Efficient Parameters Estimation Method for the Separable Nonlinear Least Squares Problem

In this work, we combine the special structure of the separable nonlinear least squares problem with a variable projection algorithm based on singular value decomposition to separate linear and nonlinear parameters. Then, we propose finding the nonlinear parameters using the Levenberg–Marquart (LM) algorithm and either solve the linear parameters using the least squares method directly or by using an iteration method that corrects the characteristic values based on the L-curve, according to whether or not the nonlinear function coefficient matrix is ill posed. To prove the feasibility of the proposed method, we compared its performance on three examples with that of the LM method without parameter separation. The results show that (1) the parameter separation method reduces the number of iterations and improves computational efficiency by reducing the parameter dimensions and (2) when the coefficient matrix of the linear parameters is well-posed, using the least squares method to solve the fitting problem provides the highest fitting accuracy. When the coefficient matrix is ill posed, the method of correcting characteristic values based on the L-curve provides the most accurate solution to the fitting problem.

State-Of-Charge Estimation for Lithium-Ion Battery Using Improved DUKF Based on State-Parameter Separation

State-of-charge estimation and on-line model modification of lithium-ion batteries are more urgently required because of the great impact of the model accuracy on the algorithm performance. This study aims to propose an improved DUKF based on the state-parameter separation. Its characteristics include: (1) State-Of-Charge (SoC) is treated as the only state variable to eliminate the strong correlation between state and parameters. (2) Two filters are ranked to run the parameter modification only when the state estimation has converged. First, the double polarization (DP) model of battery is established, and the parameters of the model are identified at both the pulse discharge and long discharge recovery under Hybrid Pulse Power Characterization (HPPC) test. Second, the implementation of the proposed algorithm is described. Third, combined with the identification results, the study elaborates that it is unreliable to use the predicted voltage error of closed-loop algorithm as the criterion to measure the accuracy of the model, while the output voltage obtained by the open-loop model with dynamic parameters can reflect the real situation. Finally, comparative experiments are designed under HPPC and DST conditions. Results show that the proposed state-parameter separated IAUKF-UKF has higher SoC estimation accuracy and better stability than traditional DUKF.

Fault diagnosis of a selective compliance assembly robot arm manipulator based on the end joint motion analysis: Threshold algorithm and experiments

This paper presented a method to carry out fault diagnosis via analyzing the motion signals of a SCARA. To analyze the motion signals of the end joint of a selective compliance assembly robot arm (SCARA) and carry out fault diagnosis. A model parameter-based threshold algorithm is proposed in this study to improve the efficiency of the fault diagnosis on the end joint of a SCARA manipulator. The operation state of the robot is determined by comparing the speed curve of the end joint of the robot with the threshold using the proposed algorithm. Firstly, the threshold range of the system output is estimated using the speed observer constructed via parameter separation. Secondly, the acceleration signals of the end joint of the robot are collected at various operational angular speeds by a single acceleration sensor installed at the end joint of the manipulator. The operation state of the robot is evaluated by analyzing the trend and vibration characteristics of its acceleration. Finally, experiments are conducted at three different speeds: 2.4rad/s, 3.12rad/s and 3.6rad/s. Some robot malfunctions are detected by comparing the actual speed with the threshold. Thus, the proposed method can be used to monitor the variation signal in each robot joint through a single accelerometer mounted on the top of the manipulator.

Approximate finite-dimensional ODE temperature model for microwave heating

In this paper, a finite-dimensional ordinary differential equation (ODE) model is proposed for predicting the temperature profile with microwave heating to accomplish lower computing complexity. The traditional parabolic partial different equation (PDE) model with integrating Maxwell's equation and heat transport equation is not suitable for designing the on-line controller. Based on the obstruction, using an auxiliary function derives an intermediate model, which is analyzed and discussed for model reduction by employing the parameter separation method and Galerkin's method. The simulation experiments on one-dimensional waveguide and cavity demonstrate that the proposed approximate model is effective.

Adaptive Output Feedback Stabilization of Nonholonomic Systems with Nonlinear Parameterization

This paper investigates the problem of adaptive output feedback stabilization for a class of nonholonomic systems with nonlinear parameterization and strong nonlinear drifts. A parameter separation technique is introduced to transform nonlinearly parameterized system into a linear-like parameterized system. Then, by using the integrator backstepping approach based on observer and parameter estimator, a constructive design procedure for output feedback adaptive control is given. And a switching strategy is developed to eliminate the phenomenon of uncontrollability. It is shown that, under some conditions, the proposed controller can guarantee that all the system states globally converge to the origin, while other signals remain bounded. An illustrative example is also provided to demonstrate the effectiveness of the proposed scheme.

Output Feedback Adaptive Stabilization of Uncertain Nonholonomic Systems

This paper investigates the problem of output feedback adaptive stabilization control design for a class of nonholonomic chained systems with uncertainties, involving virtual control coefficients, unknown nonlinear parameters, and unknown time delays. The objective is to design a robust nonlinear output-feedback switching controller, which can guarantee the stabilization of the closed loop systems. An observer and an estimator are employed for states and parameters estimates, respectively. A constructive controller design procedure is proposed by applying input-state scaling transformation, parameter separation technique, and backstepping recursive approach. Simulation results are provided to show the effectiveness of the proposed method.

Adaptive Exponential Stabilization for a Class of Stochastic Nonholonomic Systems

This paper investigates the adaptive stabilization problem for a class of stochastic nonholonomic systems with strong drifts. By using input-state-scaling technique, backstepping recursive approach, and a parameter separation technique, we design an adaptive state feedback controller. Based on the switching strategy to eliminate the phenomenon of uncontrollability, the proposed controller can guarantee that the states of closed-loop system are global bounded in probability.