Nonlinear Closed-loop Control System Research Articles

A State Feedback Linearization Controller for Enzyme- Substrate Reactions

In this paper a state feedback linearization controller is developed for enzyme-substrate reactions with ferroelectric behaviour in brain waves. The proposed control law generates a feedback signal that regulate the performance of the sate variables to their desired states. Then, the nonlinear closed loop control system is simulated to demonstrate the effectiveness of the developed control approach in obtaining the required steady state value. Keywords— Nonlinear systems, enzyme, Brain waves, feedback linearization, steady state.

An Observer-Based Backstepping Controller for Spacecraft Attitude Control System

In this paper an observer-based controller is developed for continuous-time spacecraft attitude control system. Firstly, a high gain observer is created for the system model. Then, the estimated states are used to generate a backstepping controller to regulate the performance of sate variables to the desired states. Then, the nonlinear closed loop control system is simulated to demonstrate the effectiveness of the developed control approach in regulating the performance of the system to the desired steady state.

Parameter-adaptive reference governors with learned robust constraint-admissible sets

Reference governors (RGs) provide an effective method for ensuring safety via constraint enforcement in closed-loop nonlinear control systems. When the system parameters are uncertain but constant, robust formulations of RGs that consider only the worst-case effect may be overly conservative and exhibit poor performance. This paper proposes a parameter-adaptive reference governor (PARG) architecture that is capable of generating safe trajectories in spite of parameter uncertainties, without being as conservative as robust RGs. The proposed approach employs machine learning on a combination of off-line simulations and on-line measurements to estimate parameter-robust constraint-admissible sets (PRCASs) that can be leveraged by the PARG. We illustrate the robust set learning and constraint enforcement qualities of the PARG using a two-dimensional electromagnetic actuator example, and further demonstrate the potential of the PARG on a vehicle case study for preventing rollover despite aggressive maneuvering.

Extremum seeking controller tuning for heat pump optimization using failure-robust Bayesian optimization

Extremum seeking controllers have been investigated for multivariable data-driven energy optimization in heat pumps. In particular, proportional–integral extremum seeking control (PI-ESC) has demonstrated potential for significant acceleration compared to other ESC variants for nonlinear closed-loop control systems. A barrier to PI-ESC’s utilization in self-optimizing control is the fact that the PI-ESC algorithm is fragile. That is, unless the PI-ESC gains (e.g., controller gains, estimator gains) are carefully tuned, small perturbations to these gains can render the closed-loop unstable. Since arbitrary combinations of PI-ESC gains can result in instabilities, we propose a failure-robust Bayesian optimization (FRBO) algorithm that computes PI-ESC gains that ensure the closed-loop system can be driven rapidly to the optimum, while identifying and avoiding regions in the space of PI-ESC gains that are likely to result in instabilities (i.e., failures). The FRBO-tuned PI-ESC is shown to result in rapid closed-loop convergence to optimal values both on benchmark examples and a production-level model of an air conditioning system.

A novel model-free robust saturated reinforcement learning-based controller for quadrotors guaranteeing prescribed transient and steady state performance

For the purpose of improving the performance of trajectory tracking for quadrotors with the control input saturation, a novel model-free saturated prescribed performance reinforcement learning framework is proposed in the presence of the model uncertainties, nonlinearities and external disturbances. In this paper, saturation functions are employed to deal with input saturation, and the actuator's saturation nonlinearity is compensated by an intelligent method to decrease the saturation effects. Moreover, the prescribed performance control is utilized to ensure an adjustable transient and steady state response for the tracking errors. Besides, adaptive robust controllers are introduced to handle the effects of external disturbances online. A novel controller is proposed in collaboration with a reinforcement learning method based on actor-critic neural networks. The actor neural network is employed to estimate nonlinearities, actuator saturation nonlinearity, and model uncertainties, and the critic neural network is applied to estimate the reinforcement signals, which regulates the control action of the actor neural network online. The proposed actor-critic-based control structure benefits from a model-free calculation and only depends on the measurable signals of the closed-loop system. This freedom from system dynamics leads to a significant low computational load for the controller and, therefore, the proposed control method is computationally cost-effective. The adaptive robust controllers and the proposed actor-critic structures are trained online, and the convergence behavior of their learning laws is investigated in the course of stability examination. For the proof of stability, Lyapunov's direct method is used to show that all error variables of the closed-loop nonlinear control system are uniformly ultimately bounded. Finally, simulations along with some quantitative comparisons verify the efficiency and usefulness of the proposed control scheme.

