Passivity-based control for bilateral teleoperation: A tutorial

This tutorial revisits several of the most recent passivity-based controllers for nonlinear bilateral teleoperators with guaranteed stability properties. These schemes, which include scattering–based, damping injection and adaptive controllers, ensure asymptotic stability in multiple situations that range from constant to variable time-delays, with or without scattering transformation and with or without position tracking capabilities. Although all controllers exploit the basic property of passivity of the teleoperators, they have been developed invoking various analysis and design tools, which complicates their comparison and relative performance assessment. The objective of this paper is to present a unified theoretical framework—based on a general Lyapunov–like function—that, upon slight modification, allows to analyze the stability of all the schemes.     

Asymptotic stabilization of passive systems without damping injection: A sampled integral technique

Passivity in physical systems is a restatement of energy balancing, and therefore is a ubiquitous property in engineering applications. Under some weak conditions, the unique equilibrium state of passive systems is stable. However, to ensure asymptotic stability, strict output passivity and a detectability property are required. Although strict output passivity may be enforced via a damping injection that feeds back the passive output, this signal may be noisy or unmeasurable — the paradigmatic example being velocity in mechanical systems. In this paper a sampled integral stabilization (SIS) technique for the asymptotic regulation of passive systems, that requires only the knowledge of the time integral of the passive output — i.e. position in mechanical systems — is proposed. As a generalization of the previous result, it is shown that SIS is applicable to cascade connections of passive systems measuring only the storage function of the second one. Several examples, including a planar elbow manipulator and the rigid body dynamics are shown to satisfy the assumptions for the application of SIS.     

A controller tuning methodology for the air supply system of a PEM fuel-cell system with guaranteed stability properties

Fuel cells are electrochemical devices that convert the chemical energy of a gaseous fuel directly into electricity. They are widely regarded as potential future stationary and mobile power sources. The response of a fuel-cell system depends on the air and hydrogen feed, flow and pressure regulation, and heat and water management. In this article, the study is concentrated on the air subsystem that feeds the fuel-cell cathode with oxygen and, in particular, on the problem of providing tuning rules for these controllers ensuring stability of the overall system. Proceeding from a reduced order non-linear model, that preserves the main features of the (by-now classical) ninth order model, we suggest a natural decomposition into interconnected subsystems where one of them is strictly passive, hence finite ?₂-gain stable, and the other one depends on the controller parameters. The proposed tuning methodology consists then on enforcing the required input–output property of the feedback loop, either passivity or a suitable ?₂-gain. For this end, the feedback operator is linearised, then robust Kharitonov-based positive (or bounded) realness conditions are imposed to determine the allowable ranges for the controller gains. We illustrate the methodology with a classical cascaded loop-controller structure with an inner loop feedback linearising controller and an outer loop PI regulator. Simulation results are presented to illustrate the conservativeness of the analysis as well as the performance improvement obtained with a suitable tuning.     

Nonlinear regulation of a Lorenz system by feedback linearization techniques

In this paper we analyze some dynamical properties of a chaotic Lorenz system driven by a control input. These properties are the input-state and the input-output feedback linearizability, the stability of the zero dynamics, and the phase minimality of the system. We show that the controlled Lorenz system is feedback equivalent to a controllable linear system. We also show that the zero dynamics are asymptotically stable when the output is an arbitrary state. These facts allow designing control laws such that the closed-loop system has asymptotically stable equilibrium points with dynamic behavior free from chaotic transients. The controllers are robust in the sense that the closed-loop system is stable and non chaotic around a nominal set of parameter values. The results also show that the proposed controllers give better responses compared to linear algorithms obtained from standard linearization techniques, and exhibit a good performance even when the control input is bounded.     

Dynamic analysis of weigthed-output Fuzzy Control Systems

In this paper, Fuzzy Control Systems with consecuent functions are analized using concepts from qualitative theory of nonlinear dynamic systems. Particularly, linear weigthed output fuzzy controllers and weight-output fuzzy controller are considered.The consequent function coefficients of rules around the equilibrium point are related with the stability and robustness indices. Finally, a explanatory example is presented.     

Modelling,dynamics and control of a portable DMFC system

A dynamic model for a direct methanol fuel cell and its ancillary units is presented, in which all ancillary units perform only one operation each. The system’s losses and main dynamics (cathodic oxygen fraction, anodic methanol concentration, stack temperature, system water holdup) are analysed for stability and time constants. The system is found to be stable in all of its dynamics except for that of water holdup. The influence of external conditions, such as temperature and humidity, on system feasibility is analysed; the capability of system autonomous operation depends essentially on environmental conditions and on the chosen air excess ratio. Decoupled single-input, single-output controllers, some of which employing feedback, are applied to maintain the system at a certain set point. System simulations are performed, confirming the performance of the proposed controllers, their ability to stabilise the water holdup, and the absence of interaction-induced oscillations; the system can be started up in about ten minutes with the presented parameters.     

