Output Transient Performance Research Articles

A switching-free multiple-model approach for adaptive FTC of non-Lipschitz nonlinear uncertain systems under persistent actuator failures

A novel actuator failure compensation scheme is proposed for affine nonlinear uncertain systems (not necessarily Lipschitz) subject to persistent/intermittent actuator faults/failures unknown in time, magnitude and pattern. The proposed control methodology satisfies the nonlinear separation principle through a modular backstepping control. The controller is then augmented with multiple estimation models to estimate failure induced parametric uncertainties and unknown system parameters. The output transient performance at start up and post-failure instances, is improved on account of a two layer adaptation which enhances the convergence speed and accuracy of parameter estimates. The proposed fault tolerant control (FTC) method yields a faithful accommodation of uncertain finite as well as infinite/intermittent/persistent actuator failures while ensuring satisfactory output transient and steady state performances. Further, compared to existing multiple model based adaptive fault tolerant control design for nonlinear systems, the proposed methodology circumvents the issues of stability due to switching between different models and utilizes a minimum number of estimation models for parameter estimation without compromising on the output performance. Consequently, the computational burden is also reduced. Compared to multiple model adaptive control based FTC strategies proposed earlier which assume finite actuator failures and Lipschitz nonlinear system, the proposed method is applicable to both Lipschitz and non-Lipschitz nonlinear systems affected by intermittent actuator failures. Using the concepts from stability analysis in random nonlinear impulsive systems, the L∞ and L2 bounds on tracking error for all future time are derived in the case of intermittent/persistent actuator failures obtained using the proposed fault-tolerant controller. The improvement of output transient performance in the proposed control scheme in comparison with controller with single identifier, is theoretically proved and quantified.

Adaptive Compensation of Actuator Failures using Multiple Models

In this paper, a novel actuator failure compensation scheme is proposed for affine nonlinear uncertain systems subject to actuator faults/failures unknown in time, magnitude and pattern. The proposed control methodology utilizes a backstepping procedure integrated with multiple estimation models to estimate failure induced parametric uncertainties and unknown system parameters. Relative to existing direct adaptive backstepping based fault compensation strategies, the proposed fault tolerant control (FTC) method yields a faithful accommodation of uncertain actuator failures while ensuring satisfactory output transient and steady state performances. Further, compared to multiple model based adaptive FTC design, the proposed methodology circumvents the issues of stability due to switching between different models and utilizes a minimum number of estimation models for parameter estimation without sacrificing the output performance and thereby reducing the computational burden. Simulation results illustrate the effectiveness and applicability of the proposed method to FTC design problem for longitudinal pitch control of Boeing 747-100/200 aircraft.

Design and implementation of a neuro-adaptive backstepping controller for buck converter fed PMDC-motor

A neuro-adaptive backstepping control (NABSC) method using single-layer Chebyshev polynomial based neural network is proposed for the angular velocity tracking in buck converter fed permanent magnet dc (PMDC)-motor. Owing to their universal approximation property, neural networks have been utilized for approximating the unknown nonlinear profile of instantaneous load torque. The inherent computational complexity of the neural network based adaptive scheme has been circumvented through the use of orthogonal Chebyshev polynomials as basis functions. A detailed stability and transient performance analysis has been conducted using Lyapunov stability criteria. The proposed control scheme is shown to yield a superior output performance with enhanced robustness for wide variations in load torque and set-point changes, compared to existing conventional approaches based on adaptive backstepping. The theoretical propositions are verified on an experimental prototype using dSPACE, Control Desk DS1103 setup with an embedded TM320F240 Digital Signal Processor proving its applicability to real-time electrical systems. The efficiency of the proposed strategy is quantified using performance measures and are evaluated against the conventional adaptive backstepping control (ABSC) methodology. Ultimately, this investigation confirms the effectiveness of the proposed control scheme in achieving an enhanced output transient performance while faithfully realizing its control objective in the event of abrupt and uncertain load variations.

