Single-input Single-output Plants Research Articles

Online learning of stable robust adaptive controllers design based on data-dependent feedback linearization with application to rotary inverted pendulum

This study introduces an online (supervised) learning method to design nonlinear auto-regressive moving average (NARMA) controllers for feedback-linearized nonlinear single-input single-output (SISO) systems. The algorithm ensures Schur stability of the overall closed-loop system and provides adaptiveness and robustness for the NARMA controllers. The first stage of the method derives, in a data-dependent way, a feedback-linearized model of the nonlinear plant by using its input and output sample pairs. The method’s second stage, which constitutes the novel part of the presented study, builds up an online learning scheme for the linear auto-regressive moving average (ARMA) controller based on an already learned feedback-linearized model of the nonlinear plant. During online supervised learning, ARMA parameters of the feedback-linearized SISO plant model and the closed-loop ARMA model are computed by minimizing the plant identification and the closed-loop system tracking errors. Both errors are defined as ℓ1,ε\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\ell}}_{1,{\\varvec{\\varepsilon}}}$$\\end{document}, namely ε-insensitive loss functions that provide NARMA controller the robustness against noise and outliers. The proposed online learning control algorithm is applied to a rotary inverted pendulum model and to a real rotary inverted pendulum setup. The tracking performance of the developed controller is compared with those of the linear quadratic regulator and coupled sliding mode controller in terms of mean square error.

On Stable [formula omitted] controller design for plants with infinitely many unstable zeros and poles

In this work, stable H∞ controller design problem for linear time-invariant single-input single-output plants, which have infinitely many open-right-half-plane zeros and possibly infinitely many right-half-plane poles, is considered. Interpolation-based approach is developed to solve the problem. The approach requires to construct a unit in H∞ satisfying certain interpolation conditions at the open-right-half-plane zeros of the plant and H∞ norm constraint. In order to construct such a unit function, first, construction of an H∞ function satisfying interpolation conditions at given countably many distinct points in the open-right-half plane is presented. Then, by using the upper bound on the H∞ norm of the constructed function and the small-gain theorem, first, sufficient condition is presented for the solution of the sensitivity minimization problem by a stable controller and design methodology for such a controller is presented. Then, stable H∞ controller design approach for the considered class of plants is presented under certain assumptions. A numerical example is given to verify the presented results.

Multi-Input MultiOutput Model-Following Control Design Methods for Rotorcraft

Two methods of multi-input multioutput (MIMO) command-model-following control design are compared for rotorcraft flight control. The first, explicit model following (EMF), employs single-input single-output inverse plants with a dynamic decoupling matrix, which is a purely feed-forward approach to inverting the plant. The second is dynamic inversion (DI), which involves both feed-forward and feedback path elements to invert the plant. The EMF design is purely linear, while the DI design has some nonlinear elements in vertical rate control. For each of these methods, an architecture is presented that provides angular rate model following with selectable vertical rate model following. Implementation challenges of both EMF and DI are covered, and methods of dealing with them are presented. These two MIMO model-following approaches are evaluated regarding (1) fidelity to the command model and (2) turbulence rejection. Both are found to provide good tracking of commands and reduction of cross coupling.

Optimal error governor for PID controllers

Error Governor (EG) deals with the problem of dynamically modifying the feedback error driving a controller having bounded control signals, for preventing controller or actuators saturation, avoiding integrator and/or slow dynamics windup and preserving the nominal linear controller behaviour. In this paper, an optimisation-based EG scheme is proposed for discrete-time Proportional–Integral–Derivative (PID) controllers driving Single-Input Single-Output (SISO) plants. The PID controller is considered in state-space form, and this formulation is used to pose the EG problem as a constrained quadratic program (QP). Because the QP problem is subject to inequality constraints related to controller saturation, in order to use the proposed scheme in real-world applications, it should be necessary to consider appropriate algorithms for efficiently solving the optimisation problem. An efficient way to efficiently compute the solution of the EG problem is presented, reducing the computational effort required to solve the EG QP for using the proposed scheme in real control loops with high sampling rate. An analysis of control performance and computational burden is provided, comparing in simulation studies the optimal EG scheme performance with respect to control results provided by saturated PID with and without anti-windup action.

