Perfect Control Law Research Articles

Perfect control for nonminimum-phase unstable systems defined in the multivariable continuous-time state–space framework — An inverse-based approach

In this paper, a new perfect control law dedicated to nonminimum-phase unstable LTI MIMO systems governed in the continuous-time state–space domain is proposed. Two algorithms are investigated, one of which has turned out to be definitely accurate. Henceforth, the inverse model control-based formula can be applied to any right-invertible plants having more input than output variables. Last, not least, through the application of some generalized inverses, the perfect control procedure guarantees the structural stability behavior even for unstable systems. Thus, the notion of the nonminimum-phase property should be understood in terms of a possible achieveability covering the entire class of LTI MIMO continuous-time plants. Theoretical and practical simulation examples performed in the Matlab/Simulink environment confirm the feasibility of the newly introduced approach.

Rotary Flexible Joint Control Using Adaptive Fuzzy Sliding Mode Scheme.

An adaptive fuzzy sliding control (AFSMC) approach is adopted in this paper to address the problem of angular position control and vibration suppression of rotary flexible joint systems. AFSMC consists of fuzzy-based singleton control action and switching control law. By adjusting fuzzy parameters with the self-learning ability to discard system nonlinearities and uncertainties, singleton control based on fuzzy approximation theory can estimate the perfect control law of feedback linearization. To enhance robustness, an additional switching control law is incorporated to reduce the approximation error between the derived singleton control action and the perfect control law of feedback linearization. AFSMC's closed-loop stability will be demonstrated via sliding surface and Lyapunov function analysis of error function. In order to demonstrate the effectiveness of the AFSMC in tracking performance as well as its ability to respond to model uncertainties and external perturbations, simulations are carried out using Simulink and Matlab in order to demonstrate how well it adapts to these situations. Based on these results, it can be concluded that the AFSMC performs satisfactorily in terms of tracking.

Energy Optimization of the Continuous-Time Perfect Control Algorithm

In this paper, an attempt at the energy optimization of perfect control systems is performed. The perfect control law is the maximum-speed and maximum-accuracy procedure, which allows us to obtain a reference value on the plant’s output just after a time delay. Based on the continuous-time state-space description, the minimum-error strategy is discussed in the context of possible solutions aiming for the minimization of the control energy. The approach presented within this study is focused on the nonunique matrix inverse-originated so-called degrees of freedom being the core of perfect control scenarios. Thus, in order to obtain the desired energy-saving parameters, a genetic algorithm has been employed during the inverse model control synthesis process. Now, the innovative continuous-time procedure can be applied to a wide range of multivariable plants without any stress caused by technological limitations. Simulation examples made in the MATLAB/Simulink environment have proven the usefulness of the new method shown within the paper. In the extreme case, the energy consumption has been reduced by approximately 80% in comparison with the well-known Moore–Penrose inverse.

Robust Fractional-Order Perfect Control for Non-Full Rank Plants Described in the Grünwald-Letnikov IMC Framework

Abstract The advanced analytical study in the field of fractional-order non-full rank inverse model control design is presented in the paper. Following the recent results in this matter it is certain, that the inverse model control-oriented perfect control law can be established for the non-full rank integer-order systems being under the discrete-time state-space reference with zero value. It is shown here, that the perfect control paradigm can be extended to cover the multivariable non-full rank plants governed by the more general Grünwald-Letnikov discrete-time state-space model. Indeed, the postulated approach significantly reduces both iterative and non-iterative computational effort, mainly derived from the approximation of the Moore-Penrose inverse of the non-full rank matrices to finally be inverted. A prevention provided by the new method excludes the detrimental matrix behavior in the form of singularity, often avoided due to the observed ill-conditioned sensitivity. Thus, the new defined robust fractional-order non-full rank instance of such control strategy, supported by the pole-free mechanism, gives rise to the introduction of the general unified non-full rank perfect control-originated theory. Numerical algorithms with simulation investigation clearly confirm the innovative peculiarities provided by the manuscript.

