Time-Varying Input and State Delay Compensation for Uncertain Nonlinear Systems

A robust controller is developed for uncertain, second-order nonlinear systems subject to simultaneous unknown, time-varying state delays and known, time-varying input delays in addition to additive, sufficiently smooth disturbances. An integral term composed of previous control values facilitates a delay-free open-loop error system and the development of the feedback control structure. A stability analysis based on Lyapunov-Krasovskii (LK) functionals guarantees uniformly ultimately bounded tracking under the assumption that the delays are bounded and slowly varying

Design of generalized minimum variance controllers for nonlinear multivariable systems

The design and implementation of Generalized Minimum Variance control laws for nonlinear multivariable systems that can include severe nonlinearities is considered. The quadratic cost index minimised involves dynamically weighted error and nonlinear control signal costing terms. The aim here is to show the controller obtained is simple to design and implement. The features of the control law are explored. The controller obtained includes an internal model of the process and in one form is a nonlinear version of the Smith Predictor

Global Stabilization of High-Order Time-Delay Nonlinear Systems under a Weaker Condition

Under the weaker condition on the system growth, this paper further investigates the problem of global stabilization by state feedback for a class of high-order nonlinear systems with time-varying delays. By skillfully using the homogeneous domination approach, a continuous state feedback controller is successfully designed, which preserves the equilibrium at the origin and guarantees the global asymptotic stability of the resulting closed-loop system. A simulation example is given to demonstrate the effectiveness of the proposed design procedure

A robust LMI approach on nonlinear feedback stabilization of continuous state-delay systems with Lipschitzian nonlinearities : experimental validation

This paper suggests a novel nonlinear state-fe edback stabilization control law using linear matrix inequalities for a class oftime-delayed nonlinear dynamic systems with Lipschitz nonlinearity conditions. Based on the Lyapunov–Krasovskiistability theory, the asymptotic stabilization criterion is derived in the linear matrix inequality form and the coef¿cients ofthe nonlinear state-feedback controller are determined. Meanwhile, an appropriate criterion to ¿nd the proper feedbackgain matrix F is also provided. The robustness purpose against nonlinear functions and time delays is guaranteed in thisscheme. Moreover , the problem of robust H!performance analysis for a class of nonlinear time-delayed system s withexternal disturbance is studied in this paper. Simulations are presented to demonstrate the pro¿ciency of the offeredtechnique. For this purpos e, an unstable nonlinear numerical system and a rotary inverted pendulum system have beenstudied in the simulation section. Moreover, an experimental study of the practical rotary inverted pendul um system isprovided. These results con¿rm the expected satisfactory performance of the suggested method.Peer ReviewedPostprint (author's final draft