Computing actuator bandwidth limits for model reference adaptive control

Although model reference adaptive control theory has been used in numerous applications to achieve system performance without excessive reliance on dynamical system models, the presence of actuator dynamics can seriously limit the stability and the achievable performance of adaptive controllers. In this paper, a linear matrix inequalities-based hedging approach is developed and evaluated for model reference adaptive control of uncertain dynamical systems in the presence of actuator dynamics. The hedging method modifies the ideal reference model dynamics in order to allow correct adaptation that is not affected by the presence of actuator dynamics. Specifically, we first generalise the hedging approach to cover a variety of cases in which actuator output and the control effectiveness matrix of the uncertain dynamical system are known and unknown. We then show the stability of the closed-loop dynamical system using Lyapunov-based stability analysis tools and propose a linear matrix inequality-based framework for the computation of the minimum allowable actuator bandwidth limits such that the closed-loop dynamical system remains stable. Finally, an illustrative numerical example is provided to demonstrate the efficacy of the proposed approach.     

Model-based analysis for the thermal management of open-cathode proton exchange membrane fuel cell systems concerning efficiency and stability

In this work we present a dynamic, control-oriented, concentrated parameter model of an open-cathode proton exchange membrane fuel cell system for the study of stability and efficiency improvement with respect to thermal management. The system model consists of two dynamic states which are the fuel cell temperature and the liquid water saturation in the cathode catalyst layer. The control action of the system is the inlet air velocity of the cathode air flow manifold, set by the cooling fan, and the system output is the stack voltage. From the model we derive the equilibrium points and eigenvalues within a set of operating conditions and subsequently discuss stability and the possibility of efficiency improvement. The model confirms the existence of a temperature-dependent maximum power in the moderate temperature region. The stability analysis shows that the maximum power line decomposes the phase plane in two parts, namely stable and unstable equilibrium points. The model is capable of predicting the temperature of a stable steady-state voltage maximum and the simulation results serve for the design of optimal thermal management strategies.     

Robustness of linear feedback control systems to unmodelled high-frequency dynamics

A basic issue in the control of linear time-invariant plants is the effect of neglected high-frequency dynamics on the performance, in particular on the closed-loop stability, of the control system. In this paper, the robustness of various output feedback control designs, based on a reduced-order model with neglected high-frequency dynamics, is investigated using singular perturbation techniques. A general robust design rule is to avoid static output feedback for systems with unmodelled high-frequency dynamics. From a frequency-domain standpoint, the robust design rule is to avoid closing high-frequency plant loops by using strictly proper controllers or controllers with a low-pass filtering property.     

Equilibrium-independent passivity: A new definition and numerical certification

We extend the traditional notion of passivity to a forced system whose equilibrium is dependent on the control input by defining equilibrium-independent passivity, a system property characterized by a dissipation inequality centered at an arbitrary equilibrium point. We provide a necessary input/output condition which can be tested for systems of arbitrary dimension and sufficient conditions to certify this property for scalar systems. An example from network stability analysis is presented which demonstrates the utility of this new definition. We then proceed to numerical certification of equilibrium-independent passivity using sum-of-squares programming. Finally, through numerical examples we show that equilibrium-independent passivity is less restrictive than incremental passivity.     

Digital parameter-adaptive control of an air-conditioning plant

Two parameter-adaptive (self-tuning) control algorithms for multivariable systems are described. The algorithms are designed on the basis of linear input-output system models by the combination of recursive parameter estimation and control algorithms: a parameter-adaptive deadbeat controller and a parameter-adaptive optimal state controller. These controllers are applied to a two-input two-output air-conditioning pilot plant, which consists of an air heater and an air humidifier and whose output variables are the temperature and the relative humidity of the air measured at the air outlet. The air-conditioning plant is a nonlinear system and its linearized static and dynamic behaviour is strongly dependent on the operating point characterized mainly by the output variables and by the air flow rate through the plant. The results of the real-time control experiments indicate that it is possible to use the self-tuning features of the parameter-adaptive controllers to stabilize the controlled system after a short adaption phase and to achieve at least a satisfactory control performance for time varying air flow rates and for time varying setpoints of the output variables.     