Switching Perfect Control Algorithm

The application of the switching control framework to the perfect control algorithm is presented in this paper. Employing the nonunique matrix inverses, the different closed-loop properties are obtained and further enhanced with possible switching methodology implementation. Simulation examples performed in the MATLAB/Simulink environment clearly show that the new framework can lead to benefits in terms of the control energy, speed, and robustness of the perfect control law. The possibility of transferring the new obtained results to the symmetrical nonlinear plants seems to be immediate.

A study on a new criterion for minimum-energy perfect control in the state-space framework

In this article, an advanced study concerning the energy cost of the perfect control algorithm is provided. An application of different nonunique matrix inverses into perfect control law has resulted in remarkable influence on both control and state signals. Following the newly obtained issues, covering the minimum-energy behavior, a new related criterion is proposed here. Based on deterministic norm we can, in a simple way, estimate the crucial energy performance. Simulation examples made in MATLAB/Simulink environment show the high potential of a new approach considered in the article.

DIGITAL ADAPTIVE FEEDFORWARD/FEEDBAСK CONTROLLER FOR AUTOTRACKING RADAR

The problem of designing a perfect adaptive control law for controlling the nonminimum phase discrete-time tracking system, which represents an aircraft autotracking radar, obtained by sampling a continuous-time system is proposed. The main goal is to achieve high performance indices of this class of systems. A new adaptive digital controller consisting of the adaptive feedback in conjunction with adaptiveindirect feedforward circuits is proposed. Obtained results can be useful for autotracking radar design.

Adaptive Fuzzy Sliding Mode Control for a Class of Nonlinear Dynamical Systems

This paper presents a FBFN-based (Fuzzy Basis Function Networks) adaptive sliding mode control algorithm for nonlinear dynamic systems. Firstly, we designed an perfect control law according to the nominal plant. However, there always exists discrepancy between nominal and actual mode, and the FBFN was applied to approximate the uncertainty. After that, the adaptive law was designed to update the parameters of FBFN to alleviate the approximating errors. Based on the theory of Lyapunov stability, the stability of the adaptive controller was given with a sufficient condition. Simulation example was also given to illustrate the effectiveness of the method.

Development of PI training algorithms for neuro-wavelet control on the synchronization of uncertain chaotic systems

This paper investigates a neuro-wavelet control (NWC) system to address the problem of synchronization control of uncertain chaotic systems. In this NWC system, a wavelet neural network (WNN) controller is the principal tracking controller designed to mimic the perfect control law and an auxiliary compensation controller is used to recover the residual approximation error so that the favorable synchronization can be achieved. Moreover, the proportional-integral (PI) training algorithms of the control system are derived from the Lyapunov stability theorem, which are utilized to update the adjustable parameters of WNN controller on-line for further assuring system stability and obtaining a fast convergence. In addition, to relax the requirement of unknown uncertainty bound, a bound estimation law is derived to estimate the uncertainty bound. Finally, some numerical simulations are presented to illustrate the effectiveness of the proposed control strategy. The simulation results demonstrate that the proposed NWC with PI training algorithms can synchronize the chaotic systems more accurately than the other control strategies.

A Robust Recurrent Wavelet Neural Network Controller With Improved Particle Swarm Optimization for Linear Synchronous Motor Drive

A robust recurrent wavelet neural network (RWNN) controller is proposed in this study to control the mover of a permanent magnet linear synchronous motor (PMLSM) servo drive to track periodic reference trajectories. First, the dynamic model of the PMLSM drive system is derived. Next, a perfect control law designed in the sense of feedback linearization is derived. However, in the perfect control law, the exact values of the system parameters, external force disturbance, and friction force are unknown in practical applications. Therefore, an RWNN is proposed to mimic the perfect control law and a robust compensator is proposed to compensate the approximation error. Moreover, the online learning algorithms of the connective weights, translations, and dilations of the RWNN are derived using Lyapunov stability and back-propagation (BP) method. Furthermore, an improved particle swarm optimization (IPSO) is adopted in this study to adapt the learning rates of the RWNN to improve the learning capability. Finally, the control performance of the proposed robust RWNN controller with IPSO is verified by some simulated and experimental results.

