Showing papers on "Control theory published in 2000"

Closed loop system for controlling insulin infusion

Abstract: A closed loop infusion system controls the rate that fluid is infused into the body of a user. The closed loop infusion system includes a sensor system, a controller, and a delivery system. The sensor system includes a sensor for monitoring a condition of the user. The sensor produces a sensor signal, which is representative of the condition of the user. The sensor signal is used to generate a controller input. The controller uses the controller input to generate commands to operate the delivery system. The delivery system infuses a liquid into the user at a rate dictated by the commands from the controller. Preferably, the sensor system monitors the glucose concentration in the body of the user, and the liquid infused by the delivery system into the body of the user includes insulin. The sensor system uses the sensor signal to generate a message that is sent to the delivery system. The message includes the information used to generate the controller input. The sensor may be a subcutaneous sensor in contact with interstitial fluid. Also, two or more sensors may be used by the sensor system.

Neural Networks for Modelling and Control of Dynamic Systems: A Practitioner’s Handbook

Abstract: 1. Introduction.- 1.1 Background.- 1.1.1 Inferring Models and Controllers from Data.- 1.1.2 Why Use Neural Networks?.- 1.2 Introduction to Multilayer Perceptron Networks.- 1.2.1 The Neuron.- 1.2.2 The Multilayer Perceptron.- 1.2.3 Choice of Neural Network Architecture.- 1.2.4 Models of Dynamic Systems.- 1.2.5 Recurrent Networks.- 1.2.6 Other Neural Network Architectures.- 2. System Identification with Neural Networks.- 2.1 Introduction to System Identification.- 2.1.1 The Procedure.- 2.2 Model Structure Selection.- 2.2.1 Some Linear Model Structures.- 2.2.2 Nonlinear Model Structures Based on Neural Networks.- 2.2.3 A Few Remarks on Stability.- 2.2.4 Terminology.- 2.2.5 Selecting the Lag Space.- 2.2.6 Section Summary.- 2.3 Experiment.- 2.3.1 When is a Linear Model Insufficient?.- 2.3.2 Issues in Experiment Design.- 2.3.3 Preparing the Data for Modelling.- 2.3.4 Section Summary.- 2.4 Determination of the Weights.- 2.4.1 The Prediction Error Method.- 2.4.2 Regularization and the Concept of Generalization.- 2.4.3 Remarks on Implementation.- 2.4.4 Section Summary.- 2.5 Validation.- 2.5.1 Looking for Correlations.- 2.5.2 Estimation of the Average Generalization Error.- 2.5.3 Visualization of the Predictions.- 2.5.4 Section Summary.- 2.6 Going Backwards in the Procedure.- 2.6.1 Training the Network Again.- 2.6.2 Finding the Optimal Network Architecture.- 2.6.3 Redoing the Experiment.- 2.6.4 Section Summary.- 2.7 Recapitulation of System Identification.- 3. Control with Neural Networks.- 3.1 Introduction to Neural-Network-based Control.- 3.1.1 The Benchmark System.- 3.2 Direct Inverse Control.- 3.2.1 General Training.- 3.2.2 Direct Inverse Control of the Benchmark System.- 3.2.3 Specialized Training.- 3.2.4 Specialized Training and Direct Inverse Control of the Benchmark System.- 3.2.5 Section Summary.- 3.3 Internal Model Control (IMC).- 3.3.1 Internal Model Control with Neural Networks.- 3.3.2 Section Summary.- 3.4 Feedback Linearization.- 3.4.1 The Basic Principle of Feedback Linearization.- 3.4.2 Feedback Linearization Using Neural Network Models..- 3.4.3 Feedback Linearization of the Benchmark System.- 3.4.4 Section Summary.- 3.5 Feedforward Control.- 3.5.1 Feedforward for Optimizing an Existing Control System.- 3.5.2 Feedforward Control of the Benchmark System.- 3.5.3 Section Summary.- 3.6 Optimal Control.- 3.6.1 Training of an Optimal Controller.- 3.6.2 Optimal Control of the Benchmark System.- 3.6.3 Section Summary.- 3.7 Controllers Based on Instantaneous Linearization.- 3.7.1 Instantaneous Linearization.- 3.7.2 Applying Instantaneous Linearization to Control.- 3.7.3 Approximate Pole Placement Design.- 3.7.4 Pole Placement Control of the Benchmark System.- 3.7.5 Approximate Minimum Variance Design.- 3.7.6 Section Summary.- 3.8 Predictive Control.- 3.8.1 Nonlinear Predictive Control (NPC).- 3.8.2 NPC Applied to the Benchmark System.- 3.8.3 Approximate Predictive Control (APC).- 3.8.4 APC applied to the Benchmark System.- 3.8.5 Extensions to the Predictive Controller.- 3.8.6 Section Summary.- 3.9 Recapitulation of Control Design Methods.- 4. Case Studies.- 4.1 The Sunspot Benchmark.- 4.1.1 Modelling with a Fully Connected Network.- 4.1.2 Pruning of the Network Architecture.- 4.1.3 Section Summary.- 4.2 Modelling of a Hydraulic Actuator.- 4.2.1 Estimation of a Linear Model.- 4.2.2 Neural Network Modelling of the Actuator.- 4.2.3 Section Summary.- 4.3 Pneumatic Servomechanism.- 4.3.1 Identification of the Pneumatic Servomechanism.- 4.3.2 Nonlinear Predictive Control of the Servo.- 4.3.3 Approximate Predictive Control of the Servo.- 4.3.4 Section Summary.- 4.4 Control of Water Level in a Conic Tank.- 4.4.1 Linear Analysis and Control.- 4.4.2 Direct Inverse Control of the Water Level.- 4.4.3 Section Summary.- References.