Modeling and Control System Design of Marine Controlled-Source Electromagnetic Detection Transmitter

Marine electromagnetic transmitter transmits large power variable frequency electromagnetic wave to the seabed so as to obtain the submarine structure and mineral resources. The mathematical model of controlled source circuit needs to be established to realize closed loop control for increasing control precision and output transient performance of the electromagnetic wave. The operation process of controlled circuit is analyzed in continuous current mode, two equivalent switching states of controlled source circuit are obtained through the analysis of the different states of the switch in a switching period. A small signal equivalent model of the system is established using small ripple approximation. For high output voltage fluctuation problem in single loop control, double loop control strategy of voltage loop and current loop is designed. The simulation and experimental results show that, the system has the advantages of fast transient response speed and good regulation performance.

Small-Signal Modeling of Marine Electromagnetic Detection Transmitter Controlled-Source Circuit

Marine electromagnetic transmitter transmits electromagnetic waves with large power frequency conversion to the seabed to obtain the submarine structure and mineral resources. However, the current transmitter presents several problems, such as low efficiency, serious heat, and poor adaptability to the load. Soft-switching controlled-source circuit is used to reduce circuit losses. The mathematical model of controlled-source circuit should be established to realize a closed-loop control for increasing the output transient performance of electromagnetic waves. Given that the soft-switching controlled-source circuit has more status and that direct modeling is difficult, small-signal model of soft-switching controlled-source circuit is established based on that of hard-switching controlled-source circuit by analyzing the effect of output filter inductor current transformer leakage inductance and input voltage soft-switching controlled circuit on change in the duty cycle. Finally, experiments verify the accuracy and validity of the model.

Educational Issues of PI-PID Controllers

Educational issues of Proportional, Integral (PI) and Proportional, Integral, and Derivative (PID) type controller design in undergraduate course on control, graduate course on control, advanced control topics are discussed. The main attention is devoted to multi-time-scale control systems where PI PID type controllers designed for nonlinear systems in the presence of plant parameter variations and unknown external disturbances based on application of singular perturbation technique which guarantees desired output transient performance.

Output Regulation of Pulse-Width-Modulated Nonlinear Nonaffine-in-Control Systems via Singular Perturbation

AbstractThis paper addresses the problem of output regulation for nonlinear nonaffine-in-control systems in the presence of a high-frequency pulse-width modulation (PWM) in feedback loop. The problem of controller design is reduced to the continuous-time controller design based on Filippov's average model which is affine-in-control system. The proposed controller is an extension of PI/PID control scheme. The presented design methodology guarantees desired output transient performance indices by inducing of two-time-scale motions in the closed-loop system. The analysis of the closed-loop system properties is provided via the singular perturbation method. Stability conditions imposed on the fast and slow modes and sufficiently large mode separation rate between fast and slow modes can ensure that the full-order closed-loop nonlinear system achieves the desired properties in such a way that the output transient performances are desired and insensitive to external disturbances and plant's parameter variations. Numerical example and simulation results are presented.

Tracking with Prescribed Transient Performance for Hysteretic Systems

Tracking of reference signals (assumed bounded with essentially bounded derivative) is considered for a class of single-input, single-output, nonlinear systems, described by a functional differential equation with a hysteresis nonlinearity in the input channel. The first control objective is tracking, by the output, with prescribed accuracy: determine a feedback strategy which ensures that, for every reference signal and every system of the underlying class, the tracking error ultimately satisfies the prescribed accuracy requirements. The second objective is guaranteed output transient performance: the graph of the tracking error should be contained in a prescribed set (performance funnel). Under a weak sector boundedness assumption on the hysteresis operator, both objectives are achieved by a memoryless feedback which is universal for the underlying class of systems.

