Design Of Multivariable Systems Research Articles

Observer design for multivariable transport-reaction systems based on spatially distributed measurements

This paper is concerned with the design of observers for a class of one-dimensional multi-state transport-reaction systems considering distributed in-domain measurements over the spatial domain. A design based on the Lyapunov method is proposed for the stabilization of the estimation error dynamics. The approach uses positive definite matrices to parameterize a class of Lyapunov functionals that are positive in the Lebesgue space of integrable square functions. Thus, the stability conditions can be expressed as a set of LMI constraints which can be solved numerically using sum of squares (SOS) and standard semi-definite programming (SDP) tools. In order to evaluate the proposed methodology, a state observer is designed to estimate the variables of a nonisothermal tubular reactor model. Numerical simulations are presented to demonstrate the potentials of the proposed observer.

Unknown input observer design for linear time-invariant multivariable systems based on a new observer normal form

In various applications in the field of control engineering, the estimation of the state variables of dynamic systems in the presence of unknown inputs plays an important role. Existing methods require the so-called observer matching condition to be satisfied, rely on the boundedness e variables or exhibit an increased observer order of at least twice the plant order. In this article, a novel observer normal form for strongly observable linear time-invariant multivariable systems is proposed. In contrast to classical normal forms, the proposed approach also takes the unknown inputs into account. The proposed observer normal form allows for the straightforward construction of a higher-order sliding mode observer, which ensures global convergence of the estimation error within finite time even in the presence of unknown bounded inputs. Its application is not restricted to systems which satisfy the aforementioned limitations of already existing unknown input observers. The proposed approach can be exploited for the reconstruction of unknown inputs with bounded derivative and robust state-feedback control, which is shown by means of a tutorial example. Numerical simulations confirm the effectiveness of the presented work.

Quantitative-fuzzy Controller Design for Multivariable Systems with Uncertainty

This work serves as a pioneer contribution in terms of application of Quantitative Feedback Theory (QFT) methodology and fuzzy logic method to design a controller for MIMO systems. Due to the presence of uncertainty in multivariable dynamic systems, the application of robust control methods for achieving high accuracy in tracking is inevitable. On the other hand, application of QFT to MIMO uncertain systems still remains to be one of the most difficult control problems for engineers. In this paper, authors attempt to simplify the MIMO control problem by proposing a new algorithm which joins QFT and fuzzy techniques. In order to illustrate the utility of the proposed algorithm, its application on a two degree of freedom link robot manipulator is depicted. Initially, a QFT controller is designed for each link to overcome the track and disturbance rejection problems. Then, a bi-level tuned PD-fuzzy controller is employed as one strategy for curbing probable errors in the previous controller. The controller design was carried in the following stages; first, a linear PD controller independently applied to each actuator. Then, fuzzy rules were developed to design a fuzzy PD controller. Fuzzy controller normalizing parameters were regulated according to maximum PD control errors. In the second stage, named nonlinear tuning, other parameters of the fuzzy controller were tuned using genetic algorithms. Finally, nonlinear simulations of arbitrary path tracking shows that the proposed controller has a consistent tracking ability, and also it can clearly be seen that the mentioned approach is precise and very simple in comparison to other MIMO control techniques.

Controllers Design via Given Oscillation Index: Parametric Uncertainty and Power-Bounded External Disturbances

The problem is considered of output controllers design for linear multivariable systems with deviating in prescribed bounds physical parameters of the plant, and subjected to the influence of unknown polyharmonic external disturbances, limited only in power. The controller is built so that to provide the prescribed bounds of mean-square values of controlled variables in addition to the robust stability of the closed-loop system. The problem solution is reduced to the H∞-optimization procedure produced in some specific way. The solution of the well-known “benchmark” problem is considered.

IMC-PID Fractional Order Filter Multi-loop Controller Design for Multivariable Systems Based on Two Degrees of Freedom Control Scheme

An IMC-PID fractional order filter multi-loop controller design method based on two degrees of freedom paradigm is proposed for Multiple Input-Multiple Output systems with time delays. The interactions among the control loops are considered as disturbances. Thus, a two degrees of freedom control scheme, used for monovariable system to ensure the disturbance rejection, is extended to multivariable systems in order to reduce the effect of the coupling among the control loops. The proposed controller design method requires the control pairing selection with the least interactions and a set-point controller is calculated. An interactions reduction effect controller is calculated for each loop by defining a suitable complementary sensitivity function. The proposed controller design method is simple and systematic in relation with the desired closed loop specifications of each loop. The controllers obtained ensure robustness to process variations. Two illustrative examples are presented to show the merits of the proposed method.

Multivariable Adaptive Artificial Pancreas System in Type 1 Diabetes.