Phase-Locked Loop Independent Second-Order Generalized Integrator for Single-Phase Grid Synchronization

Second-order generalized integrator (SOGI) requires fast and accurate grid voltage frequency information for quadrature signal generation (QSG) in single-phase systems. Conventionally, synchronous reference frame phase-locked loop (PLL) (SRFPLL) is used in a cascade manner and provides frequency feedback to SOGI. PLL is a non-linear closed-loop control system that requires adequate gain parameter design trade-off to provide accurate grid synchronization. Additionally, it creates interdependent loops while estimating the grid frequency and phase-angle. This results in unwanted frequency disturbances during grid transients, such as voltage sag and phase-angle jumps (PAJs) which are fed back to the SOGI as well. Thus, this article proposes two PLL independent frequency-feeding approaches for SOGI: Type-A and -B. The frequency is estimated using the normalized single-phase grid voltage signal in both types. In Type-A, the normalization is done using cascaded recursive discrete-Fourier transform (RDFT) and inverse RDFT (IRDFT). On the other hand, in Type-B, SOGI outputs are used for normalization. The grid voltage amplitude is estimated using the absolute value of the in-phase and in-quadrature components of the proposed frequency-adaptive SOGI. Furthermore, the third-order polynomial approximation of the arctangent function is implemented for phase-angle estimation in both types. The performance of both the types during transients and steady-state grid voltage disturbances (dc offset and harmonics) are compared with SOGIPLL using both simulations and experiments.

Using Interval Analysis to Compute the Invariant Set of a Nonlinear Closed-Loop Control System

In recent years, many applications, as well as theoretical properties of interval analysis have been investigated. Without any claim for completeness, such applications and methodologies range from enclosing the effect of round-off errors in highly accurate numerical computations over simulating guaranteed enclosures of all reachable states of a dynamic system model with bounded uncertainty in parameters and initial conditions, to the solution of global optimization tasks. By exploiting the fundamental enclosure properties of interval analysis, this paper aims at computing invariant sets of nonlinear closed-loop control systems. For that purpose, Lyapunov-like functions and interval analysis are combined in a novel manner. To demonstrate the proposed techniques for enclosing invariant sets, the systems examined in this paper are controlled via sliding mode techniques with subsequently enclosing the invariant sets by an interval based set inversion technique. The applied methods for the control synthesis make use of a suitably chosen Gröbner basis, which is employed to solve Bézout’s identity. Illustrating simulation results conclude this paper to visualize the novel combination of sliding mode control with an interval based computation of invariant sets.

Visualizing control systems performance: A fractional perspective

This article presents a novel method for visualizing the control systems behavior. The proposed scheme uses the tools of fractional calculus and computes the signals propagating within the system structure as a time/frequency-space wave. Linear and nonlinear closed-loop control systems are analyzed, for both the time and frequency responses, under the action of a reference step input signal. Several nonlinearities, namely, Coulomb friction and backlash, are also tested. The numerical experiments demonstrate the feasibility of the proposed methodology as a visualization tool and motivate its extension for other systems and classes of nonlinearities.

