input‐output path of the decoupled plant. To the complex unit power plant, the structure of this new intelligent coordination controller is very simple and the simulation test results show that good performances such as strong robustness and adaptability, etc. are obtained. One of the outstanding advantages is that the proposed method can separate the controller design procedure and control signals from the plant model. It can be used in practice very conveniently.     

Adaptive Passivity of Nonlinear Systems Using Time-Varying Gains

In this paper, an adaptive controller with time-varying gains is proposed to solve the problem of making a single-input single-output (SISO) nonlinear system, with explicit linear parametric uncertainty, equivalent to a passive system. Some stability issues associated to the resultant closed-loop passive system are also discussed. The results obtained are applied to two examples, a third order nonlinear system and a model of a magnetic levitation system, to show the controller methodology design.     

Control configuration selection for linear stochastic systems

An appropriate control configuration selection is identified as one of the key prerequisites for attaining the control objectives in industrial practices. To select a suitable control configuration, it is important to determine which variables should be measured and how the process should be actuated. Therefore, the first step is to determine the optimal locations for the sensors and actuators. For the multivariable processes, this step is followed by choosing the appropriate input and output pairs for the design of SISO (or block) controllers. This is due to the popularity of the distributed and decentralized control in industrial control systems. These issues, which have been studied extensively for deterministic systems, have not been closely studied for stochastic systems. In this paper however the problem of control configuration selection is studied for the linear stochastic systems. The problem of selecting the sensor locations for stochastic systems is viewed as the problem of maximizing the output energy generated by a given state and for the actuator locations is viewed as the problem of minimizing the input energy required to reach a given state. Furthermore, a gramian-based interaction measure for control structure selection of multivariable stochastic systems is proposed. This interaction measure can be used to propose a richer (sparse or block diagonal) controller structure for distributed and partially decentralized control.     

SISO approaches for linear programming based methods for tuning decentralized PID controllers

Two tuning techniques are proposed to design decentralized PID controllers for weakly coupled and general MIMO systems, respectively. Each SISO loop is designed separately, and the controller parameters are obtained as a solution of a linear programming optimization problem with constraints on the process stability margins. Despite the SISO approach, loop interactions are accounted for either by Gershgorin bands (non-iterative method) or an equivalent open-loop process (iterative method). The tuning results and performance from both methods are illustrated in four simulations of linear processes, and a laboratory-scale application in a Peltier process. Four applications contemplate closed-loop performance comparisons between the proposed techniques and techniques from the literature. One application illustrates the feasibility of the proposed iterative method, based on EOPs, in tuning decentralized PIDs for a 5 × 5 system. Moreover, an analysis of the effect of model uncertainty in the phase and gain margins of the closed-loop process is performed.     

Adaptive fuzzy tracking control of nonlinear time-delay systems with unknown virtual control coefficients

In this paper, a novel adaptive fuzzy control scheme is proposed for a class of uncertain single-input and single-output (SISO) nonlinear time-delay systems with the lower triangular form. Fuzzy logic systems are used to approximate unknown nonlinear functions, then the adaptive fuzzy tracking controller is constructed by combining Lyapunov-Krasovskii functionals and the backstepping approach. The proposed controller guarantees uniform ultimate boundedness of all the signals in the closed-loop system, while the tracking error converges to a small neighborhood of the origin. An advantage of the proposed control scheme lies in that the number of adaptive parameters is not more than the order of the systems under consideration. Finally, simulation studies are given to demonstrate the effectiveness of the proposed design scheme.     

Position control of synchronous motor drive by modified adaptive two-phase sliding mode controller

A modified adaptive two-phase sliding mode controller for the synchronous motor drive that is highly robust to uncertain-ties and external disturbances is proposed in this paper. The proposed controller uses two-phase sliding mode control (SMC) where the 1st phase mainly controls the system in steady states and disturbed states-it is a smoothing phase. The 2nd phase is used mainly in the case of disturbed states. Also, it is an autotuning phase and uses a simple adaptive algorithm to tune the gain of conventional variable structure control (VSC). The modified controller is useful in position control of a permanent magnet synchronous drive.     

Non-interacting control design for multivariable industrial processes

In this paper, a systematic method is proposed for the design of general multivariable controller for complex processes to achieve the goal of fast loop responses with acceptable overshoots and minimum loop interaction while maintaining low complexity of the feedback controller. The design of general transfer function type controller is based on the fundamental relations under decoupling of a multivariable process, and the characterization of the unavoidable time delays and non-minimum phase zeros that are inherent in the decoupled loops. The objective loop transfer functions are then suitably specified to achieve fast loop response taking into account the performance limitation imposed by those non-minimum phase zeros and time delays. The ideal controller is then obtained which is in general a complicated irrational transfer matrix, for which model reduction with recursive least squares is applied in the frequency domain to obtain a much simpler transfer matrix with its elements in the form of rational transfer function plus delay. Simulations show that very satisfactory control performance is achieved.     

Approximation-based adaptive fuzzy control for a class of non-strict-feedback stochastic nonlinear systems

This paper considers the problem of adaptive fuzzy control of a class of single-input/single-output （SISO） nonlinear stochastic systems in non-strict-feedback form. Fuzzy logic systems are used to approximate the uncertain nonlinearities and backstepping technique is utilized to construct an adaptive fuzzy controller. The proposed controller guarantees that all the signals in the resulting closed-loop system are bounded in probability. The main contribution of this note lies in providing a control strategy for a class of nonlinear systems in non- strict-feedback form. Simulation result is used to test the effectiveness of the suggested approach.     

Linear adaptive control of a class of SISO nonaffine nonlinear systems

This paper addresses the problem of linear adaptive control for a class of uncertain continuous-time single-input single-output (SISO) nonaffine nonlinear dynamic systems. Using the implicit function theory, the existence of an ideal controller which can achieve control objectives is firstly demonstrated. However, this ideal controller cannot be known and computed even if the system model is well known. The aim of our work is to construct this unknown ideal controller using a simple linear controller with the free parameters updated online by a stable adaptation mechanism designed to minimise the error between the unknown ideal controller and the used linear controller. Since the mathematical model of the system is assumed unknown in this work, the proposed control scheme can be regarded as a simple model free controller for the studied class of nonaffine systems. We prove that the closed-loop system is stable and all the signals are bounded. An application of the proposed linear adaptive controller for a nonaffine system is illustrated through the simulation results to demonstrate the effectiveness of the proposed control scheme.     

Multivariable PID control by decoupling

This paper presents a new methodology to design multivariable proportional-integral-derivative (PID) controllers based on decoupling control. The method is presented for general n × n processes. In the design procedure, an ideal decoupling control with integral action is designed to minimise interactions. It depends on the desired open-loop processes that are specified according to realisability conditions and desired closed-loop performance specifications. These realisability conditions are stated and three common cases to define the open-loop processes are studied and proposed. Then, controller elements are approximated to PID structure. From a practical point of view, the wind-up problem is also considered and a new anti-wind-up scheme for multivariable PID controller is proposed. Comparisons with other works demonstrate the effectiveness of the methodology through the use of several simulation examples and an experimental lab process.     

Multivariable adaptive control without a prior knowledge of the delay matrix

This paper is concerned with the structure and role of the time-delay matrix in discrete-time multivariable processes. Interpretations and properties of this matrix as a multivariable generalization of the SISO delay term are discussed. It is formally shown that a finite-time horizon or multi-step cost function for the multivariable case can be minimized subject to a suitable choice of output and control horizons and without prior knowledge of the system delay matrix.