Lyapunov-based Control Design For Uncertain Mimo Systems

In this dissertation. we document the progress in the control design for a class of MIMO nonlinear uncertain system from five papers. In the first part, we address the problem of adaptive control design for a class of multi-input multi-output (MIMO) nonlinear systems. A Lypaunov based singularity free control law, which compensates for parametric uncertainty in both the drift vector and the input gain matrix, is proposed under the mild assumption that the signs of the leading minors of the control input gain matrix are known. Lyapunov analysis shows global uniform ultimate boundedness (GUUB) result for the tracking error under full state feedback (FSFB). Under the restriction that only the output vector is available for measurement, an output feedback (OFB) controller is designed based on a standard high gain observer (HGO) stability under OFB is fostered by the uniformity of the FSFB solution. Simulation results for both FSFB and OFB controllers demonstrate the efcacy of the MIMO control design in the classical 2-DOF robot manipulator model. In the second part, an adaptive feedback control is designed for a class of MIMO nonlinear systems containing parametric uncertainty in both the drift vector and the input gain matrix, which is assumed to be full-rank and non-symmetric in general. Based on an SDU decomposition of the gain matrix, a singularity-free adaptive tracking control law is proposed that is shown to be globally asymptotically stable (GAS) under full-state feedback. iii Output feedback results are facilitated via the use of a high-gain observer (HGO). Under output feedback control, ultimate boundedness of the error signals is obtained the size of the bound is related to the size of the uncertainty in the parameters. An explicit upper bound is also provided on the size of the HGO gain constant. In third part, a class of aeroelastic systems with an unmodeled nonlinearity and external disturbance is considered. By using leading- and trailing-edge control surface actuations, a full-state feedforward/feedback controller is designed to suppress the aeroelastic vibrations of a nonlinear wing section subject to external disturbance. The full-state feedback control yields a uniformly ultimately bounded result for two-axis vibration suppression. With the restriction that only pitching and plunging displacements are measurable while their rates are not, a high-gain observer is used to modify the full-state feedback control design to an output feedback design. Simulation results demonstrate the ef cacy of the multi-input multioutput control toward suppressing aeroelastic vibration and limit cycle oscillations occurring in pre and post utter velocity regimes when the system is subjected to a variety of external disturbance signals. Comparisons are drawn with a previously designed adaptive multi-input multi-output controller. In the fourth part, a continuous robust feedback control is designed for a class of high-order multi-input multi-output (MIMO) nonlinear systems with two degrees of freedom containing unstructured nonlinear uncertainties in the drift vector and parametric uncertainties in the high frequency gain matrix, which is allowed to be non-symmetric in general. Given some mild assumptions on the system model, a singularity-free continuous robust tracking coniv trol law is designed that is shown to be semi-globally asymptotically stable under full-state feedback through a Lyapunov stability analysis. The performance of the proposed algorithm have been verified on a two-link robot manipulator model and 2-DOF aeroelastic model

Backpropagating constraints-based trajectory tracking control of a quadrotor with constrained actuator dynamics and complex unknowns

In this paper, a backpropagating constraints-based trajectory tracking control (BCTTC) scheme is addressed for trajectory tracking of a quadrotor with complex unknowns and cascade constraints arising from constrained actuator dynamics, including saturations and dead zones. The entire quadrotor system including actuator dynamics is decomposed into five cascade subsystems connected by intermediate saturated nonlinearities. By virtue of the cascade structure, backpropagating constraints (BCs) on intermediate signals are derived from constrained actuator dynamics suffering from nonreversible rotations and nonnegative squares of rotors, and decouple subsystems with saturated connections. Combining with sliding-mode errors, BC-based virtual controls are individually designed by addressing underactuation and cascade constraints. In order to remove smoothness requirements on intermediate controls, first-order filters are employed, and thereby contributing to backstepping-like subcontrollers synthesizing in a recursive manner. Moreover, universal adaptive compensators are exclusively devised to dominate intermediate tracking residuals and complex unknowns. Eventually, the closed-loop BCTTC system stability can be ensured by the Lyapunov synthesis, and trajectory tracking errors can be made arbitrarily small. Simulation studies demonstrate the effectiveness and superiority of the proposed BCTTC scheme for a quadrotor with complex constrains and unknowns

Asymmetric bounded neural control for an uncertain robot by state feedback and output feedback

In this paper, an adaptive neural bounded control scheme is proposed for an n-link rigid robotic manipulator with unknown dynamics. With the combination of the neural approximation and backstepping technique, an adaptive neural network control policy is developed to guarantee the tracking performance of the robot. Different from the existing results, the bounds of the designed controller are known a priori, and they are determined by controller gains, making them applicable within actuator limitations. Furthermore, the designed controller is also able to compensate the effect of unknown robotic dynamics. Via the Lyapunov stability theory, it can be proved that all the signals are uniformly ultimately bounded. Simulations are carried out to verify the effectiveness of the proposed scheme

