Constant Reference Inputs Research Articles

Saturating PI Control of Stable Nonlinear Systems Using Singular Perturbations

This article presents an antiwindup propor- tional-integral (PI) controller, using a saturating integrator, for a single-input and single-output (SISO) stable nonlinear plant, whose steady-state input–output map is increasing. We prove that, under reasonable assumptions, there exists an upper bound on the controller gain such that for any constant reference input, the corresponding equilibrium point of the closed-loop system is exponentially stable, with a “large” region of attraction. When the state of the closed-loop system converges to this equilibrium point, then the tracking error tends to zero. The closed-loop stability analysis employs Lyapunov methods in the framework of the singular perturbations theory. Finally, we show that if the plant satisfies the asymptotic gain property, then the closed-loop system is globally asymptotically stable for any sufficiently small controller gain. The effectiveness of the proposed PI controller is proved by showing how it performs as part of the control algorithm of a synchronverter (a special type of dc to ac power converter).

A spatio-temporal reference trajectory planner approach to collision-free continuum deformation coordination

This paper proposes a spatio-temporal reference trajectory planner approach to safely plan continuum deformation coordination of a multi-agent system (MAS) in an obstacle-laden environment. We formulate a desired n-D continuum deformation as a leader–follower problem guided by n+1 leaders and followed by the remaining follower agents either through direct communication with leaders or communication with neighboring agents. To plan a safe continuum deformation coordination, we first provide sufficient conditions for inter-agent and obstacle collision avoidance. Then, we spatially optimize the continuum deformation coordination using the A* search to determine leaders’ desired waypoints in an obstacle-laden environment. Leaders’ desired waypoints are connected through C1 continuous paths that are assigned by the spline curve fitting method. The desired trajectories of the leaders are then determined by planning a piece-wise constant reference input such that travel time is minimized and safety of the continuum deformation coordination is ensured.

Direct Sliding Mode Control of a Three-Phase AC/DC Power Converter for the Velocity Regulation of a DC Motor

A DC voltage source and a DC/DC power converter can be used to control the position, speed, or torque of a DC motor. In such operational conditions, a rectifier is needed to use a DC voltage source if only a three-phase voltage source is available. The objective of this study is to replace a rectifier and DC/DC power converter by one AC/DC power converter, such that its output would be equal to the voltage needed to control a DC motor. It is assumed that the control algorithm of a DC motor is selected, which means that the desired output voltage of the AC/DC converter as a time function or function of the motor state is known. First, a sliding mode methodology is applied to control the converter’s three shoulders to make the three-phase input current track the source voltages multiplied by a time-varying gain. The gain is then selected such that the converter output voltage is equal to the desired input of the DC motor. It is shown that this condition holds if the time-varying gain satisfies a first-order differential equation, which can be implemented as part of the controller. The application of Lyapunov theory confirms that the speed regulation process has a stable equilibrium point at the origin and that the time gain variation is bounded. The power efficiency is equal to one if the gain is positive. A numerical simulation demonstrates application of the developed control methodology for both constant and time-varying angular speed reference inputs.

Neumann trace tracking of a constant reference input for 1-D boundary controlled heat-like equations with delay

This paper discusses the Proportional Integral (PI) regulation control of the left Neumann trace of a one-dimensional reaction-diffusion equation with a delayed right Dirichlet boundary control. Specifically, a PI controller is designed based on a finite-dimensional truncated model that captures the unstable dynamics of the original infinite-dimensional system. In this setting, the control input delay is handled by resorting to the Artstein transformation. The stability of the resulting infinite-dimensional system, as well as the tracking of a constant reference signal in the presence of a constant distributed perturbation, is assessed based on the introduction of an adequate Lyapunov function. The theoretical results are illustrated with numerical simulations.

Average-consensus tracking of multi-agent systems with additional interconnecting agents

Average-consensus tracking problem is investigated for first-order multi-agent systems composed of valid agents and additional interconnecting agents. Valid agents have constant reference inputs, while additional interconnecting agents do not have reference inputs. Average-consensus tracking algorithms are proposed for the agents converging to the average value of constant reference inputs of valid agents. Under symmetric and connected topology, consensus conditions are obtained for the agents without and with communication delay, respectively, by using generalized Nyquist criterion. Numerical examples illustrate the correctness of theoretical results.

