Multivariable Nonlinear Systems Research Articles

Newton-like phasor extremum seeking control with application to cooling data centers

We design a Newton-like phasor-based Extremum Seeking Control (ESC) aimed at multi-variable nonlinear control systems. We first augment the derivative estimator underlying the phasor approach to capture the Hessian of the plant index. Then we use these estimates to steer the system along a Newton-like direction. We assess the closed-loop stability of the proposed scheme and demonstrate its effectiveness in a data center cooling scenario.

Reentry Attitude Control for RLV Based on Adaptive Event-Triggered Sliding Mode

An adaptive event-triggered sliding mode control (AETSMC) algorithm is designed for the attitude control of the Reusable Launch Vehicle (RLV) subject to unknown external disturbances. First, an AETSMC strategy for a multi-variable second-order nonlinear system is proposed. Then, the stability of the proposed method is proved via the Lyapunov technique and the Zeno-free execution of triggering sequences is guaranteed. Furthermore, the proposed AETSMC strategy is applied to the attitude control of RLV. Finally, the developed method is validated by simulation, and the results show that the chattering phenomenon of control inputs is significantly weakened, and about 77.6% of the computational cost is saved while the desired performance of the system is ensured.

Iterative learning control of multivariable uncertain nonlinear systems with nonrepetitive trajectory

Iterative learning control (ILC) theory is based on the traditional assumptions of resetting condition and repetitive trajectory. To overcome these restrictions, a novel ILC is developed in this paper for MIMO uncertain nonlinear systems subject to external disturbances and performing nonrepetitive trajectory. The proposed ILC scheme works under alignment condition and nonrepetitive trajectory that can be varied from iteration to iteration in time interval length, in magnitude scale as well as in initial and final positions. A time-scale transformation is introduced and combined with Lyapunov method to synthesise the control law and to prove the asymptotic convergence. The tracking error converges to zero as the number of iterations increases. Simulation of pick-and-place operations is carried out on a parallel Delta robot in order to show the feasibility and the effectiveness of the proposed approach.

Multidimensional membership functions in T–S fuzzy models for modelling and identification of nonlinear multivariable systems using genetic algorithms

In this work, a new method for Takagi–Sugeno (T–S) fuzzy modelling based on multidimensional membership functions (MDMFs) is proposed. It is verified that the fuzzy inference method of one-dimensional membership functions (1DMFs) may place the fuzzy rules in inappropriate locations for modelling of nonlinear multivariable systems, while the application of MDMFs allows a better identification through a smaller number of fuzzy rules. The proposed method uses a genetic algorithm (GA) for the adjustment of the MDMFs and the T–S method for modelling and identification of the nonlinear system. As a validation example, a nonlinear multivariable system, a coupled tanks system, is chosen. The results show that the proposed method presents less identification error than the T–S method, with less number of fuzzy rules.

Modeling and application of industrial process fault detection based on pruning vine copula

Industrial processes are usually nonlinear multivariate stochastic systems. Describing the distribution characteristics of variables through a vine copula model can well define complex correlation information. However, modeling based on vine copula involves computational complexity. This study proposes a method to prune vine copula and introduces an indicator to conduct pruning process. This technique constructs a simplified model by removing the weakly correlated component from the copula structure without reducing the accuracy of model. Lastly, fault detection for industrial processes based on pruning vine copula is conducted based on a generalized local probability monitoring index. Experimental results of the monitoring process show that the method can reduce the time of modeling and improve the effect of fault detection.

Restricted structure predictive control for linear and nonlinear systems

ABSTRACT An optimal predictive control algorithm is introduced for the control of linear and nonlinear discrete-time multivariable systems. The controller is specified in a ‘restricted structure’ form involving a set of given linear transfer-functions and a set of gains that minimise a Generalised Predictive Control (GPC) cost-index. The set of functions can be chosen as proportional, integral and derivative terms, however, a wide range of controller structures is possible. This is referred to as Restricted-Structure GPC control. The multi-step predictive control cost-function is novel, since it includes weightings on the ‘low-order’ controller gains and the rate of change of gains. This considerably improves the numerical computations ensuring critical inverse computations cannot lead to a singular matrix. It also provides the option of adding soft or hard constraints on the controller gains which provides additional flexibility for control design. The ability to include a plant model that can include a general nonlinear operator is also new for restricted structure control solutions. The low-order controller provides a potential improvement in robustness, since it is often less sensitive to plant uncertainties. The simple controller structure also enables relatively unskilled staff to retune the system using familiar tuning terms, and provides a potentially simpler QP problem for the constrained case.