Design of Control Laws Based on Inverted Decoupling and Linear Matrix Inequality for a Turboprop Engine

Abstract This paper proposes a systematic approach to design control laws for a turboprop engine. The proposed approach includes interactions decoupling and control laws design based on linear matrix inequality (LMI). First, since the main objective of the turboprop engine control system is to ensure propeller-absorbed power at a constant propeller speed, the linear model of a turboprop engine can be linearized into a two-input two-output (TITO) plants, and there exist the interactions between two control loops. Because inverted decoupling can well retain the dynamic characteristics of the original system, it is used to decouple the interactions so that the TITO plant can be divided into two single-input single-output plants, that is, gas-generator shaft speed is controlled by fuel flowrate and power turbine shaft speed is controlled by blade angle. Then, the control laws are designed separately for each control loop by solving the LMI group derived from static output feedback (SOF) and regional pole placement. Finally, the proposed approach is implemented on a two-spool turboprop engine (TSTPE) integrated model. The simulation results show that there exist strong interactions between two control loops of TSTPE, applying inverted decoupling to decouple these interactions is effective, and the gas-generator shaft speed and the power turbine speed can track their commands with appropriate performance by controlling the fuel flowrate and blade angle under the action of the designed control laws and inverted decoupling.

Multivariable Virtual Reference Feedback Tuning for Non-Minimum Phase Plants

When applying model reference control to a non-minimum phase (NMP) plant, it is important to include the NMP (transmission) zero(s) in the reference model, otherwise the controller will tend to cancel out these zeros, often causing loss of internal stability. In data-driven (DD) control it is not possible to conceive a priori a reference model with the NMP zero(s) because no model of the plant is available; accordingly, DD design methods tend to fail in NMP plants. For single-input–single-output plants, this problem has been solved by using a flexible reference model in a DD design. This letter presents an extension of that method for multi-input–multi-output plants.

Deadbeat controller with two additional steps

An nth-order closed-loop hybrid system will exhibit a deadbeat response if the system output approaches the reference input in n steps. This paper studies the problem of obtaining a deadbeat response for an nth-order single-input single-output plant (process) in n + 2 steps with a minimum deadbeat controller output deviation from the steady state value. We identify the requirements for the design of a deadbeat controller with two additional steps and present worked examples for the problem. A deadbeat controller is then used to control a piezoelectric micro-robot model. The second order continuous transfer function is used to simulate the robot’s piezoelectric actuator. This research presents the advantages of a deadbeat controller with two additional steps when applied to a robot control problem.DOI: http://dx.doi.org/10.5755/j01.eie.23.5.19115

Stochastic Approximation Approach to Design of Linear Controllers for Tracking Systems With Asymmetric Saturation

Reference-tracking closed-loop systems with saturating actuators often operate in asymmetric regimes. This is because reference signals cause the operating points away from the point of saturation symmetry (even if the actuator itself is symmetric, i.e., odd, function). Stability analysis and stabilizing controller design for asymmetric systems can be carried out using the same techniques as those for the symmetric case. In contrast, currently available methods for controller design in the framework of reference tracking are not applicable to asymmetric systems. The goal of this paper is to develop such a method for single-input single-output (SISO) plants having no poles in the open right-side plane. The approach is based on a global quasi-linearization technique referred to as stochastic linearization, which approximates the saturation function by an equivalent gain and equivalent bias. The main qualitative result obtained is that the asymmetry leads to a constant disturbance acting at the input of the plant. The quantitative results are analytical expressions for this disturbance and the ensuing steady-state tracking errors. It is shown that these errors exhibit a behavior incompatible with the linear control theory. Specifically, they may be increasing or nonmonotonic functions of the controller gain. In view of this fact, the paper develops a time-domain technique for linear tracking controller design based on two loci: the saturating root locus (to account for dynamics) and the saturating tracking error locus (to accounts for statics). Methods for sketching these loci are provided and applied to controllers design.

Self-tuning PID controller using quantum neural network with qubit-inspired neurons

This paper investigates the performance of an adaptive controller using a multi-layer quantum neural network QNN comprising qubit-inspired neurons as information processing units. The control system is a self-tuning controller whose control parameters are tuned online by the QNN to track plant output relative to the desired plant output generated by a reference model. A proportional-integral-derivative PID controller is utilized as a conventional controller, with its parameters tuned by the QNN. Computational experiments to control a single-input single-output discrete-time non-linear plant are conducted to evaluate the capability and characteristics of the quantum neural self-tuning controller. The experiment results demonstrate the feasibility and effectiveness of the proposed controller.