Adaptive Control of Unknown Pure Feedback Systems with Pure State Constraints

This paper deals with the tracking control problem for a class of unknown pure feedback system with pure state constraints on the state variables and unknown time-varying bounded disturbances. An adaptive controller is presented for such systems for the very first time. The controller is designed using the backstepping method. While designing it, Barrier Lyapunov Functions is used so that the state variables do not contravene its constraints. In order to cope with the unknown dynamics of the system, an online approximator is designed using a neural network with a novel adaptive law for its weight update. In the stability analysis of the system, the time derivative of Lyapunov function involves known virtual control coefficient with unknown direction and to deal with such problem Nussbaum gain is used to design the control law. Furthermore, to make the controller robust and computationally inexpensive, a novel disturbance observer is designed to estimate the disturbance along with neural network approximation error and the time derivative of virtual control input. The effectiveness of the proposed approach is demonstrated through a simulation study on the third-order nonlinear system

Control of Quarter-Car Active Suspension System Based on Optimized Fuzzy Linear Quadratic Regulator Control Method

Vehicle suspension systems, which affect driving performance and passenger comfort, are actively researched with the development of technology and the insufficient quality of passive suspension systems. This paper establishes the suspension model of a quarter of the car and active control is realized. The suspension model was created using the Lagrange–Euler method. LQR, fuzzy logic control (FLC), and fuzzy-LQR control algorithms were developed and applied to the suspension system for active control. The purpose of these controllers is to improve car handling and passenger comfort. Undesirable vibrations occur in passive suspension systems. These vibrations should be reduced using the proposed control methods and a robust system should be developed. To enhance the performance of the fuzzy logic control (FLC) and fuzzy-LQR control methods, the optimal values of the coefficients of the points where the feet of the member functions touch are calculated using the particle swarm optimization (PSO) algorithm. Then, the designed controllers were simulated in the computer environment. The success of the control performance of the applied methods concerning the passive suspension system was compared in percentages. The results are presented and evaluated graphically and numerically. Using the integral time-weighted absolute error (ITAE) criterion, the methods were compared with each other and with the studies in the literature. As a result, it was found that the proposed control method (fuzzy-LQR) is about 84.2% more successful in body motion, 90% in car acceleration, 84.5% in suspension deflection, and 86.7% in tire deflection compared to the studies in the literature. All these results show that the car’s ride comfort has been significantly improved

Adaptive Systems: History, Techniques, Problems, and Perspectives

We survey some of the rich history of control over the past century with a focus on the major milestones in adaptive systems. We review classic methods and examples in adaptive linear systems for both control and observation/identification. The focus is on linear plants to facilitate understanding, but we also provide the tools necessary for many classes of nonlinear systems. We discuss practical issues encountered in making these systems stable and robust with respect to additive and multiplicative uncertainties. We discuss various perspectives on adaptive systems and their role in various fields. Finally, we present some of the ongoing research and expose problems in the field of adaptive control

Development of Robust Control Strategies for Autonomous Underwater Vehicles

The resources of the energy and chemical balance in the ocean sustain mankind in many ways. Therefore, ocean exploration is an essential task that is accomplished by deploying Underwater Vehicles. An Underwater Vehicle with autonomy feature for its navigation and control is called Autonomous Underwater Vehicle (AUV). Among the task handled by an AUV, accurately positioning itself at a desired position with respect to the reference objects is called set-point control. Similarly, tracking of the reference trajectory is also another important task. Battery recharging of AUV, positioning with respect to underwater structure, cable, seabed, tracking of reference trajectory with desired accuracy and speed to avoid collision with the guiding vehicle in the last phase of docking are some significant applications where an AUV needs to perform the above tasks. Parametric uncertainties in AUV dynamics and actuator torque limitation necessitate to design robust control algorithms to achieve motion control objectives in the face of uncertainties. Sliding Mode Controller (SMC), H / μ synthesis, model based PID group controllers are some of the robust controllers which have been applied to AUV. But SMC suffers from less efficient tuning of its switching gains due to model parameters and noisy estimated acceleration states appearing in its control law. In addition, demand of high control effort due to high frequency chattering is another drawback of SMC. Furthermore, real-time implementation of H / μ synthesis controller based on its stability study is restricted due to use of linearly approximated dynamic model of an AUV, which hinders achieving robustness. Moreover, model based PID group controllers suffer from implementation complexities and exhibit poor transient and steady-state performances under parametric uncertainties. On the other hand model free Linear PID (LPID) has inherent problem of narrow convergence region, i.e.it can not ensure convergence of large initial error to zero. Additionally, it suffers from integrator-wind-up and subsequent saturation of actuator during the occurrence of large initial error. But LPID controller has inherent capability to cope up with the uncertainties. In view of addressing the above said problem, this work proposes wind-up free Nonlinear PID with Bounded Integral (BI) and Bounded Derivative (BD) for set-point control and combination of continuous SMC with Nonlinear PID with BI and BD namely SM-N-PID with BI and BD for trajectory tracking. Nonlinear functions are used for all P,I and D controllers (for both of set-point and tracking control) in addition to use of nonlinear tan hyperbolic function in SMC(for tracking only) such that torque demand from the controller can be kept within a limit. A direct Lyapunov analysis is pursued to prove stable motion of AUV. The efficacies of the proposed controllers are compared with other two controllers namely PD and N-PID without BI and BD for set-point control and PD plus Feedforward Compensation (FC) and SM-NPID without BI and BD for tracking control. Multiple AUVs cooperatively performing a mission offers several advantages over a single AUV in a non-cooperative manner; such as reliability and increased work efficiency, etc. Bandwidth limitation in acoustic medium possess challenges in designing cooperative motion control algorithm for multiple AUVs owing to the necessity of communication of sensors and actuator signals among AUVs. In literature, undirected graph based approach is used for control design under communication constraints and thus it is not suitable for large number of AUVs participating in a cooperative motion plan. Formation control is a popular cooperative motion control paradigm. This thesis models the formation as a minimally persistent directed graph and proposes control schemes for maintaining the distance constraints during the course of motion of entire formation. For formation control each AUV uses Sliding Mode Nonlinear PID controller with Bounded Integrator and Bounded Derivative. Direct Lyapunov stability analysis in the framework of input-to-state stability ensures the stable motion of formation while maintaining the desired distance constraints among the AUVs