Adaptive tracking control of a nonholonomic mobile robot

Abstract: A mobile robot is one of the well-known nonholonomic systems. The integration of a kinematic controller and a torque controller for the dynamic model of a nonholonomic mobile robot has been presented (Fierro and Lewis, 1995). In this paper, an adaptive extension of the controller is proposed. If an adaptive tracking controller for the kinematic model with unknown parameters exists, an adaptive tracking controller for the dynamic model with unknown parameters can be designed by using an adaptive backstepping approach. A design example for a mobile robot with two actuated wheels is provided. In this design, a new kinematic adaptive controller is proposed, then a torque adaptive controller is derived by using the kinematic controller.

Iterative learning control and repetitive control for engineering practice

Abstract: This paper discusses linear iterative learning and repetitive control, presenting general purpose control laws with only a few parameters to tune The method of tuning them is straightforward, maki

Semiactive Control Strategies for MR Dampers: Comparative Study

Abstract: This paper presents the results of a study to evaluate the performance of a number of recently proposed semiactive control algorithms for use with multiple magnetorheological (MR) dampers. Various control algorithms used in recent semiactive control studies are considered including the Lyapunov controller, decentralized bang-bang controller, modulated homogeneous friction algorithm, and a clipped optimal controller. Each algorithm is formulated for use with the MR damper. Additionally, each algorithm uses measurements of the absolute acceleration and device displacements for determining the control action to ensure that the algorithms could be implemented on a physical structure. The performance of the algorithms is compared through a numerical example, and the advantages of each algorithm are discussed. The numerical example considers a six-story structure controlled with MR dampers on the lower two floors. In simulation, an El Centro earthquake is used to excite the system, and the reduction in the drif...

Variable current limit control for vehicle electric drive system

Abstract: A vehicle electric drive system includes an internal combustion engine, an electric motor/generator driven by the engine, a first inverter/rectifier coupled to motor/generator, a bus coupled to the first inverter/rectifier, a second inverter/rectifier coupled to the bus, and a traction motor/generator coupled to an output of the second inverter/rectifier, an operator speed control member, and a controller coupled to the second inverter/rectifier for controlling a current output of the second inverter/rectifier as a function of a position of the speed control member Also included is an operator controlled foot pedal and a transducer coupled to the foot pedal and generating a signal representing foot pedal position which is supplied to the controller The controller limits current supplied by the second inverter/rectifier to the traction motor/generator to a limit current as a function of the transducer signal The controller, foot pedal and transducer cooperate to vary the limit current in response to movement of the foot pedal A spring biases the foot pedal to an upper limit position The controller causes the second inverter/rectifier to supply to the traction motor/generator a maximum amount of current, (such maximum current being a function of the foot pedal position), but not more than that required to achieve the speed commanded by the speed control