Fixed-order stabilising controller design by a mixed randomised/deterministic method

A novel mixed randomised/deterministic method for fixed-order controller design is proposed for discrete-time single-input single-output plants. It is based on the random generation of Schur stable polynomials using reflection coefficients and reflection segments of polynomials. Stable reflection segments are then projected onto the affine set of closed-loop characteristic polynomials and the stable line segments in the controller parameter space are determined. A novel approach is proposed for global and local optimisation over reflection segment bunches on the basis of the weighted sum of absolute values of reflection coefficients.

Frequency-Domain Analysis of Nonlinear Active Disturbance Rejection Control via the Describing Function Method

Active disturbance rejection control (ADRC) is a new design concept that shows promising power in dealing with the uncertainties of control systems. However, most of the previous work has been numerical time-domain development and frequency-domain analysis for the linear framework. This paper focuses on the frequency-domain analysis of the nonlinear ADRC behavior using the describing function method and characterizes the effect of the fal nonlinearity parameter on the performance of the closed-loop system. Both the describing function of the nonlinearity and the transfer function description of the system's linear portion are derived. The stability, dynamic stiffness, and tracking performance are analyzed for a second-order single-input single-output plant. The analysis results show that the nonlinearity parameter plays a crucial role in the system performance. The nonlinear ADRC has higher control efficiency than the linear ADRC but reduces the stability margin of the system. Using the fast tool servo case, simulations and hardware experiments are conducted, and the results further support the analysis.

Pole placement adaptive control with persistent jumps in the plant parameters

In this paper we consider the control objective of step tracking and pole placement in the context of significant plant uncertainty and occasional, but persistent, jumps in the plant parameters. Here we have a compact set of admissible single-input single-output, controllable and observable plant models of a fixed order. The controller incorporates an integrator, and its action emulates the behaviour of a pole placement state feedback compensator. We demonstrate that this controller has the facility to tolerate occasional (but persistent) switches between these models without an undue effect on the performance.

Adaptive-type servo controller utilizing a quantum neural network with qubit neurons

This study presents an adaptive-type controller based on a quantum neural network and investigates its characteristics for control systems. A multi-layer quantum neural network which uses qubit neurons as an information processing unit is utilized to design three types of the adaptive-type quantum-neural-network-based controllers which conduct the learning of the quantum neural network as an online process: a direct controller, a parallel controller and an indirect controller. Computational experiments to control the single-input single-output non-linear discrete-time plant are conducted to evaluate the learning performance and capability of quantum neural controllers. The results of the computational experiments confirm the feasibility and effectiveness of adaptive-type quantum neural controllers.

Implementación de un algoritmo de control predictivo en espacio de estados sobre una plataforma de simulación desarrollada en Matlab

El control predictivo basado en modelo (MPC) esuna metodología que se enmarca dentro de la ingeniería de control moderno y que desde sus inicios ha venido evolucionando como una herramienta capaz de mitigar mayormente los problemas que enfrenta la industria desde el enfoque de la teoría de control. En su esencia la estrategia de control predictivo hace uso de un modelo matemático interno y de una estrategia de optimización para predecir las salidas del sistema dentro de un intervalo de tiempo al que se le denomina horizonte de predicción. La formulación que sustenta el algoritmo demanda un coste computacional elevado y es por ello que desde sus inicios esta estrategia ha tenido su nicho de implementación en ordenadores que agilicen y soporten un cálculo matricial considerable. En el presente artículo se detalla el análisis matemático y el procedimiento para la implementación de un algoritmo de control predictivo bajo Matlab®, además, se presenta los resultados de la aplicación a una planta de simple entrada y simple salida (SISO) y a una planta de múltiples entradas y múltiples salidas (MIMO). En ambos casos se incorporan restricciones a las variables del proceso, atendiendo a una de las características más atractivas de esta estrategia.