Mathematical Modeling, Simulation and Control of Flexible Vehicles

Possible approaches to the mathematical description of different types of flexible vehicles in view of structural oscillations, oscillations of fluid in tanks and moving masses inside the vehicle are observed. Elastic bending of a body surface in interaction with a surrounding medium in a broad band of speed variation are taken into account. Problems of regulator's synthesis and effective damping of elastic oscillations are solved for nonstationary flexible controlled plant. In the process of regulator's synthesis the local aerodynamic effects, dynamics and metering errors of sensors, time lag of engines and other elements of control system are considered. Methods of varying eigenfrequencies estimation in the real time are used for the control quality increasing. Principles of universal software design were developed for solving these complex problems of dynamic properties research, simulations of elastic vehicles motion and synthesis of perfect control law. Functioning of the program package is demonstrated and outcomes of calculations are presented.

Car-Following Control Using Recurrent Cerebellar Model Articulation Controller

Car following for traffic safety has been an active area of research. However, when a human is driving, it involves reaction time, delay, and human error that adversely affects safe driving. One way to eliminate human error and delay in vehicle following is to integrate an automated car-following control system into the driving system. This paper presents a recurrent-cerebellar-model-articulation-controller (RCMAC)-based control system for the car-following control of a platoon of automated vehicles. In this control system, an RCMAC is the main controller that is used to mimic a perfect control law, and a compensation controller is designed to compensate for the difference between the perfect control law and the RCMAC. The online adaptive laws of the control system are derived from the Lyapunov stability theorem so that the stability of the system can be guaranteed. Finally, a comparison of a sliding-mode control (SMC), an intelligent adaptive SMC, and the proposed RCMAC-based control for the car-following control is made. Simulation results demonstrate that the proposed RCMAC-based control system can achieve better control performance than other control systems.

CMAC-based supervisory control for nonlinear chaotic systems

Abstract This study proposes a supervisory control system based on a cerebellar-model-articulation-controller (CMAC) to resolve the tracking control problem of nonlinear chaotic systems. This CMAC-based supervisory control (CSC) system is composed of a CMAC and an H∞ supervisor. CMAC is a main tracking controller that is investigated to mimic a perfect control law and the H∞ supervisor is a supervisory controller that is developed to attenuate the effect of the approximation error between CMAC and the perfect control law. The gradient descent method and H∞ control technique are utilized to derive the on-line parameter tuning laws to achieve favorable tracking performance. Finally, the proposed CSC system is applied to control a Duffing–Holmes chaotic system and a chaotic Chua’s circuit. A comparison between a sliding-mode control and the proposed CSC for these nonlinear chaotic systems are presented. Simulation results show that the proposed CSC scheme can effectively achieve favorable control performance for nonlinear chaotic systems.

Intelligent hybrid control for uncertain nonlinear systems using a recurrent cerebellar model articulation controller

An intelligent hybrid control scheme, using an adaptive recurrent cerebellar model articulation controller (CMAC), is developed for a class of nonlinear dynamical systems. In this control system, an adaptive recurrent CMAC is used as the main tracking controller which mimics a perfect control law, and a compensated controller is designed to compensate for the difference between the perfect control law and the adaptive recurrent CMAC. The online adaptive laws of the control system are derived based on the Lyapunov stability theorem, so that the stability of the system can be guaranteed. In addition, in order to relax the requirement for a bound on the minimum approximation error, an adaptive estimation law is derived to estimate the approximation error bound in the compensated controller. Finally, the proposed control system is applied to control a Duffing forced oscillation system and a rocking motion for an aircraft wing. Simulation results demonstrate the effectiveness of the proposed control scheme for nonlinear systems with unknown dynamic functions.