Stabilization and Speed Control of a Permanent Magnet Synchronous Motor with Dual-Rotating Rotors

The permanent magnet synchronous motor (PMSM) with dual-rotating rotors is a typical nonlinear multi-variable coupled system. It is sensitive to load disturbances and the change of interior parameters. The traditional proportional-integral (PI) controller is widely used in the speed control of a motor because of its simplicity; however, it cannot meet the requirements needed for high performance. In addition, when the loads of both of the rotors change, it is difficult to ensure that the system runs stably. With an aim to mitigate these problems, a method called master-slave motor control is proposed to guarantee the stability of the motor system in all cases. And then, a speed controller is designed to eliminate the influence of uncertain terms. The proposed control strategy is implemented both in simulations and in experiments. Through the analysis and comparison of the proportional-integral (PI) controller and the sliding-mode controller, the effectiveness of the proposed control strategy is validated.

Adaptive asymptotic stabilization of a class of unknown nonlinear systems with specified convergence rate

SummaryThis paper focuses on the asymptotic stabilization problem for a class of multivariable nonlinear systems with relative degree one, practical examples of which incorporate the liquid level control of water tanks, and the speed control of interconnected carts. The presence of the unknown (other than uncertain) additive and multiplicative nonlinearities renders asymptotic stability difficult to be achieved by the existing robust control methods. To conquer this obstacle, a novel adaptive control strategy is proposed. In the control design, the state constraint technique is newly introduced to the adaptive design to generate a proper control gain to compensate for unknown nonlinearities, instead of the use of extra approximating structures. By this means, both the prescribed transient performance regarding the convergence rate and the expected asymptotic stability are preserved. Finally, simulation results are given to illustrate the established theoretical findings.

Fractional comparison method and asymptotic stability results for multivariable fractional order systems

This paper investigates the asymptotic stability of equilibrium points of multivariable fractional order systems where its state equations contain different fractional orders which lie between 0 and 1. First, a fractional comparison principle is presented. Then, some elementary comparison results for linear fractional order systems of different fractional orders are developed. Based on continuously differentiable quadratic function and comparison results, new sufficient conditions are established for the asymptotic stability of linear and nonlinear multivariable fractional order systems. Finally, a few illustrative examples are presented.

Adaptive sensor fault-tolerant control for a class of multi-input multi-output nonlinear systems: Adaptive first-order filter-based dynamic surface control approach

This paper is concerned with the adaptive fault-tolerant control (FTC) problem for a class of multivariable nonlinear systems with external disturbances, modeling errors and time-varying sensor faults. The bias, drift, loss of accuracy and loss of effectiveness faults can be effectively accommodated by this scheme. The dynamic surface control (DSC) technique and adaptive first-order filters are brought together to design an adaptive FTC scheme which can reduce significantly the computational burden and improve further the control performance. The adaptation laws are constructed using novel low-pass filter based modification terms which enable under high learning or modification gains to achieve robust, fast and high-accuracy estimation without incurring undesired high-frequency oscillations. It is proved that all signals in the closed-loop system are uniformly ultimately bounded and the tracking-errors can be made arbitrary close to zero. Simulation results are provided to verify the effectiveness and superiority of the proposed FTC method.

Moth-Flame Optimization-Based Fuzzy-PID Controller for Optimal Control of Active Magnetic Bearing System

In this paper, the application of moth-flame optimization (MFO) algorithm for the optimal control of an active magnetic bearing (AMB) system is studied. Active magnetic bearings are known to be highly nonlinear multivariable systems. An AMB system is used in motors, generators, turbines and various other machineries in different industries to provide an active suspension to the rotor shafts. The comparison of controlled responses of various closed-loop systems resulting from the use of conventional proportional–integral–derivative (PID) and fuzzy logic-based intelligent control strategies is discussed. The heuristic MFO algorithm is applied to optimize the scaling factors of the fuzzy-PID controller. The proposed controller performance is superior as compared to the very famous industrial PID and fuzzy-PID controllers with respect to various time response parameters. A comparative study with other heuristic algorithms such as PSO and SA is also performed. Three performance indices, namely integral square error, integral time absolute of error (ITAE) and integral time absolute of error plus Integral time absolute of control action (ITAE + ITAU), are chosen for designing the optimization problem.