Decentralized overlapping control of a platoon of vehicles

Abstract: A methodology is proposed for longitudinal control design of platoons of automotive vehicles within intelligent vehicle/highway systems (IVHSs). The proposed decentralized overlapping control law is obtained by using the inclusion principle, i.e., by decomposing the original system model by an appropriate input/state expansion, and by applying the linear quadratic (LQ) optimization to the locally extracted subsystems. The local quadratic criteria directly reflect the desired system performance. Optimization is carried out by using a sequential algorithm adapted to the lower block triangular (LBT) structure of the closed-loop system model. Contraction to the original space provides a decentralized platoon controller which preserves the asymptotic stability and the steady-state behavior of the controller obtained in the expanded space. Conditions for eliminating the "slinky effect" and obtaining the strict string stability are defined; it is shown that the corresponding constraints on the controller parameters are not too restrictive. A new dynamic platoon controller structure, consisting of a reduced order observer and a static feedback map, is obtained by applying the inclusion principle to the decentralized overlapping platoon control design in the case when the information from the preceding vehicle is missing. Numerous simulation results show that the proposed methodology provides a reliable tool for a systematic and efficient design of platoon controllers within IVHS.

A game theoretic approach to controller design for hybrid systems

Abstract: We present a method to design controllers for safety specifications in hybrid systems. The hybrid system combines discrete event dynamics with nonlinear continuous dynamics: the discrete event dynamics model linguistic and qualitative information and naturally accommodate mode switching logic, and the continuous dynamics model the physical processes themselves, such as the continuous response of an aircraft to the forces of aileron and throttle. Input variables model both continuous and discrete control and disturbance parameters. We translate safety specifications into restrictions on the system's reachable sets of states. Then, using analysis based on optimal control and game theory for automata and continuous dynamical systems, we derive Hamilton-Jacobi equations whose solutions describe the boundaries of reachable sets. These equations are the heart of our general controller synthesis technique for hybrid systems, in which we calculate feedback control laws for the continuous and discrete variables, which guarantee that the hybrid system remains in the "safe subset" of the reachable set. We discuss issues related to computing solutions to Hamilton-Jacobi equations. Throughout, we demonstrate out techniques on examples of hybrid automata modeling aircraft conflict resolution, autopilot flight mode switching, and vehicle collision avoidance.

Adaptive robust motion control of single-rod hydraulic actuators: theory and experiments

Abstract: High-performance robust motion control of single-rod hydraulic actuators with constant unknown inertia load is considered. The two chambers of a single-rod actuator have different areas, so the dynamic equations describing the pressure changes in them cannot be combined into a single load pressure equation. This complicates controller design since it not only increases the system dimension but also brings in the stability issue of the added internal dynamics. A discontinuous projection-based adaptive robust controller (ARC) is constructed. The controller takes into account not only the effect of parameter variations coming from the inertia load and various hydraulic parameters but also the effect of hard-to-model nonlinearities such as uncompensated friction forces and external disturbances. It guarantees a prescribed output tracking transient performance and final tracking accuracy in general while achieving asymptotic output tracking in the presence of parametric uncertainties. In addition, the zero error dynamics for tracking any nonzero constant velocity trajectory is shown to be globally uniformly stable. Experimental results are obtained for the swing motion control of a hydraulic arm and verify the high-performance nature of the proposed strategy. In comparison to a state-of-the-art industrial motion controller, the proposed algorithm achieves more than a magnitude reduction of tracking errors. Furthermore, during the constant velocity portion of the motion, it reduces the tracking errors almost down to the measurement resolution level.

The Design of closed loop controllers for wind turbines

Abstract: This article reviews the design of algorithms for wind turbine pitch control and also for generator torque control in the case of variable speed turbines. Some recent and possible future developments are discussed. Although pitch control is used primarily to limit power in high winds, it also has a significant effect on various loads. Particularly as turbines become larger, there is increasing interest in designing controllers to mitigate loads as far as possible. Torque control in variable speed turbines is used primarily to maximize energy capture below rated wind speed and to limit the torque above rated. Once again there are opportunities for designing these controllers so as to mitigate certain loads. In addition to improving the design of the control algorithms, it is also possible to use additional sensors to help the controller to achieve its objectives more effectively. The use of additional actuators in the form of individual pitch controllers for each blade is also discussed. It is important to be able to quantify the benefits of any new controller. Although computer simulations are useful, field trials are also vital. The variability of the real wind means that particular care is needed in the design of the trials. Copyright © 2001 John Wiley & Sons, Ltd.