Controlled functional differential equations: approximate and exact asymptotic tracking with prescribed transient performance

A tracking problem is considered in the context of a class S of multi-input, multi-output, nonlinear systems modelled by controlled functional differential equations. The class contains, as a prototype, all finite-dimensional, linear, m-input, m-output, minimum-phase systems with sign-definite high-frequency gain. The first control objective is tracking of reference signals r by the output y of any system in S :g ivenλ ≥ 0, construct a feedback strategy which ensures that, for every r (assumed bounded with essentially bounded derivative) and every system of class S, the tracking error e = y − r is such that, in the case λ> 0, lim supt→∞ � e(t)� <λ or, in the case λ = 0, limt→∞ � e(t)� =0 . The second objective is guaranteed output transient performance: the error is required to evolve within a prescribed performance funnel Fϕ (determined by a function ϕ). For suitably chosen functions α, ν and θ, both objectives are achieved via a control structure of the form u(t )= −ν(k(t))θ(e(t)) with k(t )= α(ϕ(t)� e(t)� ), whilst maintaining boundedness of the control and gain functions u and k .I n the case λ = 0, the feedback strategy may be discontinuous: to accommodate this feature, a unifying framework of differential inclusions is adopted in the analysis of the general case λ ≥ 0.

Output Regulation of Uncertain Nonaffine in Control Systems via Singular Perturbation Technique

The problem of output regulation for nonlinear control systems with guaranteed transient performances in the presence of uncertainties is discussed, where the nonlinear systems are nonaffine in the control. The fast dynamical controller with the highest output derivative in feedback loop is used, where the controller is proper and can be implemented without ideal differentiation. Two-time-scale motions are induced in the closed-loop system and the method of singular perturbations is used to analyze the closed-loop system properties. Stability conditions imposed on the fast and slow modes and sufficiently large mode separation rate can ensure that the full-order closed-loop system achieves the desired properties in such a way that the output transient performances are desired and insensitive to external disturbances and variations of nonlinear system parameters. The problem of absolute stability analysis of the fast-motion subsystem for nonaffine systems with two-time-scale motions is considered in the presence of a sector-like condition in the control.

Tracking with Prescribed Transient Behavior for Nonlinear Systems of Known Relative Degree

Tracking of a reference signal (assumed bounded with essentially bounded derivative) is considered in the context of a class $\Sigma_{\rho}$ of multi‐input, multi‐output dynamical systems, modelled by functional differential equations, affine in the control and satisfying the following structural assumptions: (i) arbitrary—but known—relative degree $\rho \ge 1; (ii) the “high‐frequency gain” is sign definite—but possibly of unknown sign. The class encompasses a wide variety of nonlinear and infinite‐dimensional systems and contains (as a prototype subclass) all finite‐dimensional, linear, m‐input, m‐output, minimum‐phase systems of known strict relative degree. The first control objective is tracking, by the output y, with prescribed accuracy: given $\lambda >0$ (arbitrarily small), determine a feedback strategy which ensures that, for every reference signal r and every system of class $\Sigma_{\rho}$, the tracking error $e=y-r$ is ultimately bounded by λ (that is, $\|e(t)\| < \lambda$ for all t sufficiently large). The second objective is guaranteed output transient performance: the tracking error is required to evolve within a prescribed performance funnel $\mathcal{F}_\varphi$ (determined by a function φ). Both objectives are achieved using a filter in conjunction with a feedback function of the tracking error, the filter states, and the funnel parameter φ.