Network-based PI control for output tracking of continuous-time systems with time-varying sampling and network-induced delays

For a continuous-time linear system with constant reference input, the network-based proportional-integral (PI) control is developed to solve the output tracking control problem by taking time-varying sampling and network-induced delays into account. A traditional PI control system is introduced to obtain the equilibriums of state and control input. Using the equilibriums, a discrete-time PI tracking controller in a network environment is constructed. The resulting network-based PI control system is described by an augmented system with two input delays and the output tracking objective is transformed into ensuring asymptotic stability of the augmented system. A delay-dependent stability condition is established by a discontinuous augmented Lyapunov–Krasovskii functional approach. The PI controller design result of in-wheel motor as a case study is provided in terms of linear matrix inequalities. Matlab simulation and experimental results resorting to a test-bed for ZigBee-based control of in-wheel motor are given to validate the proposed method.

Observer‐based tracking controller design for quasi‐one‐sided Lipschitz nonlinear systems

SummaryIn this paper, the observer‐based controller design problem for tracking a constant reference input for quasi‐one‐sided Lipschitz nonlinear systems is considered. For this purpose, at first, a state feedback controller is proposed and sufficient conditions for solvability of the problem are obtained in terms of linear matrix inequality feasibility conditions. Then, an observer for estimating the states of the system is designed. Subsequently, it is shown that the separation principle for the proposed feedback controller holds, and consequently, the designing of the state feedback controller and the observer can be done separately. Simulation results are given to verify the effectiveness of the proposed methodology.

Input Design-Based Compensation Control for Networked Nonlinear Systems With Random Delays and Packet Dropouts

This brief investigates the data-based networked control problem of a class of nonlinear systems, where random network-induced delays and packet dropouts in the feedback and forward channels are considered simultaneously and further treated as random round-trip time (RTT) delays. The main contributions of this brief are as follows: 1) To actively compensate for RTT delays, a novel compensation control scheme is proposed based on the control input design, and thus, only one control command needs to be transmitted to the actuator through the network; 2) an explicit sufficient condition is derived to ensure the stability of the resulting closed-loop system as well as a zero steady-state output error for a constant reference input; and 3) numerical simulation and comparison with existing methods are carried out to show the effectiveness of the proposed method.

Fault Tolerance Enhance DC-DC Converter Lifetime Extension

One of the most crucial renewable energy sources today is solar energy. Power convertors play an important role in adjusting the output voltage or current of photovoltaic (PV) systems. Using efficient and reliable switches for power converters and inverters is crucial for enhancing the safety and reliability of a platform. Generally, power converters suffer from failure mechanisms, such as wire bond fatigue, wire bond lift up, solder fatigue and loose gate control voltage, which mainly occur in power switches. In this paper, the junction temperature of the Insulated Gate Bipolar Transistor (IGBT) acting as a power switch used in the Impedance-Source DC-DC converter is estimated using an electro-thermal model in order to develop an adaptive thermal stress control (ATSC). The proposed stress control adjusts reference input of the PI control to extend the life expectancy of the device under the mission. The accuracy of results present using The Modified Coffin-Manson Law has been used to determine the life of IGBT and the lifetime has been successfully increased base on implementing imperative ATSC and comparing the result with the constant reference input of the PI controller. The result integrates with converter health management to develop advanced intelligent predictive maintenance.

Collaborative Tracking Control of Dual Linear Switched Reluctance Machines Over Communication Network With Time Delays.

This paper investigates the collaborative tracking control for dual linear switched reluctance machines (LSRMs) over a communication network with random time delays. Considering the spatio-temporal constraint relationship of the dual LSRMs in complex industrial processes, the collaborative tracking control scheme is proposed based on the networked motion control method. The stability conditions and the controller design method for the networked dual LSRMs are obtained from the two motors relative position error by using Lyapunov theory and delay systems approach. Four different allocation schemes combined with two kinds of external control signals are applied onto the collaborative tracking control experiment platform of the dual LSRMs to validate the effectiveness of the proposed method. The maximum steady-state relative position error within 0.104 mm can be achieved under the constant absolute position reference input signal of 3 mm, and the maximum absolute relative position error within ±0.46 mm can be achieved under the sinusoidal reference of 8 mm amplitude and 0.2 Hz.