A fast online multivariable identification method for greenhouse environment control problems

Abstract Growing and pruning radial basis function (GAP-RBF) is extended for identification and control of multivariable nonlinear systems in this work. The proposed MGAP-RBF algorithm utilizes a sliding data window in the growing criterion and limits the number of hidden neurons by introducing a soft constraint in the pruning strategy to reduce the effect of disturbance and to improve learning speed, respectively. The performance of the proposed method is tested through some benchmark problems, and the results show that the proposed method can gain faster speed than the original GAP-RBF method and Ran algorithm, and more importantly, it can obtain an overwhelming advantages especially for some large-scale data sets with some complex attributes. Finally, the proposed method is applied to online PID tuning on a greenhouse environment control process. Simulation results show the proposed MGAP-RBF algorithm has better performance than the traditional RBF method and the original GAP-RBF method, in particular, it is faster and provides a more compact network with reduced computational complexity than the original GAP-RBF method.

Data-driven predictive control of molten iron quality in blast furnace ironmaking using multi-output LS-SVR based inverse system identification

Abstract Control of blast furnace (BF) ironmaking process has always been a hot and difficult issue in metallurgic engineering and automation. In this paper, a novel data-driven inverse system identification based predictive control method is proposed for multivariate molten iron quality (MIQ) indices in BF ironmaking process. First, since the widely used least-square support regression (LS-SVR) algorithm cannot cope with the multi-output problem directly, this paper uses multi-task transfer learning technology to construct a novel multi-output LS-SVR (M-LS-SVR) for multivariable nonlinear systems. Then, this M-LS-SVR is adopted to identify the inverse system model of the controlled BF ironmaking process with the help of the presented modeling performance comprehensive evaluation and NSGA II based multi-objective parameter optimization. In order to better perform the control of the MIQ indices, the identified inverse system model is used to compensate the controlled nonlinear BF system to a compounded pseudo linear system with linear transitive relation. Such an inverse system based data-driven predictive control can effectively improve the control performance of the conventional nonlinear predictive control. Data experiments using actual industrial data from a large BF show that the proposed methods are effective, advanced and practical, and provide a solution to the operational control and optimization of the BF ironmaking process.

Experimental Study in Taguchi Method on Surface Quality Predication of HSM

Based on the study of ball milling mechanism and machining surface formation mechanism, the formation of high speed ball-end milling surface is a time-varying and cumulative Thermos-mechanical coupling process. The nature of this problem is that the uneven stress field and temperature field affect the machined surface Process, the performance of the processing parameters in the processing interaction in the elastic-plastic materials produced by the elastic recovery and plastic deformation. The surface quality of machining surface is characterized by multivariable nonlinear system. It is still an indispensable and effective method to study the surface quality of high speed ball milling by experiments.

Adaptive population extremal optimization-based PID neural network for multivariable nonlinear control systems

Abstract The connection weights parameters play important roles in adjusting the performance of PID neural network (PIDNN) for complex control systems. However, how to obtain an optimal set of initial values of these connection weight parameters in a multivariable PIDNN called MPIDNN is still an open issue for system designers and engineers. This paper formulates this issue as a typical constrained optimization problem firstly by minimizing the cumulative sum of the product of exponential time and the system errors, and a real-time penalty function for overshoots of the system outputs, and then proposes an adaptive population extremal optimization-based MPIDNN method called PEO-MPIDNN for the optimal control issue of multivariable nonlinear control systems. The simulation results for two typical multivariable nonlinear control systems have demonstrated the superiority of the proposed PEO-MPIDNN to real-coded genetic algorithm (RCGA) and particle swarm optimization (PSO)-based MPIDNN, traditional MPIDNN with back propagation algorithm, and population extremal optimization-based multivariable PID control algorithm in terms of transient-state, steady-state, and robust control performance.

