Online identification and nonlinear control of the electrically stimulated quadriceps muscle

A new approach for estimating nonlinear models of the electrically stimulated quadriceps muscle group under nonisometric conditions is investigated. The model can be used for designing controlled neuro-prostheses. In order to identify the muscle dynamics (stimulation pulsewidth-active knee moment relation) from discrete-time angle measurements only, a hybrid model structure is postulated for the shank-quadriceps dynamics. The model consists of a relatively well known time-invariant passive component and an uncertain time-variant active component. Rigid body dynamics, described by the Equation of Motion (EoM), and passive joint properties form the time-invariant part. The actuator, i.e. the electrically stimulated muscle group, represents the uncertain time-varying section. A recursive algorithm is outlined for identifying online the stimulated quadriceps muscle group. The algorithm requires EoM and passive joint characteristics to be known a priori. The muscle dynamics represent the product of a continuous-time nonlinear activation dynamics and a nonlinear static contraction function described by a Normalised Radial Basis Function (NRBF) network which has knee-joint angle and angular velocity as input arguments. An Extended Kalman Filter (EKF) approach is chosen to estimate muscle dynamics parameters and to obtain full state estimates of the shank-quadriceps dynamics simultaneously. The latter is important for implementing state feedback controllers. A nonlinear state feedback controller using the backstepping method is explicitly designed whereas the model was identified a priori using the developed identification procedure

Observer-Based Robust Tracking Control for a Class of Switched Nonlinear Cascade Systems

This paper is devoted to robust output feedback tracking control design for a class of switched nonlinear cascade systems. The main goal is to ensure the global input-to-state stable (ISS) property of the tracking error nonlinear dynamics with respect to the unknown structural system uncertainties and external disturbances. First, a nonlinear observer is constructed through state transformation to reconstruct the unavailable states, where only one parameter should be determined. Then, by virtue of the nonlinear sliding mode control (SMC), a discontinuous nonlinear output feedback controller is designed using a backstepping like design procedure to ensure the ISS property. Finally, an example is provided to show the effectiveness of the proposed approach

Control of power electronic interfaces in distributed generation.

Renewable energy has gained popularity as an alternative resource for electric power generation. As such, Distributed Generation (DG) is expected to open new horizons to electric power generation. Most renewable energy sources cannot be connected to the load directly. Integration of the renewable energy sources with the load has brought new challenges in terms of the system’s stability, voltage regulation and power quality issues. For example, the output power, voltage and frequency of an example wind turbine depend on the wind speed, which fluctuate over time and cannot be forecasted accurately. At the same time, the nonlinearity of residential electrical load is steadily increasing with the growing use of devices with rectifiers at their front end. This nonlinearity of the load deviates both current and voltage waveforms in the distribution feeder from their sinusoidal shape, hence increasing the Total Harmonics Distortions (THD) and polluting the grid. Advances in Power Electronic Interfaces (PEI) have increased the viability of DG systems and enhanced controllability and power transfer capability. Power electronic converter as an interface between energy sources and the grid/load has a higher degree of controllability compared to electrical machine used as the generator. This controllability can be used to not only overcome the aforementioned shortfalls of integration of renewable energy with the grid/load but also to reduce THD and improve the power quality. As a consequence, design of a sophisticated controller that can take advantage of this controllability provided by PEIs to facilitate the integration of DG with the load and generate high quality power has become of great interest. In this study a set of nonlinear controllers and observers are proposed for the control of PEIs with different DG technologies. Lyapunov stability analysis, simulation and experimental results are used to validate the effectiveness of the proposed control solution in terms of tracking objective and meeting the THD requirements of IEEE 519 and EN 50160 standards for US and European power systems, respectively

Lyapunov functions and finite time stabilization in optimal time for homogeneous linear and quasilinear hyperbolic systems

Hyperbolic systems in one dimensional space are frequently used in modeling of many physical systems. In our recent works, we introduced time independent feedbacks leading to the finite stabilization for the optimal time of homogeneous linear and quasilinear hyperbolic systems. In this work, we present Lyapunov's functions for these feedbacks and use estimates for Lyapunov's functions to rediscover the finite stabilization results.Comment: arXiv admin note: text overlap with arXiv:2005.1326