Energy based control of the Pendubot

Abstract: This paper presents the control of an underactuated two-link robot called the Pendubot. We propose a controller for swinging the linkage and raise it to its uppermost unstable equilibrium position. The balancing control is based on an energy approach and the passivity properties of the system.

Control design of an automated highway system

Abstract: Describes the design of an automated highway system (AHS) developed over the past ten years in the California PATH program. The AHS is a large, complex system, in which vehicles are automatically controlled. The design and implementation of the AHS required advances in actuator and sensor technologies, as well as the design, analysis, simulation, and testing of large-scale, hierarchical hybrid control systems. The paper focuses on the multilayer AHS control architecture and some questions of implementation. It discusses in detail the design and safety verification of the on-board vehicle control system and the design of the link-layer traffic-flow controller.

Robust backstepping control of nonlinear systems using neural networks

Abstract: A controller is proposed for the robust backstepping control of a class of general nonlinear systems using neural networks (NNs). A tuning scheme is proposed which can guarantee the boundedness of tracking error and weight updates. Compared with adaptive backstepping control schemes, we do not require the unknown parameters to be linear parametrizable. No regression matrices are needed, so no preliminary dynamical analysis is needed. One salient feature of our NN approach is that there is no need for the off-line learning phase. Three nonlinear systems, including a one-link robot, an induction motor, and a rigid-link flexible-joint robot, were used to demonstrate the effectiveness of the proposed scheme.

Control with random communication delays via a discrete-time jump system approach

Abstract: Digital control systems with random but bounded delays in the feedback loop can be modeled as finite-dimensional, discrete-time jump linear systems, with the transition jumps being modeled as finite-state Markov chains. This type of system can be called a "stochastic hybrid system". Due to the structure of the augmented state-space model, control of such a system is an output feedback problem, even if a state feedback law is intended for the original system. We present a V-K iteration algorithm to design switching and non-switching controllers for such systems. This algorithm uses an outer iteration loop to perturb the transition probability matrix. Inside this loop, one or more steps of V-K iteration is used to do controller synthesis, which requires the solution of two convex optimization problems constrained by LMIs.

Mechatronic design and control of hybrid electric vehicles

Abstract: The work in this paper presents techniques for design, development, and control of hybrid electric vehicles (HEV). Toward these ends, four issues are explored. First, the development of HEV is presented. This synopsis includes a novel definition of degree of hybridization for automotive vehicles. Second, a load-leveling vehicle operation strategy is developed. In order to accomplish the strategy, a fuzzy logic controller is proposed. Fuzzy logic control is chosen because of the need for a controller for a nonlinear, multidomain, and time-varying plant with multiple uncertainties. Third, a novel technique for system integration and component sizing is presented. Fourth, the system design and control strategy is both simulated and then implemented in an actual vehicle. The controller examined in this study increased the fuel economy of a conventional full-sized vehicle from 40 to 55.7 mi/h and increased the average efficiency over the Federal Urban Driving Schedule from 23% to 35.4%. The paper concludes with a discussion of the implications of intelligent control and mechatronic systems as they apply to automobiles.

Control Theory: Multivariable and Nonlinear Methods

Abstract: Preface. Introduction. 1. Representation of linear systems 2. Properties of linear systems 3. Sampled data systems 4. Disturbance models 5. The closed loop system 6. Limitations and conflicts 7. Controller structures and design 8. Minimization of quadratic criteria 9. Shaping the loop again 10. Descriptions of nonlinear systems 11. Stability of nonlinear systems 12. Qualitative beviour. Phase Plane 13. Oscillations and describing functions 14. Controller synthesis for nonlinear systems 15. Model predictive control : MPC, GPC, and DMM 16. To compensate exactly for nonlinearities 17. Optimal control 18. Conclusion. Literature. Index. Index of examples.