Robust model-based fault estimation and fault-tolerant control : towards an integration

To maintain robustly acceptable system performance, fault estimation (FE) is adopted to reconstruct fault signals and a fault-tolerant control (FTC) controller is employed to compensate for the fault effects. The inevitably existing system and estimation uncertainties result in the so-called bi-directional robustness interactions defined in this work between the FE and FTC functions, which gives rise to an important and challenging yet open integrated FE/FTC design problem concerned in this thesis. An example of fault-tolerant wind turbine pitch control is provided as a practical motivation for integrated FE/FTC design.To achieve the integrated FE/FTC design for linear systems, two strategies are proposed. A H∞ optimization based approach is first proposed for linear systems with differentiable matched faults, using augmented state unknown input observer FE and adaptive sliding mode FTC. The integrated design is converted into an observer-based robust control problem solved via a single-step linear matrix inequality formulation.With the purpose of an integrated design with more freedom and also applicable for a range of general fault scenarios, a decoupling approach is further proposed. This approach can estimate and compensate unmatched non-differentiable faults and perturbations by combined adaptive sliding mode augmented state unknown input observer and backstepping FTC controller. The observer structure renders a recovery of the Separation Principle and allows great freedom for the FE/FTC designs.Integrated FE/FTC design strategies are also developed for Takagi-Sugeno fuzzy modelling nonlinear systems, Lipschitz nonlinear systems, and large-scale interconnected systems, based on extensions of the H∞ optimization approach for linear systems.Tutorial examples are used to illustrate the design strategies for each approach. Physical systems, a 3-DOF (degree-of-freedom) helicopter and a 3-machine power system, are used to provide further evaluation of the proposed integrated FE/FTC strategies. Future research on this subject is also outlined

Nonlinear Model-Based Control for Neuromuscular Electrical Stimulation

Neuromuscular electrical stimulation (NMES) is a technology where skeletal muscles are externally stimulated by electrodes to help restore functionality to human limbs with motor neuron disorder. This dissertation is concerned with the model-based feedback control of the NMES quadriceps muscle group-knee joint dynamics. A class of nonlinear controllers is presented based on various levels of model structures and uncertainties. The two main control techniques used throughout this work are backstepping control and Lyapunov stability theory. In the first control strategy, we design a model-based nonlinear control law for the system with the exactly known passive mechanical that ensures asymptotical tracking. This first design is used as a stepping stone for the other control strategies in which we consider that uncertainties exist. In the next four control strategies, techniques for adaptive control of nonlinearly parameterized systems are applied to handle the unknown physical constant parameters that appear nonlinearly in the model. By exploiting the Lipschitzian nature or the concavity/convexity of the nonlinearly parameterized functions in the model, we design two adaptive controllers and two robust adaptive controllers that ensure practical tracking. The next set of controllers are based on a NMES model that includes the uncertain muscle contractile mechanics. In this case, neural network-based controllers are designed to deal with this uncertainty. We consider here voltage inputs without and with saturation. For the latter, the Nussbaum gain is applied to handle the input saturation. The last two control strategies are based on a more refined NMES model that accounts for the muscle activation dynamics. The main challenge here is that the activation state is unmeasurable. In the first design, we design a model-based observer that directly estimates the unmeasured state for a certain activation model. The second design introduces a nonlinear filter with an adaptive control law to handle parametric uncertainty in the activation dynamics. Both the observer- and filter-based, partial-state feedback controllers ensure asymptotical tracking. Throughout this dissertation, the performance of the proposed control schemes are illustrated via computer simulations