Tracking control with prescribed transient behaviour for systems of known relative degree

Tracking of a reference signal (assumed bounded with essentially bounded derivative) is considered for multi-input, multi-output linear systems satisfying the following structural assumptions: (i) arbitrary—but known—relative degree, (ii) the “high-frequency gain” matrix is sign definite—but of unknown sign, (iii) exponentially stable zero dynamics. The first control objective is tracking, by the output y , with prescribed accuracy: given λ > 0 (arbitrarily small), determine a feedback strategy which ensures that, for every reference signal r, the tracking error e = y - r is ultimately bounded by λ (that is, ∥ e ( t ) ∥ < λ for all t sufficiently large). The second objective is guaranteed output transient performance: the evolution of the tracking error should be contained in a prescribed performance funnel F ϕ (determined by a function ϕ ). Both objectives are achieved by a filter in conjunction with a feedback function of the filter states, the tracking error and a gain parameter. The latter is generated via a feedback function of the tracking error and the funnel parameter ϕ . Moreover, the feedback system is robust to nonlinear perturbations bounded by some continuous function of the output. The feedback structure essentially exploits an intrinsic high-gain property of the system/filter interconnection by ensuring that, if ( t , e ( t ) ) approaches the funnel boundary, then the gain attains values sufficiently large to preclude boundary contact.

Controller Design in Presence of Non-Smooth Nonlinearity: A Flight Control Example

The problem of output regulation with guaranteed transient performances in the presence of non-smooth nonlinearity is discussed. The fast dynamical controller with the relative highest derivative of output signal in feedback loop is used. Consequently, two-time-scale motions are induced in the closed-loop system. Stability conditions imposed on the fast and slow modes and sufficiently large mode separation rate can ensure that the full-order closed-loop system achieves the desired properties in such a way that the output transient performances are desired and insensitive to external disturbances and parameter variations in the system. The existence of stable limit cycle in the fast motion subsystem gives the robustness of the output transient performances in the presence of non-smooth nonlinearity and model uncertainty.

DESIGN OF DIGITAL MIMO CONTROL SYSTEMS WITH TWO-TIME-SCALE MOTIONS

The systematic approach of designing a robust sampled-data controller to solve output regulation problem for a MIMO nonlinear systems with unknown external disturbances and varying parameters is presented. The design methodology is based on the construction of two-time-scale motions in the closed-loop system. It has been shown that the proposed dynamical controller with a sufficiently small sampling period induces a two-time-scale separation of the fast and slow modes in the closed-loop system. Stability conditions imposed on the fast and slow modes and small sampling period can ensure that the full-order closed-loop system achieves the desired properties so that the output transient performances are desired and insensitive to parameter variations and external disturbances. Finally, an example with simulation results is presented.

Tracking Digital Controller for Robot Manipulator

The problem of the robust digital controller design to solve a tracking problem for robotic manipulators is studied. The design method based on the formation of two-time scale motions in the closed loop system is used. It has been shown that if a sufficient time-scale separation between the fast and slow modes in the discussed closed loop system and stability of fast modes are provided then slow modes have the desired form and thus the output transient performance indices are insensitive to parameter variations and external disturbances of the robotic manipulator. Numerical simulations of the two-link robotic manipulator are presented.

Accuracy Analysis of Digital Control Systems With Two-Time-Scale Motions

The problems of the robust digital controller design and control accuracy analysis are discussed. The design method based on the formation of two-time scale motions in the closed loop system is used. If a sufficient time-scale separation between the fast and slow modes in the discussed closed loop system and stability of fast modes are provided then slow modes have the desired form. Thus the output transient performance indices are insensitive to external disturbances. The relationships for control accuracy analysis and choice of the sampling period are obtained. Finally, an example with simulation results is presented.

Robust two-time-scale discrete-time system design

Abstract The problem of forming desired output transients for discrete-time system is discussed under assumption of incomplete information about varying parameters of the system and unknown external disturbances. The main result of the paper is the procedure to analyse of fast and slow motions in the discrete-time control system with small parameter where control system is designed by dynamic contraction method. It is shown, that if a sufficient time-scale separation between the fast and slow modes in the closed loop system and stability of fast motions are provided then in the closed loop system the output transient performance indices are insensitive to parameter variations of the plant and external disturbances. Finally, in order to guaranteed cost control an universal digital control law for a sampled-data system with small sampling period is received and numerical example is presented.