An improved control algorithm of shunt active filter for voltage regulation, harmonic elimination, power-factor correction, and balancing of nonlinear loads

Abstract: This paper deals with an implementation of a new control algorithm for a three-phase shunt active filter to regulate load terminal voltage, eliminate harmonics, correct supply power-factor, and balance the nonlinear unbalanced loads. A three-phase insulated gate bipolar transistor (IGBT) based current controlled voltage source inverter (CC-VSI) with a DC bus capacitor is used as an active filter (AF). The control algorithm of the AF uses two closed loop PI controllers. The DC bus voltage of the AF and three-phase supply voltages are used as feedback signals in the PI controllers. The control algorithm of the AF provides three-phase reference supply currents. A carrier wave pulse width modulation (PWM) current controller is employed over the reference and sensed supply currents to generate gating pulses of IGBTs of the AF. Test results are presented and discussed to demonstrate the voltage regulation, harmonic elimination, power-factor correction and load balancing capabilities of the AF system.

Robust H∞ glucose control in diabetes using a physiological model

Abstract: A robust H∞ controller was developed to deliver insulin via a mechanical pump in Type I diabetic patients. A fundamental nonlinear diabetic patient model was linearized and then reduced to a third-order linear form for controller synthesis. Uncertainty in the nonlinear model was characterized by up to ± 40% variation in eight physiological parameters. A sensitivity analysis identified the three-parameter set having the most significant effect on glucose and insulin dynamics over the frequency range of interest ω = [0.002, 0.2] (rad/min). This uncertainty was represented in the frequency domain and incorporated in the controller design. Controller performance was assessed in terms of its ability to track a normoglycemic set point (81.1 mg/dL) in response to a 50 g meal disturbance. In the nominal continuous-time case, the controller maintained glucose concentrations within ± 3.3 mg/dL of set point. A controller tuned to accommodate uncertainty yielded a maximum deviation of 17.6 mg/dL for the worst-case parameter variation.

Control of Linear Systems with Regulation and Input Constraints

Abstract: From the Publisher: The issue of tracking a desired reference signal in the presence of external disturbances is a classical control problem that resides at the core of control engineering. This is referred to as the output regulation problem. In this book the output regulation problem is examined in depth. New, highly significant dimensions are added to the problem and all pertinent topics associated with it are discussed. These topics include: Analysis and design of controllers for the output regulation problem subject to physical constraints on actuators such as amplitude and rate saturation. Incorporating transient performance requirements into output regulation problem formulation, thus creating an optimal framework for the output regulation problem. Uniting the output regulation problem formulation with other performance requirements of modern control theory such as H2 and Hinfinity optimal and suboptimal performance criteria. Opening up a novel framework of output regulation problem formulation in order to enlarge the class of signals dealt with whilst at the same time adding new possibilities. This book is designed to meet the needs of a variety of readers including practising control engineers, graduate students, and researchers in control engineering.

Supervisory control of hybrid systems

Abstract: In this paper, the supervisory control of hybrid systems is introduced and discussed at length. Such control systems typically arise in the computer control of continuous processes, for example, in manufacturing and chemical processes, in transportation systems, and in communication networks. A functional architecture of hybrid control systems consisting of a continuous plant, a discrete-event controller, and an interface is used to introduce and describe analysis and synthesis concepts and approaches. Our approach highlights the interaction between the continuous and discrete dynamics, which is the cornerstone of any hybrid system study. Discrete abstractions are used to approximate the continuous plant. Properties of the discrete abstractions to be appropriate representations of the continuous plant are presented, and important concepts such as determinism and controllability are discussed. Supervisory control design methodologies are presented to satisfy control specifications described by formal languages. Several examples are used throughout the paper to illustrate our approach.