An Analytical Study on Structure, Stability and Design of General Nonlinear Takagi–Sugeno Fuzzy Control Systems

In this paper, we first study analytical structure of general nonlinear Takagi-Sugeno (TS, for short) fuzzy controllers, then establish a condition for analytically determining asymptotic stability of the fuzzy control systems at the equilibrium point, and finally use the stability condition in design of the control systems that are at least locally stable. The general TS fuzzy controllers use arbitrary input fuzzy sets, any types of fuzzy logic AND, TS fuzzy rules with linear consequent and the generalized defuzzifier which contains the popular centroid defuzzifier as a special case. We have mathematically proved that the general TS fuzzy controllers are nonlinear controllers with variable gains continuously changing with controllers’ input variables. Using Lyapunov’s linearization method, we have established a necessary and sufficient condition for analytically determining local asymptotic stability of TS fuzzy control systems, each of which is made up of a fuzzy controller of the general class and a nonlinear plant. We show that the condition can be used in practice even when the plant model is not explicitly known. We have utilized the stability condition to design, with or without plant model, general TS fuzzy control systems that are at least locally stable. Three numerical examples are given to illustrate in detail how to use our new results. Our results offer four important practical advantages: (1) our stability condition, being a necessary and sufficient one, is the tightest possible stability condition, (2) the condition is simple and easy to use partially because it only needs the fuzzy controller structure around the equilibrium point, (3) the condition can be used for determining system local stability and designing fuzzy control systems that are stable at least around the equilibrium point even when the explicit plant models are unavailable, and (4) the condition covers a very broad range of nonlinear TS fuzzy control systems, for which a meaningful global stability condition seems impossible to establish.     

A numerical study of the ground state and dynamics of atomic–molecular Bose–Einstein condensates

In this paper, we numerically investigate the ground-state structure and dynamics of atomic–molecular Bose–Einstein condensates at zero temperature, which are modeled by coupled Gross–Pitaevskii equations (GPEs). To get the ground state, we evolve a gradient flow with discrete normalization numerically. To study the dynamics, we employ an efficient numerical method—the time-splitting Fourier pseudospectral method for solving the coupled GPEs. The proposed numerical methods have been numerically tested and employed in studying the mechanism on how an atomic condensate can be converted into an atomic–molecular mixture or a pure molecular condensate from an atomic condensate either in equilibrium or dynamically.     

Fuzzy Sliding‐mode Strategy for Air–fuel Ratio Control of Lean‐burn Spark Ignition Engines

Minimization of emissions of carbon dioxide and harmful pollutants and maximization of fuel economy for lean‐burn spark ignition (SI) engines relies to a large extent on precise air–fuel ratio (AFR) control. However, the main challenge of AFR control is the large time‐varying delay in lean‐burn engines. Since the system is usually subject to external disturbances and uncertainties, a high level of robustness in AFR control design must be considered. We propose a fuzzy sliding‐mode control (FSMC) to track the desired AFR in the presence of periodic disturbances. The proposed method is model free and does not need any system characteristics. Based on the fuzzy system input–output data, two scaling factors are first employed to normalize the sliding surface and its derivative. According to the concept of the if‐then rule, an appropriate rule table for the logic system is designed. Then, based on Lyapunov stability criteria, the output scaling factor is determined such that the closed‐loop stability of the internal dynamics with uniformly ultimately bounded (UUB) performance is guaranteed. Finally, the feasibility and effectiveness of the proposed control scheme are evaluated under various operating conditions. The baseline controllers, namely, a PI controller with Smith predictor and sliding‐mode controller, are also used to compare with the proposed FSMC. It is shown that the proposed FSMC has superior regulation performance compared to the baseline controllers.     

Transient Stability Enhancement of Multi–Machine Power Systems: Synchronization via Immersion of a Pendular System

In this paper the problem of designing excitation controllers to improve the transient stability of multi‐machine power systems is addressed adopting two new perspectives. First, instead of the standard formulation of stabilization of an equilibrium point, we aim here at the more realistic objective of keeping the difference between the generators rotor angles bounded and their speeds equal—which is called synchronization in the power literature—and translates into a problem of stabilization of a set. Second, we adopt the classical viewpoint of power systems as a set of coupled nonlinear pendula, and express our control objective as ensuring that some suitable defined pendula dynamics are (asymptotically) immersed into the power system dynamics. Our main contribution is the explicit computation of a control law for the two–machine system that achieves global synchronization. The same procedure is applicable to the n–machine case, for which the existence of a locally stabilizing solution is established.     