Inertia and Friction Estimation of a Velocity-Controlled Servo Using Position Measurements

This paper proposes a method that estimates the parameters of a velocity-controlled servo. A proportional-integral controller, which uses only position measurements, closes the loop. The proposed approach uses the steady-state response produced by steps and sine-wave signals; they do not produce high levels of vibration on the servo compared with random signals commonly used with the least squares algorithm; moreover, it relies on simple numerical calculations. The method, which is called in the sequel as the steady-state response method (SSRM), consists of two steps. The first step uses three constant reference inputs in order to identify a constant disturbance and the viscous and Coulomb friction coefficients of the servo. In the second step, the SSRM estimates the servo inertia using a sine wave plus a constant signal as a velocity reference input and employs the estimate of the viscous friction coefficient obtained in the first step. Experiments on a testbed employing a brushless servomotor allow comparing the results obtained using the SSRM and those produced by a standard recursive least squares method (RLSM).

Stability Analysis of a Type of T-S Fuzzy Control Systems Using Off-Axis Circle Criterion

Abstract In this paper, based on the off-axis circle criterion, a sufficient condition with a simple graphical explanation is derived to analyze the global asymptotic stability of a type of Takagi-Sugeno (T-S) fuzzy control systems in case of different constant reference inputs. Three numerical examples are given to demonstrate how to use the proposed method in analyzing the T-S fuzzy control systems.

Reconfigurable control of piecewise affine systems with actuator and sensor faults: Stability and tracking

A reconfigurable control approach for continuous-time piecewise affine (PWA) systems subject to actuator and sensor faults is presented. The approach extends the concept of virtual actuators and virtual sensors from linear to PWA systems on the basis of the fault-hiding principle that provides the underlying conceptual idea: the fault is hidden from the nominal controller and the fault effects are compensated. Sufficient linear matrix inequality (LMI) conditions for the existence of virtual actuators and virtual sensors are given that guarantee the recovery of closed-loop stability and the tracking of constant reference inputs. Since LMIs are efficiently solvable, this solution leads to a tractable computational algorithm that solves the reconfiguration problem. The approach is proven to be robust against model uncertainties and inaccurate fault diagnosis, and is evaluated using an example system of interconnected tanks.

Fault detection for output feedback control systems with actuator stuck faults: A steady‐state‐based approach

AbstractThe paper studies the fault detection problem for output feedback control systems with bounded disturbances and nonzero constant reference inputs. A steady‐state‐based approach is proposed which can be used to detect small actuator stuck faults including actuator outage (the stuck value is zero). These small stuck faults, especially the outage faults, cannot be detected effectively using the existing techniques. A dynamic output feedback controller and a weighting matrix are designed simultaneously. The dynamic output feedback controller stabilizes the closed‐loop system for both fault‐free and faulty cases and attenuates the effects of disturbances. By manipulating the steady‐state values of system states with the detection weighting matrix, a residual is then generated, through which actuator stuck faults including actuator outages can be detected effectively. Simulation results are included to demonstrate our design procedure. Copyright © 2009 John Wiley & Sons, Ltd.

Fault detection for linear uncertain systems with sensor faults

The study paper deals with sensor fault detection problem for a class of linear uncertain systems with bounded disturbances and non-zero constant reference inputs. The sensor faults are modelled as multi-mode, named as fault-free mode and faulty modes. A steady-state-based approach is proposed to detect the sensor faults. The steady-state-based approach can be used to detect lock-in-place sensor faults with arbitrary small magnitudes, which has not been well investigated in the literature. A convergent iterative algorithm based on linear matrix inequalities is given to obtain the solutions. A numerical example is given to illustrate the effectiveness of the proposed methods.

