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

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

Adaptive control of sinusoidal brushless DC motor actuators

Electrical Power Assisted Steering system (EPAS) will likely be used on future automotive power steering systems. The sinusoidal brushless DC (BLDC) motor has been identified as one of the most suitable actuators for the EPAS application. Motor characteristic variations, which can be indicated by variations of the motor parameters such as the coil resistance and the torque constant, directly impart inaccuracies in the control scheme based on the nominal values of parameters and thus the whole system performance suffers. The motor controller must address the time-varying motor characteristics problem and maintain the performance in its long service life. In this dissertation, four adaptive control algorithms for brushless DC (BLDC) motors are explored. The first algorithm engages a simplified inverse dq-coordinate dynamics controller and solves for the parameter errors with the q-axis current (iq) feedback from several past sampling steps. The controller parameter values are updated by slow integration of the parameter errors. Improvement such as dynamic approximation, speed approximation and Gram-Schmidt orthonormalization are discussed for better estimation performance. The second algorithm is proposed to use both the d-axis current (id) and the q-axis current (iq) feedback for parameter estimation since id always accompanies iq. Stochastic conditions for unbiased estimation are shown through Monte Carlo simulations. Study of the first two adaptive algorithms indicates that the parameter estimation performance can be achieved by using more history data. The Extended Kalman Filter (EKF), a representative recursive estimation algorithm, is then investigated for the BLDC motor application. Simulation results validated the superior estimation performance with the EKF. However, the computation complexity and stability may be barriers for practical implementation of the EKF. The fourth algorithm is a model reference adaptive control (MRAC) that utilizes the desired motor characteristics as a reference model. Its stability is guaranteed by Lyapunov’s direct method. Simulation shows superior performance in terms of the convergence speed and current tracking. These algorithms are compared in closed loop simulation with an EPAS model and a motor speed control application. The MRAC is identified as the most promising candidate controller because of its combination of superior performance and low computational complexity. A BLDC motor controller developed with the dq-coordinate model cannot be implemented without several supplemental functions such as the coordinate transformation and a DC-to-AC current encoding scheme. A quasi-physical BLDC motor model is developed to study the practical implementation issues of the dq-coordinate control strategy, such as the initialization and rotor angle transducer resolution. This model can also be beneficial during first stage development in automotive BLDC motor applications