The review summarizes the current state of the artificial pancreas (AP) systems and introduces various new modules that should be included in future AP systems. A fully automated AP must be able to detect and mitigate the effects of meals, exercise, stress and sleep on blood glucose concentrations. This can only be achieved by using a multivariable approach that leverages information from wearable devices that provide real-time streaming data about various physiological variables that indicate imminent changes in blood glucose concentrations caused by meals, exercise, stress and sleep. The development of a fully automated AP will necessitate the design of multivariable and adaptive systems that use information from wearable devices in addition to glucose sensors and modify the models used in their model-predictive alarm and control systems to adapt to the changes in the metabolic state of the user. These AP systems will also integrate modules for controller performance assessment, fault detection and diagnosis, machine learning and classification to interpret various signals and achieve fault-tolerant control. Advances in wearable devices, computational power, and safe and secure communications are enabling the development of fully automated multivariable AP systems.

A data-driven fault-tolerant control design of linear multivariable systems with performance optimization

In this paper, an integrated data-driven fault-tolerant control (FTC) design scheme is proposed under the configuration of the Youla parameterization for multiple-input multiple-output (MIMO) systems. With unknown system model parameters, the canonical form identification technique is first applied to design the residual observer in fault-free case. In faulty case, with online tuning of the Youla parameters based on the system data via the gradient-based algorithm, the fault influence is attenuated with system performance optimization. In addition, to improve the robustness of the residual generator to a class of system deviations, a novel adaptive scheme is proposed for the residual generator to prevent its over-activation. Simulation results of a two-tank flow system demonstrate the optimized performance and effect of the proposed FTC scheme.

Design of multivariate alarm systems based on online calculation of variational directions

Alarm systems are critically important for safety and efficiency of industrial plants, but are severely suffering from alarm overloading. This paper proposes a method to design a multivariate alarm system based on variational directions of involved process variables, in order to alleviate the severity of alarm overloading. By using adaptive time scales, time gradients of signals are extracted to calculate variational directions in an online manner. Adaptive time scales are determined from a function between time scales and volatilities of process variables. Alarms arise at the moment that a nominal relationship of variational directions among process variables is invalidated. Numerical and industrial examples illustrate the effectiveness of the proposed method.

Based on the Multi Variable System Design and Parameter Tuning Method of PID Controller

Based on the Multi Variable System Design and Parameter Tuning Method of PID Controller

An Online Tuning Method for Robust Control of Multivariable Nonlinear Processes With Nonanalytical Modules and Time Delay

Control design for multivariable nonlinear systems has cultivated into a mature research area. A variety of control design methodologies have been well established. In most of the approaches, however, it is implicitly assumed that an analytically mathematical model can be available. This is not always feasible since in many practical control problems, system dynamics may be represented by nonanalytical modules, such as look-up tables, c or Fortran codes, etc. As a consequence, conventional methods can only be performed after analytical models are obtained. In this paper, an approach is proposed where the nonanalytical modules can be handled directly. Important results are obtained on optimal control laws and their implementation; robust control is achieved using a new online tuning method; input saturation and stability issues are also discussed. A numerical study is provided to validate the effectiveness of the proposed method.

Controller design for nonlinear and non-Gaussian multivariable systems based on survival information potential criterion

In this paper, a new model-free control strategy for general nonlinear and non-Gaussian multivariable stochastic systems has been proposed. The strategy applies minimum survival information potential control (MSIPC) scheme to decrease the closed-loop randomness of the output in the information theory framework. Compared with traditional entropy measures, survival information potential (SIP) has many advantages, such as validity in a wide range of distributions, robustness, the simplicity in computation, and so on. In order to calculate the SIP, the empirical SIP formulation under scalar data case is derived directly based on ordered error sample data. By minimizing the performance index mainly consists of SIP, a new model-free control algorithm is obtained for the considered multivariable nonlinear and non-Gaussian stochastic systems. The analysis on the proposed MSIPC convergence is made and a numerical example is provided to show the effectiveness of the obtained control algorithm, where encouraging results have been obtained.

Controller design for multivariable nonlinear control systems based on gradient-based ant colony optimisation

In the present study, a swarm intelligent algorithm called gradient-based continuous ant colony optimisation (GCACO) was utilised for controller design in multi-variable nonlinear control systems. The time domain objectives subject to the frequency domain constraints were considered in the proposed procedure. In order to be able to incorporate the time domain requirements in an overall controller design technique, the appropriate linearisation techniques utilised here was the exponential input describing function (EIDF). Experimental results obtained showed that GCACO technique developed here for controller design of nonlinear multivariable feedback control systems was capable to produce optimal and practical controllers that meet the design requirement in an efficient manner and computationally acceptable amount of time.

Multivariable disturbance observer-based H2 analytical decoupling control design for multivariable systems

In this paper, an H2 analytical decoupling control scheme with multivariable disturbance observer for both stable and unstable multi-input/multi-output (MIMO) systems with multiple time delays is proposed. Compared with conventional control strategies, the main merit is that the proposed control scheme can improve the system performances effectively when the MIMO processes with severe model mismatches and strong external disturbances. Besides, the design method has three additional advantages. First, the derived controller and observer are given in analytical forms, the design procedure is simple. Second, the orders of the designed controller and observer are low, they can be implemented easily in practice. Finally, the performance and robustness can be adjusted easily by tuning the parameters in the designed controller and observer. It is useful for practical application. Simulations are provided to illustrate the effectiveness of the proposed control scheme.