Operator-based robust nonlinear control and fault detection for a Peltier actuated thermal process

In this paper, operator-based robust nonlinear control design scheme and fault detection technique using robust right coprime factorization approach are considered for a Peltier actuated thermal process. The Peltier actuated thermal process is a typical nonlinear control affine system, where the process temperature depends not only on input current, but also on the square of the input current. In addition, the real system is likely to contain a fault signal owing to various factors. As a result, it is difficult to stabilize the control system and to achieve high accurate control performance, and to detect the fault signal to guarantee the engineering safety when a fault occurs. In this paper, for pursuing robust stability and tracking performance of the nonlinear closed-loop control system, a design scheme of operator-based robust tracking control system is proposed by using robust right coprime factorization approach. Then, for the tracking operator control system, a fault detection design technique based on robust right coprime factorization approach is also investigated. Finally, simulation and experimental results are given to confirm the effectiveness of the proposed method.

Codimension-two singularities on the stability boundary in 2D Filippov systems

AbstractBifurcation theory provides powerful tools for the analysis of the dynamics of open-loop or closed-loop nonlinear control systems. These systems are Filippov (or piecewise smooth) when the dynamics depends discontinuously on the state, for example as a consequence relay feedback actions. In this paper we contribute to the analysis of codimension-two bifurcations in Filippov systems by reporting some results on the equilibrium bifurcations of 2D systems that involve a sliding limit cycle. There are only two such local bifurcations: a degenerate boundary focus that we call homoclinic boundary focus; and the boundary Hopf. We address both of them, and provide the complete set of curves that exist around such codimension-two bifurcation points. Existing numerical software can be used to exploit these results for the analysis of the stability boundaries of nonlinear piecewise smooth control systems. In the final part of this paper, we discuss a 2D Filippov system modelling an ecosystem subject to on-off harvesting control that exhibits both codimension-two bifurcations.

Sampled-data control and stability of sets for nonlinear systems

This paper is devoted to the investigation of the relation between stability properties of nonlinear closed-loop control systems and those of families of approximations with respect to a given set. Firstly, such relation is derived for continuous-time closed-loop systems and the associated sampled-data systems. Secondly, stability results are presented for parametrized families of exact and approximate discrete-time models considered with parametrized family of feedbacks. In both cases, the sampling period is allowed to vary from step to step, and the stability is investigated with respect to nonempty closed (not necessarily compact) sets. Necessary and sufficient conditions are presented on the stability of approximations ensuring stability of the approximated systems.

Suboptimal minimax design of constrained parabolic systems with mixed boundary control

The paper concerns minimax control problems for linear multidimensional parabolic systems with distributed uncertain perturbations and control functions acting in mixed (Robin) boundary conditions. The main goal is to design a feedback control regulator that ensures the required state performance and robust stability under any feasible perturbations and minimize an energy-type functional under the worst perturbations from the given area. We design and justify an easily implemented suboptimal structure of the feedback boundary regulator and compute its optimal parameters ensuring the required state performance and robust stability of the nonlinear closed-loop control system on the infinite horizon.

ON-LINE IDENTIFICATION OF A ROBOT MANIPULATOR USING NEURAL NETWORK WITH AN ADAPTIVE LEARNING RATE

This paper proposes an extension of neural network identification capabilities for on-line identification of a nonlinear closed-loop control system. The neural network (NN) is trained on-line using the backpropagation optimization algorithm with an adaptive learning rate. The optimization algorithm is performed at each sample time to compute the optimal control input. The results confirm the effectiveness of the proposed neural network based identification scheme and control architecture.

Recurrent Neural Networks for Nonlinear Output Regulation

Based on a power-series approximation method, recurrent neural networks (RNN) are proposed for real-time synthesis and auto-tuning of feedback controllers for nonlinear output regulation systems. The proposed neurocontrol approach represents a novel application of recurrent neural networks to the nonlinear output regulation problem. The proposed approach completely inherits the stability and asymptotic tracking properties guaranteed by original nonlinear output regulation systems, due to its globally exponential convergence. Excellent operating characteristics of the proposed RNN-based controller and the closed-loop nonlinear control systems are demonstrated by using simulation results of the ball and beam system.