Fuzzy Control and Modeling: Analytical Foundations and Applications

Abstract: From the Publisher: "The emerging, powerful fuzzy control paradigm has led to the worldwide success of countless commercial products and real-world applications. Fuzzy control is exceptionally practical and cost-effective due to its unique ability to accomplish tasks without knowing the mathematical model of the system, even if it is nonlinear, time varying and complex. Nevertheless, compared with the conventional control technology, most fuzzy control applications are developed in an ad hoc manner with little analytical understanding and without rigorous system analysis and design.Fuzzy Control and Modeling is the only book that establishes the analytical foundations for fuzzy control and modeling in relation to the conventional linear and nonlinear theories of control and systems. The coverage is up-to-date, comprehensive, in-depth and rigorous. Numeric examples and applications illustrate the utility of the theoretical development. In the forward to Fuzzy Control and Modeling, Professor Lotfi Zadeh, the founder of fuzzy logic, declares:?Professor Ying?s book contains much that is new, important and detailed? . His linkage of basic theory to real-world applications is very impressive? . The last chapter in the book deals with a subject in which Professor Ying is a foremost authority, namely, application of fuzzy control to biomedical systems?. Professor Ying?s work should go a long way toward countering the view that fuzzy control is a collection of applications without a solid theory. The deep theory of fuzzy control developed by Professor Ying is of great importance both as a theory and as a foundation for major advances in applications of fuzzy control in industry, biomedicine, and otherfields.?Important topics discussed include: *Structures of fuzzy controllers/models with respect to conventional fuzzy controllers/models* Analysis of fuzzy control and modeling in relation to their classical counterparts*Stability analysis of fuzzy systems and design of fuzzy control systems*Sufficient and necessary conditions on fuzzy systems as universal approximators*Real-time fuzzy control systems for treatment of life-critical problems in biomedicineFuzzy Control and Modeling is a self-contained, invaluable resource for professionals and students in diverse technical fields who aspire to analytically study fuzzy control and modeling.About the AuthorHao Ying left the faculty of University of Texas Medical Branch in 2000, and is currently an associate professor in the Department of Electrical Engineering at Wayne State University. He began fuzzy control research in 1981. In 1987, Dr. Ying established the world?s first analytical connection between a fuzzy controller and a conventional controller. In 1989, he developed the world?s first clinical fuzzy control application ? real-time control of blood pressure. Dr. Ying has been making systematic contributions to analytical issues fundamental to fuzzy control and systems ever since."Sponsored by:IEEE Engineering in Medicine and Biology Society.

Sensorless sliding-mode control of induction motors

Abstract: This paper develops the ideas of speed- and flux-sensorless sliding-mode control for an induction motor illustrated in previous work by one of the authors. A sliding-mode observer/controller is proposed in this paper. The convergence of the nonlinear time-varying observer along with the asymptotic stability of the controller is analyzed. Pulsewidth modulation implementation using sliding-mode concepts is also discussed. Major attention is paid to torque control, and then the developed approach is utilized for speed control. Computer simulations and experiments have been carried out to test the proposed estimation and control algorithm. The experimental results demonstrated high efficiency of the proposed estimation and control method.

Control of variable geometry turbocharged diesel engines for reduced emissions

Abstract: The emission control problem for an automotive direct injected compression ignition (diesel) engine equipped with exhaust gas recirculation (EGR) and a variable geometry turbocharger (VGT) is considered The objective is to operate the engine to meet driver's torque demand and minimize NO/sub x/ emissions while at the same time avoiding visible smoke generation It is demonstrated that the steady-state optimization of engine emissions results in operating points where EGR and VGT actuators are in effect redundant in their effect on the variables that most directly affect the emissions A multivariable feedback controller is proposed which accounts for this actuator redundancy Furthermore, it coordinates the two actuators to fully utilize their joint effect on engine emission performance Experimental results confirm good response properties of the proposed controller

Robust nonlinear speed control of PM synchronous motor using boundary layer integral sliding mode control technique

Abstract: A digital signal processor (DSP)-based robust nonlinear speed control of a permanent magnet synchronous motor (PMSM) is presented. A quasi-linearized and decoupled model including the influence of parameter variations and speed measurement error on the input-output feedback linearization of a PMSM is derived. Based on this model, a boundary layer integral sliding mode controller is designed and compared to a feedback linearization-based controller that uses proportional plus derivative (PD) controller in the outer loop. To show the validity of the proposed control scheme, DSP-based experimental works are carried out and compared with the conventional control scheme.

An analysis and design method for linear systems subject to actuator saturation and disturbance

Abstract: We present a method for estimating the domain of attraction of a system under a saturated linear feedback. A simple condition is derived in terms of an auxiliary feedback matrix for determining if a given ellipsoid is contractive invariant. This condition is shown to be less conservative than the existing conditions which are based on the circle criterion or the vertex analysis. Moreover, the condition can be expressed as LMIs in terms of all the varying parameters and hence can easily be used for controller synthesis. This condition is then extended to determine the invariant sets for systems with persistent disturbances. LMI based methods are developed for constructing feedback laws that achieve disturbance rejection with guaranteed stability requirements. The effectiveness of the developed methods are illustrated with examples.