Observer-based parametric decoupling controller design for a class of multi-variable non-linear uncertain systems

ABSTRACTThis paper presents a novel decoupling control strategy for Lipschitz multi-variable non-linear uncertain systems. Using the explicit parametric design, an observer-based output feedback controller has been developed with free parameters while the closed-loop system can be further described by transfer function matrix with these free parameters. The coupling effects of the systems would be attenuated if the free parameters are optimised where the performance criterion is given based on the norm of the transfer functions. Moreover, the sufficient conditions of stabilization have been obtained for observer, controller and closed-loop system, respectively. Following the procedure of the presented control strategy, an illustrative numerical example is given to demonstrate the effectiveness of the presented control strategy. In addition, the similar design approach has been discussed for filtering problem which is a potential extension of the presented control strategy.

Sim3Tanks: A Benchmark Model Simulator for Process Control and Monitoring

This paper describes a simulator for the three-tank system process named Sim3Tanks. This process presents a hybrid and nonlinear behavior and it is subject to different kinds of perturbations, faults, and noises. Sim3Tanks was developed in the MATLAB/Simulink environment and can be used via graphical user interface, Simulink block diagram, and command-line. Sim3Tanks is suitable for studying and developing process control, fault detection and isolation, and fault tolerant control strategies for nonlinear multi-variable systems. In order to illustrate the potential of Sim3Tanks, four scenarios are discussed throughout this paper: PID control strategies for the level and flow rates; a fault detection algorithm based on unscented Kalman filter and generalized likelihood ratio; a fault isolation system based on Bayesian networks; and a control reconfiguration based on static virtual actuator and sensor. A video demonstration of Sim3Tanks can be found at https://github.com/e-controls/Sim3Tanks

Output Regulation of Multivariable Nonlinear Systems Using Extra Outputs

We consider the output regulation problem for a class of nonlinear multivariable systems in the case, besides the regulated error, also additional measurements not necessarily zero in steady state are available. To offset the steady state value of the extra measurements and make the latter effective for stabilisation purposes, we propose a control structure in which those measurements are filtered by a post-processor specifically designed to block their steady state value. The specific scenario we have in mind is the one of nonlinear systems that are nonminimum-phase between the input and the regulated error and for which extra measurements are necessary, or simply desirable, to succeed in robust output feedback stabilisation.

A novel sliding mode controller scheme for a class of nonlinear uncertain systems

This paper considers a continuous sliding mode control for a class of nonlinear systems with uncertainties including both parameter variations and external disturbances. Under the framework of sliding mode and using the upper bounds of the uncertainties, the proposed controller is derived to guarantee the stability of an overall closed-loop system and ensure robustness against modelling errors, parameter uncertainties and external disturbances. As for chattering elimination in sliding mode control, a boundary layer around the sliding surface is used and the continuous control is applied within the boundary. Moreover, an extended schema of a higher-order sliding mode controller is developed in this paper as another solution to avoid the problem of chattering effect. Simulation results demonstrate the efficacy of the proposed control methodology to stabilise an inverted pendulum, which is a standard nonlinear benchmark system. The applicability of the proposed algorithm will be extended, via suitable modifications, to the case of multivariable nonlinear systems with uncertainties of more general type, covering a wide class of processes.

The Decomposition Method in Issues of Researching Electric-Power Systems with Dry Friction

Electrical engines are widespread in all areas of industry and technology. Electrical actuators are widely used as an actuating motor regulating the interconnected controls of different machines. Increased demands for precision in interconnected controls make it very important to consider dry friction in the executive mechanism. The consideration of dry friction in a mathematical model of an automatic system considerably complicates its analysis. In all known practical cases of research into such issues, the research is carried out by means of computing or analytically, but using a considerably simplified model of the dry-friction law. This simplified presentation does not allow one to uncover and understand the true (or apparent) reasons for loss of stability in a system accompanied by friction self-oscillations of different kinds (periodical, chaotic etc.). The decomposition method of parameter space presented in the current work allows investigation of nonautonomous nonlinear multivariable systems via basic subsystems (both linear and nonlinear) that have a lower-order state space and are amenable to strict analysis.