Nonlinear generalization of scaled ℋ︁∞ control: global robustification against nonlinearly bounded uncertainties

This paper proposes a novel approach to the problem of ??₂ disturbance attenuation with global stability for nonlinear uncertain systems by placing great emphasis on seamless integration of linear and nonlinear controllers. This paper develops a new concept of state‐dependent scaling adapted to dynamic uncertainties and nonlinear‐gain bounded uncertainties that do not necessarily have finite linear‐gain, which is a key advance from previous scaling techniques. The proposed formulation of designing global nonlinear controllers is not only a natural extension of linear robust control, but also the approach renders the nonlinear controller identical with the linear control at the equilibrium. This paper particularly focuses on scaled ??^∞ control which is widely accepted as a powerful methodology in linear robust control, and extends it nonlinearly. If the nonlinear system belongs to a generalized class of triangular systems allowing for unmodelled dynamics, the effect of the disturbance can be attenuated to an arbitrarily small level with global asymptotic stability by partial‐state feedback control. A procedure of designing such controllers is described in the form of recursive selection of state‐dependent scaling factors. Copyright © 2004 John Wiley & Sons, Ltd.     

Analysis of dynamic nonlinearity of flow control loop through modified relay test probing

Most of the controller tuning methods in process control are based on linear models. Through the development of a detail model of the actuator-pneumatic valve dynamics, we show that even if the static characteristic of the valve is linear (including possible linearity of the flow dependence on the valve opening) the actuator-valve dynamics are strongly nonlinear. Therefore, tuning of the flow loop will be affected by the selection of the operating point and the amplitude of the relay in the relay feedback test (RFT) or modifications of this test. It is shown that Lyapunov linearisation around an equilibrium point fails to provide a local linear model of the system, and modified RFT probing is used for investigation of the system dynamics. The same test is used for the proportional-integral controller tuning in various operating points. It is recommended that the difference in the dynamic response of the loop for different relay amplitudes and operating points should be accounted for by larger stability margins.     

Stability analysis of non-interacting control of continuous stirred tank reactor†

A continuous stirred tank reactor operating around a stable equilibrium point and having interaction may become unstable when made noii-intcractivo by tho addition of compensators. Procedures for selecting the settings of tho feedback controllers to obtain any desired degree of stability in the non-interacting system are worked out in this paper. A numerical example of a continuous stirred tank reactor with an irreversible, exothermic first-order reaction is taken and controller settings for its stable non-interacting operation worked out.     

Flow analysis of a ribbed helix lip seal with consideration of fluid–structure interaction

Ribbed helix lip seals for rotating shafts have been widely used to retain oil and exclude contaminants in many applications throughout the industry. The objective of this study is to better understand the basic flow behavior associated with the pumping process of a ribbed helix lip seal. The theoretical model consists of a flow analysis of the lubricating film of the hydraulic fluid in conjunction with a stress analysis of the lip seal distortion. The complicated mechanical interaction between the oil flow and rubber deformation was simulated using a coupled fluid–structure approach implemented in a commercial computational fluid dynamics (CFD) code ESI-CFD, ACE+®. The flow characteristics and rubber deformation around a ribbed helix lip seal were fully resolved in a pumping-rate test environment, where both air and oil sides were filled with oil initially. The three-dimensional pressure field solved by the model via the coupled flow-stress analysis was compared with the predictions obtained from the model via the nondeformable rubber assumption to elucidate the significant effect of the fluid–structure interaction on accurate simulation of the oil pumping behavior. In the rotating speed ranging from 1000 to 6000 rpm, both measured and calculated pumping rates increase with the shaft speed for a ribbed helix lip seal. As compared to the baseline case, calculations with considering the fluid–structure interaction at higher rotary speeds can result in thicker oil films, and in turn produce greater pumping rates.     

An embedding approach for the design of state‐feedback tracking controllers for references with jumps

We study the problem of designing state‐feedback controllers to track time‐varying state trajectories that may exhibit jumps. Both plants and controllers considered are modeled as hybrid dynamical systems, which are systems with both continuous and discrete dynamics, given in terms of a flow set, a flow map, a jump set, and a jump map. Using recently developed tools for the study of stability in hybrid systems, we recast the tracking problem as the task of asymptotically stabilizing a set, the tracking set, and derive conditions for the design of state‐feedback tracking controllers with the property that the jump times of the plant coincide with those of the given reference trajectories. The resulting tracking controllers guarantee that solutions of the plant starting close to the reference trajectory stay close to it and that the difference between each solution of the controlled plant and the reference trajectory converges to zero asymptotically. Constructive conditions for tracking control design in terms of LMIs are proposed for a class of hybrid systems with linear maps and input‐triggered jumps. The results are illustrated by various examples. Copyright © 2013 John Wiley & Sons, Ltd.