Robust fuzzy neural network control for nonlinear motor-toggle servomechanism

In this study, a robust control system using an Takagi–Sugeno–Kang (TSK) type fuzzy-neural-network (FNN) is proposed to control a nonlinear toggle mechanism that is driven by a permanent magnet (PM) synchronous servo motor. First, the dynamic model of a motor-toggle servomechanism is introduced. Then, a robust control system is proposed to control the motor-mechanism coupling system for periodic motion. The design procedure of the proposed robust control system is described in detail. In the robust control system, the FNN controller is the main tracking controller, which is used to mimic a perfect control law, and the compensated controller is proposed to compensate the difference between the perfect control law and the FNN controller. Moreover, an on-line parameter training methodology, which is derived using the Lyapunov stability theorem and the backpropagation method, is proposed to increase the learning capability of the FNN. In addition, to relax the requirement for the bound of minimum approximation error, a simple bound estimation algorithm is investigated to control the motor-mechanism coupling system. The effectiveness of the proposed control scheme is verified by both numerical simulation and experimental results.

Hybrid fuzzy neural-network control for nonlinear motor-toggle servomechanism

This study addresses the application of a hybrid fuzzy neural network control (HFNNC) system to control a nonlinear mechanism system. First, the design procedures of the proposed HFNNC system are described in detail. In the HFNNC system, a fuzzy neural network (FNN) controller is the main tracking controller, which is used to mimic a perfect control law, and a compensated controller is proposed to compensate the difference between the perfect control law and the FNN controller. Then, an online parameter training methodology, which is derived using the Lyapunov stability theorem and the gradient descent method, is proposed to increase the learning capability of the FNN. Moreover, a toggle mechanism, which is driven by a permanent magnet (PM) synchronous motor, is studied as an example to demonstrate the effectiveness of the proposed control technique. The effectiveness of the proposed control scheme is verified by both the simulated and experimental results. In addition, the advantages of the proposed control system are indicated in comparison with the traditional computed torque control system.

Hybrid control using recurrent fuzzy neural network for linear induction motor servo drive

A hybrid control system using a recurrent fuzzy neural network (RFNN) is proposed to control a linear induction motor (LIM) servo drive. First, feedback linearization theory is used to decouple the thrust force and the flux amplitude of the LIM. Then, a hybrid control system is proposed to control the mover of the LIM for periodic motion. In the hybrid control system, the RFNN controller is the main tracking controller, which is used to mimic a perfect control law, and the compensated controller is proposed to compensate the difference between the perfect control law and the RFNN controller. Moreover, an online parameter training methodology, which is derived using the Lyapunov stability theorem and the gradient descent method is proposed to increase the learning capability of the RFNN. The effectiveness of the proposed control scheme is verified by both the simulated and experimental results. Furthermore, the advantages of the proposed control system are indicated in comparison with the sliding mode control system.

Perfect explicit model-following control solution to imperfect model-following control problems

For cases in which perfect model-following is not possible for a particular desired model, a class of candidate models is defined that can be followed perfectly by the given plant. A candidate model that most closely matches the dynamics of the desired model is then determined through constrained parameter optimization. The result is perfect model-following of a model that has an eigenstructure which resembles that of the desired model. In the development of this method, a new variation on perfect model-following control law development is shown. This method explicitly displays the feed-forward and feedback gains that determine the system error dynamics, which may be artibrarily selected by conventional pole placement methods if the plant is completely controllable. The method is applied to a problem involving the linearized lateral-directional equations of motion of the B-26 airplane. The results show that a candidate model can be found that has virtually the same dynamic behavior as the desired model, and that it can be followed perfectly by the original plant with arbitrarily assigned error dynamics.