Heterogeneous and hybrid control with application in automotive systems

Control systems for automotive systems have acquired a new level of complexity. To fulfill the requirements of the controller specifications new technologies are needed. In many cases high performance and robust control cannot be provided by a simple conventional controller anymore. In this case hybrid combinations of local controllers, gain scheduled controllers and global stabilisation concepts are necessary. A considerable number of state-of-the-art automotive controllers (anti-lock brake system (ABS), electronic stabilising program (ESP)) already incorporate heterogeneous and hybrid control concepts as ad-hoc solutions. In this work a heterogeneous/hybrid control system is developed for a test vehicle in order to solve a clearly specified and relevant automotive control problem. The control system will be evaluated against a state-of-the-art conventional controller to clearly show the benefits and advantages arising from the novel approach. A multiple model-based observer/estimator for the estimation of parameters is developed to reset the parameter estimate in a conventional Lyapunov based nonlinear adaptive controller. The advantage of combining both approaches is that the performance of the controller with respect to disturbances can be improved considerably because a reduced controller gain will increase the robustness of the approach with respect to noise and unmodelled dynamics. Several alternative resetting criteria are developed based on a control Lyapunov function, such that resetting guarantees a decrease in the Lyapunov function. Since ABS systems have to operate on different possibly fast changing road surfaces the application of hybrid methodologies is apparent. Four different model based wheel slip controllers will be presented: two nonlinear approaches combined with parameter resetting, a simple linear controller that has been designed using the technique of simultaneously stabilising a set of linear plants as well as a sub-optimal linear quadratic (LQ)-controller. All wheel slip controllers operate as low level controllers in a modular structure that has been developed for the ABS problem. The controllers will be applied to a real Mercedes E-class passenger car. The vehicle is equipped with a brake-by-wire system and electromechanical brake actuators. Extensive real life tests show the benefits of the hybrid approaches in a fast changing environment

Stabilization of cascaded nonlinear systems under sampling and delays

Over the last decades, the methodologies of dynamical systems and control theory have been playing an increasingly relevant role in a lot of situations of practical interest. Though, a lot of theoretical problem still remain unsolved. Among all, the ones concerning stability and stabilization are of paramount importance. In order to stabilize a physical (or not) system, it is necessary to acquire and interpret heterogeneous information on its behavior in order to correctly intervene on it. In general, those information are not available through a continuous flow but are provided in a synchronous or asynchronous way. This issue has to be unavoidably taken into account for the design of the control action. In a very natural way, all those heterogeneities define an hybrid system characterized by both continuous and discrete dynamics. This thesis is contextualized in this framework and aimed at proposing new methodologies for the stabilization of sampled-data nonlinear systems with focus toward the stabilization of cascade dynamics. In doing so, we shall propose a small number of tools for constructing sampled-data feedback laws stabilizing the origin of sampled-data nonlinear systems admitting cascade interconnection representations. To this end, we shall investigate on the effect of sampling on the properties of the continuous-time system while enhancing design procedures requiring no extra assumptions over the sampled-data equivalent model. Finally, we shall show the way sampling positively affects nonlinear retarded dynamics affected by a fixed and known time-delay over the input signal by enforcing on the implicit cascade representation the sampling process induces onto the retarded system

Robust Control Methods for Nonlinear Systems with Uncertain Dynamics and Unknown Control Direction

Robust nonlinear control design strategies using sliding mode control (SMC) and integral SMC (ISMC) are developed, which are capable of achieving reliable and accurate tracking control for systems containing dynamic uncertainty, unmodeled disturbances, and actuator anomalies that result in an unknown and time-varying control direction. In order to ease readability of this dissertation, detailed explanations of the relevant mathematical tools is provided, including stability denitions, Lyapunov-based stability analysis methods, SMC and ISMC fundamentals, and other basic nonlinear control tools. The contributions of the dissertation are three novel control algorithms for three different classes of nonlinear systems: single-input multipleoutput (SIMO) systems, systems with model uncertainty and bounded disturbances, and systems with unknown control direction. Control design for SIMO systems is challenging due to the fact that such systems have fewer actuators than degrees of freedom to control (i.e., they are underactuated systems). While traditional nonlinear control methods can be utilized to design controllers for certain classes of cascaded underactuated systems, more advanced methods are required to develop controllers for parallel systems, which are not in a cascade structure. A novel control technique is proposed in this dissertation, which is shown to achieve asymptotic tracking for dual parallel systems, where a single scalar control input directly affects two subsystems. The result is achieved through an innovative sequential control design algorithm, whereby one of the subsystems is indirectly stabilized via the desired state trajectory that is commanded to the other subsystem. The SIMO system under consideration does not contain uncertainty or disturbances. In dealing with systems containing uncertainty in the dynamic model, a particularly challenging situation occurs when uncertainty exists in the input-multiplicative gain matrix. Moreover, special consideration is required in control design for systems that also include unknown bounded disturbances. To cope with these challenges, a robust continuous controller is developed using an ISMC technique, which achieves asymptotic trajectory tracking for systems with unknown bounded disturbances, while simultaneously compensating for parametric uncertainty in the input gain matrix. The ISMC design is rigorously proven to achieve asymptotic trajectory tracking for a quadrotor system and a synthetic jet actuator (SJA)-based aircraft system. In the ISMC designs, it is assumed that the signs in the uncertain input-multiplicative gain matrix (i.e., the actuator control directions) are known. A much more challenging scenario is encountered in designing controllers for classes of systems, where the uncertainty in the input gain matrix is extreme enough to result in an a priori-unknown control direction. Such a scenario can result when dealing with highly inaccurate dynamic models, unmodeled parameter variations, actuator anomalies, unknown external or internal disturbances, and/or other adversarial operating conditions. To address this challenge, a SMCbased self-recongurable control algorithm is presented, which automatically adjusts for unknown control direction via periodic switching between sliding manifolds that ultimately forces the state to a converging manifold. Rigorous mathematical analyses are presented to prove the theoretical results, and simulation results are provided to demonstrate the effectiveness of the three proposed control algorithms