Recurrent neural networks for nonlinear output regulation

Based on a power-series approximation method, recurrent neural networks (RNN) are proposed for real-time synthesis and auto-tuning of feedback controllers for nonlinear output regulation systems. The proposed neurocontrol approach represents a novel application of recurrent neural networks to the nonlinear output regulation problem. The proposed approach completely inherits the stability and asymptotic tracking properties guaranteed by original nonlinear output regulation systems, due to its globally exponential convergence. Excellent operating characteristics of the proposed RNN-based controller and the closed-loop nonlinear control systems are demonstrated by using simulation results of the ball-and-beam system and the inverted pendulum on a cart system.

Adaptive fuzzy control of MIMO nonlinear systems

This paper presents a novel fuzzy basis function approach for adaptive control of multi-input and multi-output (MIMO) systems. In the method the nonlinear plant is first linearised and the fuzzy basis function vector is introduced to adaptively learn the upper bound of the system uncertainty vector, while its output is used as the parameter of the compensator in the sense that both the robustness and the asymptotic error convergence can be obtained for the closed loop nonlinear control system.

Multivariable fuzzy adaptive control approach of nonlinear systems 1

Abstract This paper presents a new fuzzy basis function approach for adaptive control of Multi-input and Multi-output (MTMO) system. In this method the nonlinear plants is first linearised and the fuzzy basis function vector is introduced to adaptively learn the upper bound of the system uncertainty vector, while its output is used as the parameters of the compensator in the sense that both the robustness and the asymptotic error convergence can be obtained for the closed loop nonlinear control system.

Observer Based Linearization of I/O Linearizable Nonlinear Systems

In this paper, a design method of special purpose observers which will be used in the feedback linearization of MIMO linearizable nonlinear systems is proposed. The basic idea of this method is as follows. A so-called pseudo-linearized model is constructed first by imposing the linearizing control law, which is implemented by an assumed observer, and then the assumed observer is designed. It is striking to note that the nonlinear observer thus obtained possesses a standard linear structure, which makes a practical nonlinear closed-loop control system considerably easy to implement.

オブザーバフィードバックによる厳密線形化

In this paper, instead of trying to establish the design method of general purpose observers, we propose a design method of the special purpose observers which will be used in the feedback linearization of MIMO linearizable nonlinear systems. The basic idea of this method is as follows. We assume there exists an observer and construct a so-called pseudo-linearized model by imposing the observer-based linearizing control law on the original system first and then design the observer. It is striking to note that the nonlinear observer thus obtained possesses a standard linear structure, which makes a practical nonlinear closed-loop control system considerably easy to implement. manipulator case is presented to illustrate the design method. A sufficient condition for Separation Principle in the weak sense that the control design does not influence the observer design, and the observer design does not depend on the new input is also derived.

Nonlinear closed-loop control system for intracranial pressure regulation.

A nonlinear closed-loop control system with flat pressure-versus-flow characteristics that is aimed at regulating intracranial pressure (ICP) by adjusting the volume of cerebral spinal fluid (CSF) was designed, built, and tested. The control system design allows both the pressure setpoint and hysteresis to be adjusted to overcome the difficulties inherent in differential pressure-activated, fixed resistance, open-loop shunts. A dynamic six-compartment bench-top fluid system, which mimics the cerebral spinal fluid system, was designed, built, and tested. A computer simulation was developed which included the nonlinear on-off controller with hysteresis and a sixth-order, linear, multicompartmental model of the CSF system. The computer model and in vitro system results showed the ability of the system to track and compensate for pressure variations above and below normal as well as for spurious outputs that mimic such in vivo problems as blood pressure changes, sneezing, or coughing. There was one discrepancy between the simulated and in vitro results. The in vitro system had a higher rate of increase in pressure due to the more rigid compliance of the materials used, whereas the computer model compliance, based on the basal in vivo compliance of the CSF system, was less rigid. Based on these findings, the controller was modified to account for short-duration, extremely elevated pressures.