Regulator configuration design by means of model predictive control

This paper presents new concepts and methods for regulator configuration design for stable and unstable multivariable systems. Nowadays the self-definitions of dynamic relative gain rarely consider the interaction influences of closed-loop controllers, and the interaction measurement can be also showed from the effects from controlled variables to manipulated variables through closed-loop controllers. Model Predictive Control (MPC) is an important multivariable centralized control strategy; by means of SFPC (State Feedback Predictive Control) and MGPC (Multivariable Generalized Predictive Control), two closed-loop interaction analysis methods are first put forward. Based on the control rate optimized, two inverse normalized gain arrays are obtained from SFPC and MGPC which show the dynamic effects of controlled variables on manipulated variables. With the inverse normalized gain arrays, the regulator configuration design of unstable systems can be carried out due to the effect of multivariable centralized control. Finally the advantages and effectiveness of proposed interaction analysis approaches are highlighted via several examples.

Design of Multivariable Systems Controlled by Novelty Based Techniques

This paper proposes to build up a rotary inverted pendulum; its state space model was derived using Euler-Lagrange equation. This model was highly nonlinear. Stabilization and Self erecting a rotary inverted pendulum from sliding position and assessment of the pendulum in a straight up position was achieved by designing a control techniques like minimum order model, dead bead controller and Linear quadratic Regulator (LQR) using MATLAB domain. This concept was used in JCB, GRAIN and entertainment instrument in park.

PREDICTIVE GENERALIZED MINIMUM VARIANCE CONTROL OF NONLINEAR MULTIVARIABLE SYSTEMS WITH NON-ANALYTICAL MODULES

For most of the control methods, it is implicitly assumed that a mathematically analytical model can be obtained before control design. This is not always feasible for many engineering systems whose analytical models are either very difficult or expensive to obtain. To handle this situation, linearization or identification techniques are usually deployed to obtain an analytical model. This paper, however, proposes a novel method to tackle directly those systems with non-analytical modules. The method does not rely on the inversion of the nonlinear system and is henceforth computationally economic. Important results are obtained on control design for nonlinear multivariable systems with nonanalytical modules. Input saturation, robustness and practical implementation issues are also discussed. The proposed method is finally validated through its application to a robotic manipulator.

QFT prefilter design for multivariable systems using interval constraint satisfaction technique

In this paper, a computationally efficient method is proposed for automated design of the prefilters for multivariable systems. In quantitative feedback theory (QFT) method, proposed by Horowitz, the prefilter is designed to achieve the desired tracking specifications. In the proposed approach, we pose the prefilter design problem as an interval constraint satisfaction problem and solve it using the well-established interval constraint satisfaction techniques. The proposed method finds optimal values of the parameters of fixed structure prefilter within the initial search domain. An approach based on prefilter synthesis for single-input single-output is already developed. The purpose of this paper is to extend this approach to QFT prefilter design for general multivariable systems. To validate the above design approach, we applied the method to a laboratory setup of magnetic levitation system.

Observer design and output feedback stabilization for nonlinear multivariable systems with diffusion PDE-governed sensor dynamics

This paper addresses the problems of observer design and output feedback stabilization for a class of nonlinear multivariable systems, where the nonlinear system dynamics are described by ordinary differential equations (ODEs), and the sensor dynamics are governed by diffusion partial differential equations (PDEs). Based on the Luenberger observer theory, a Luenberger-type PDE-ODE cascaded observer is derived to estimate the state variables of the system. Then, an observer-based output feedback stabilizing controller is developed. The exponential stability of both the observer error system and closed-loop control system is proven via the Lyapunov direct method. Finally, numerical examples are provided to illustrate the effectiveness of the proposed design methods.

Integrated Process Identification and Control Design based on Dissipativity

An approach to the identification of the dissipativity properties of process systems from input-output data is presented, this approach lends itself to analysis and control design for multivariable process systems. In particular, the dissipativity based approach facilitates the design of decentralized or distributed control systems. The proposed approach has the intuitive advantage that only information that is used in the proceeding analysis and design steps is gathered in the system identification step, and not any extraneous information. Quadratic difference forms are used as supply rates and storage functions for the processes. Extensions, including applications to data driven control and thermodynamic properties of nonlinear systems are discussed.

Criterion of the Relative Degree Applied to Design of Multivariable Systems

The question, whether and when the criterion of the relative degree equal to one (RD1), may be applied for designing a multivariable system, is analyzed in the paper. The criterion is commonly utilized in sliding mode control in the case of the plants with single input and single output (SISO). For the multivariable case, first the decoupling of the fast transients is proposed, basing on a conversion of the matrix transfer function (MTF) description of the plant. Then, the controllers with high gain and derivatives are designed separately for each plant output, using the criterion RD1. It is noticed that the same approach may be applied for the multivariable systems with sliding mode control. It is noticed that both the multivariable systems: continuous with control saturation and relay with sliding mode control are in some sense equivalent. The considerations of the paper are confirmed by the performed simulations.