Fault Detection for a Class of Uncertain State-Feedback Control Systems

This brief studies the problem of fault detection for a class of uncertain state-feedback tracking control systems with constant reference inputs and bounded disturbances. The considered systems are modeled via multiple modes, namely, fault-free case and faulty cases. Actuator stuck faults, including outage cases, are considered. With the aid of the finite-frequency positive-realness approach, a new linear-matrix-inequality-based fault detection method for control systems is obtained and applied to fault detection for flight control systems. An F-18 aircraft model is included in the simulation to illustrate the effectiveness of the proposed method.

Precise motion control of a nanopositioning PZT microstage using integrated capacitive displacement sensors

We propose a hysteresis and drift compensation scheme using proportional-integral feedback control for a nanopositioning Pb(ZrTi)O3 (PZT) microstage. A multi-degree of freedom PZT microstage with integrated differential capacitive displacement sensors has been fabricated and tested, demonstrating the feasibility of compensating for hysteresis and creep. The feedback signal to the PZT actuators is fed from differential capacitive sensors of the displacement of the microstage. Experimental results show that the sensitivity of the displacement sensor is approximately 0.53 V µm−1. A maximum resolution of 16 nm is achieved when hysteresis is compensated for, and the minimum detectable variation of capacitance ΔC is 1.25 × 10−3 pF. The hysteresis of the system varies with the proportional gain Kp, integral time constant Ti and reference input frequency. By using feedback control with a proportional and integration (PI) controller, the hysteresis decreases from 30% in open-loop operation to approximately 1% in closed-loop operation at a gain of 20, when the frequency of the sine reference input is 1 Hz and Ti is 20 ms. Efficient compensation of hysteresis is validated by the closed-loop control, especially when the frequency of the reference input is low. Elimination of creep/drift is also verified by the closed-loop control.

Dynamic Anti-Integrator-Windup Controller Design for Linear Systems With Actuator Saturation

The present paper is concerned with the design of dynamic anti-integrator-windup controllers for critically stable linear systems with a single pole at the origin. The constant gain term in the conventional anti-windup controller is extended to have dynamics represented by a transfer function. The proposed dynamic anti-windup compensator is similar to the one based on co-prime factorization of the plant. The overall controller includes an internal model for constant signals and achieves regulation for constant disturbance and reference inputs as long as the asymptotic control input stays within the saturation limits. The effectiveness of the proposed method is demonstrated on a one-link flexible arm through simulations and experiments.

Nonlinear Robust Servo Systems using Switching of Control Gains and Reference Inputs

In this paper, we consider a design problem of robust nonlinear servo systems which achieve asymptotic tracking for constant reference inputs. We assume that the region ℜ to which reference commands belong is given and that we can observe the whole state of the plant. The servo system which we will propose in this paper has two components: One is a kind of reference governor, which switch reference input and the other is the controller for regulation. Both reference input and controller are switched according to the region to which state of the system belongs. Polytopic Lyapunov functions are used to estimate the positively invariant set and show the stability of the equilibrium for each mode. Moreover, the idea of piecewise linear Lyapunov functions is used to design controllers and controllers are obtained by solving bilinear programming problems.

Fuzzy linear pulse-transfer function-based sliding-mode control for nonlinear discrete-time systems

In this paper, a nonlinear discrete-time system in the presence of input disturbance and measurement noise is approximated by N subsystems described by the linear pulse-transfer functions. Although the input disturbance and the measurement noise are unknown, they are modeled as known pulse-transfer functions. The approximation error between the nonlinear discrete-time system and the fuzzy linear pulse-transfer function system is represented by the linear time-invariant dynamic system in every subsystem, whose degree can be larger than that of the corresponding subsystem. Besides the input disturbance and the measurement noise, uncertainties are caused by the approximation error of the fuzzy-model and the interconnected dynamics resulting from the other subsystems. Owing to the presence of input disturbance, measurement noise, or uncertainties, a disadvantageous response occurs. Based on Lyapunov redesign, the switching control in every subsystem is designed to reinforce the system performance. Due to the time-invariant feature for a constant reference input, the operating point can approach the sliding surface in the manner of finite-time steps. The stability of the overall system is verified by Lyapunov stability theory.