A robust output-feedback adaptive dynamic surface control for linear systems with input disturbance

In this paper, a robust output-feedback adaptive control is proposed for linear time-invariant (LTI) singleinput single-output (SISO) plants with unmeasurable input disturbance. Using dynamic surface control (DSC) technique, it is shown that the explosion of complexity problem in backstepping control can be eliminated. Furthermore, the proposed adaptive DSC scheme has the following merits: 1) by introducing an initialization technique, the L ∞ performance of system tracking error can be guaranteed even if the plant high-frequency gain is unknown and the input disturbance exists, and 2) the adaptive law is necessary only at the first design step, which significantly reduces the design procedure. It is proved that with the proposed scheme, all the closed-loop signals are semiglobally uniformly ultimately bounded. Simulation results are presented to demonstrate the effectiveness of the proposed scheme.

A robust synthesis methodology for neutrally stable uncertain SISO plants under input amplitude saturation

In this article, a control system design methodology for neutrally stable, uncertain, single-input single-output plants under input amplitude saturation is presented. Based on Horowitz's original three degree of freedom design and extensions developed afterwards, this approach concentrates on neutrally stable, higher type, uncertain plants. A three degree of freedom non-interfering loop structure is used for the synthesis, along with the structure of the additional, independent loop transmission around the saturating element proposed for designing the third degree of freedom H(s). Robust stability and performance are established. The circle criterion, the describing function and non-overshooting conditions are utilised to obtain design constraints. Finally, all these design constraints are expressed in frequency domain bounds and synthesis follows from loop shaping methods such as quantitative feedback theory.

A robust adaptive dynamic surface control for linear systems

In this article, a robust output-feedback adaptive dynamic surface control (DSC) is proposed for linear time-invariant single-input single-output plants with unmodelled dynamics and unmeasurable output disturbance. With the proposed adaptive DSC scheme, the ‘explosion of terms’ problem inherent in backstepping control is eliminated and the adaptive law is necessary only at the first design step, which significantly reduces the design procedure. More importantly, it is proved that with an initialisation technique, the ℒ∞ performance of the tracking error can be guaranteed even with unmodelled dynamics, bounded output disturbance exists and the plant high-frequency gain is unknown.

Modified adaptive backstepping design method for linear systems

In this study, a modified adaptive backstepping control is proposed for linear time-invariant (LTI) single-input single-output (SISO) plants. By introducing arbitrary-order finite-time convergence exact differentiators, the explosion of complexity problem in backstepping control is eliminated and the tracking error converges to zero asymptotically. Furthermore, the adaptive laws are necessary only at the first design step, which significantly reduce the design procedure. It is proved that, with the proposed scheme, all the closed-loop signals are semi-globally uniformly ultimately bounded. Simulation results are presented to demonstrate the effectiveness of the proposed scheme.

Strong Stabilization of a Class of MIMO Systems

Stabilization of finite dimensional linear, time-invariant, multi-input multi-output plants by stable feedback controllers, known as the strong stabilization problem, is considered for a class of plants with restrictions on the zeros in the right-half complex plane. The plant class under consideration has no restrictions on the poles, or on the zeros in the open left-half complex plane, or on the zeros at the origin or at infinity; but only one finite positive real zero is allowed. A systematic strongly stabilizing controller design procedure is proposed. The freedom available in the design parameters may be used for additional performance objectives although the only goal here is strong stabilization. In the special case of single-input single-output plants within the class considered, the proposed stable controllers have order one less than the order of the plant.

Control of LTI plants over erasure channels

This paper studies linear time-invariant (LTI) control architectures for LTI plants when communication takes place over a scalar erasure channel. Assuming i.i.d. data dropouts, we first show that such a channel is equivalent, in a second order moment sense, to an additive white noise channel subject to an instantaneous signal-to-noise ratio constraint. This key result is then exploited in two ways: First, we use it to characterize the set of all LTI controllers that achieve mean square stability in control architectures closed over scalar erasure channels. Second, we use it to show that the optimal design of LTI controllers over scalar erasure channels can be carried out by using tools from standard quadratic optimal control theory. We finally apply our results to the dynamic output feedback control of LTI single-input single-output (SISO) plants subject to data dropouts. In this case, we are able to establish closed form necessary and sufficient conditions on the minimal successful transmission probability that allows one to design mean square stabilizing controllers.