Performing heavy transfers for offshore wind maintenance

As offshore wind farms become larger and further from the shore, there are strong economic and climate incentives to perform transfers required for operations and maintenance from floating vessels, rather than employing expensive and slow jack up rigs. However, successful transfers of heavy and sensitive equipment from a floating vessel (in all but benign sea/wind conditions) are heavily dependent on multiple degrees of freedom, high performance control. This project aims to bring a novel modelling and simulation methodology in Simulink that could be used to assess offshore wind installation and maintenance procedures. More specifically, the goal is to demonstrate that a crane prototype assumed to be located on a floating ship can transfer loads of hundreds of tons onto a fixed platform. Furthermore, this process should be completed with good precision and minimal impact force during equipment loading onto the stand. This problem has not yet been answered in research, with the only relevant patent in the field being the Ampelmann platform, a motionless bridge allowing technicians to access the offshore turbine. The first main contribution to knowledge of this thesis was the design of a 90 m crane that could handle a 660 tons load. This thesis presents a procedure, based on both mechanical/hydraulics design as well as empirical findings, which could be re-used for scaling the crane model to a more realistic dimension. It is worth noting that the goal here was to assess whether a realistically weighing piece of equipment could be stably handled, while the actual size of the crane was deemed unimportant. Another missing gap in literature this project wanted to fill was achieving active motion compensation for a larger scale system such as the current one. This refers to balancing out the base motions on multiple axes, so the payload can be moved on a given trajectory unaffected by them. Currently, research in the field mainly consists of crane mechanisms that feature active heave compensation, which only refers to the vertical axis. Hence, two control design methods were employed to assess the viability of heavy payload positioning from floating vessels through the development of a simulation approach using Simulink. The crane prototype was designed and modelled to operate under simulated vessel motions given by sea states with a significant wave height of 5 m and maximum wave frequency of 1 rad/s. Then, traditional control (feedback and feedforward) was designed to achieve active motion compensation with steady-state position errors under 20 cm. A second controller architecture was then designed/implemented as a comparison basis for the first one, with the aim being to find the most robust solution of the two. The nonlinear generalised minimum variance (NGMV) control algorithm was chosen for control design in this application. Due to its ability to compensate for significant system nonlinearities and the ease of implementation, NGMV was a good candidate for the task at hand. Tuning controller parameters to stabilize the system could also be based on the previously determined traditional control solutions. An investigation of controllers’ robustness against model mismatch was carried out by introducing various levels of uncertainty which influence actuators’ natural frequency to assess system sensitivity. The outcome of the investigation determined that traditional and NGMV controllers provided comparable regulating performance in terms of reference tracking and disturbance rejection, for the nominal case. This confirmed the assertion that the PID-based NGMV weightings selection is a useful starting point for controller tuning. Increasing the mismatch between the nominal system based on which the controllers’ were designed and the actual plant showed that the traditional control was marginally more robust in this application. The final contribution to knowledge this thesis aimed to bring was minimising the impact force during load placement on a fixed and rigid platform. To that end, the contact forces between the payload and a platform were first successfully modelled and measured. A switching algorithm between position and force control was then developed based on a methodology found in literature but on a microscopic scale project. To execute smooth load placement, an automated hybrid force/position control scheme was implemented. The proposed algorithm enabled position control on x and y axes, while minimising impact forces on the z-axis. Unfortunately, preliminary findings showed that there is still work to be done to claim any success in this regard. However, the author hopes this offers a good starting point for future work.As offshore wind farms become larger and further from the shore, there are strong economic and climate incentives to perform transfers required for operations and maintenance from floating vessels, rather than employing expensive and slow jack up rigs. However, successful transfers of heavy and sensitive equipment from a floating vessel (in all but benign sea/wind conditions) are heavily dependent on multiple degrees of freedom, high performance control. This project aims to bring a novel modelling and simulation methodology in Simulink that could be used to assess offshore wind installation and maintenance procedures. More specifically, the goal is to demonstrate that a crane prototype assumed to be located on a floating ship can transfer loads of hundreds of tons onto a fixed platform. Furthermore, this process should be completed with good precision and minimal impact force during equipment loading onto the stand. This problem has not yet been answered in research, with the only relevant patent in the field being the Ampelmann platform, a motionless bridge allowing technicians to access the offshore turbine. The first main contribution to knowledge of this thesis was the design of a 90 m crane that could handle a 660 tons load. This thesis presents a procedure, based on both mechanical/hydraulics design as well as empirical findings, which could be re-used for scaling the crane model to a more realistic dimension. It is worth noting that the goal here was to assess whether a realistically weighing piece of equipment could be stably handled, while the actual size of the crane was deemed unimportant. Another missing gap in literature this project wanted to fill was achieving active motion compensation for a larger scale system such as the current one. This refers to balancing out the base motions on multiple axes, so the payload can be moved on a given trajectory unaffected by them. Currently, research in the field mainly consists of crane mechanisms that feature active heave compensation, which only refers to the vertical axis. Hence, two control design methods were employed to assess the viability of heavy payload positioning from floating vessels through the development of a simulation approach using Simulink. The crane prototype was designed and modelled to operate under simulated vessel motions given by sea states with a significant wave height of 5 m and maximum wave frequency of 1 rad/s. Then, traditional control (feedback and feedforward) was designed to achieve active motion compensation with steady-state position errors under 20 cm. A second controller architecture was then designed/implemented as a comparison basis for the first one, with the aim being to find the most robust solution of the two. The nonlinear generalised minimum variance (NGMV) control algorithm was chosen for control design in this application. Due to its ability to compensate for significant system nonlinearities and the ease of implementation, NGMV was a good candidate for the task at hand. Tuning controller parameters to stabilize the system could also be based on the previously determined traditional control solutions. An investigation of controllers’ robustness against model mismatch was carried out by introducing various levels of uncertainty which influence actuators’ natural frequency to assess system sensitivity. The outcome of the investigation determined that traditional and NGMV controllers provided comparable regulating performance in terms of reference tracking and disturbance rejection, for the nominal case. This confirmed the assertion that the PID-based NGMV weightings selection is a useful starting point for controller tuning. Increasing the mismatch between the nominal system based on which the controllers’ were designed and the actual plant showed that the traditional control was marginally more robust in this application. The final contribution to knowledge this thesis aimed to bring was minimising the impact force during load placement on a fixed and rigid platform. To that end, the contact forces between the payload and a platform were first successfully modelled and measured. A switching algorithm between position and force control was then developed based on a methodology found in literature but on a microscopic scale project. To execute smooth load placement, an automated hybrid force/position control scheme was implemented. The proposed algorithm enabled position control on x and y axes, while minimising impact forces on the z-axis. Unfortunately, preliminary findings showed that there is still work to be done to claim any success in this regard. However, the author hopes this offers a good starting point for future work

Output-Feedback Control for a Class of Stochastic High-Order Feedforward Nonlinear Systems with Delay

The problem of global output-feedback stabilization for a class of stochastic high-order time-delay feedforward nonlinear systems with different power orders is investigated. By combining the adding one power integrator technique with the homogeneous domination approach, an output-feedback controller design is proposed, which ensures the global asymptotical stability in probability of the closed-loop system

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

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

EPSAC for wastewater treatment process (BSM1)

Predictive control is one of the most spread advanced control algorithms in industrial application field. Extended Prediction Self-Adaptive Control (EPSAC) is a part of this family of algorithms and is suitable for wastewater treatment plants control. The main goal of those industrial processes is to fulfil effluent water quality legal provisions with minimal energy consumption. In order to achieve this goal EPSAC control methodology has been applied to the wastewater treatment process. Benchmark Simulation Model No. 1 (BSM1) has been used to simulate the process dynamics. Two types of control strategies were implemented and tested: predictive control without taking into account measured disturbances and predictive control with feedforward. Feedforward control with two measured disturbances (the influent flow rate and ammonium concentration) has been tested