This article deals with tracking control and active vibration suppression of a hybrid rigid‐elastic vibrational mobile system with a nonlinear elastic foundation in the presence of actuator bandwidth limitation and control input saturation. The system consists of a rigid rectilinearly mobile frame on an elastic foundation, and a flexible Timoshenko beam clamped to it with a heavy attached concentrated mass. The hybrid partial differential equation (PDE)‐ordinary differential equation (ODE) system of the plant is obtained using Hamilton's principle and then is converted to a system of ODEs using the assumed mode method (AMM). Next, the model will be discretized in the time domain using the two‐step Adams‐Bashforth technique. Considering the first‐order dynamics to cover the bandwidth limitation of the actuator, a discrete‐time sliding mode controller (DSMC) is designed based on a positive definite Lyapunov functional. Following that, an innovative optimal predictive algorithm is proposed to compensate for the effects of input saturation. The proposed algorithm is based on a positive definite cost function and using an intelligent regime of optimizations and decisions, minimizes the cost function in a predefined prediction horizon. The vibratory behavior of the system also is included in the mentioned cost function. Consequently, the overall control scheme called optimal rigid‐elastic interaction control (OREIC) will be able to follow the desired tracking trajectory, suppress the beam vibrations, and compensate for the effect of bandwidth limitation as well as the effect of input saturation. The performance of the OREIC algorithm is compared with a saturated DSMC controller and the simulation results demonstrate the efficiency of the method in vibration control of mobile rigid‐elastic systems subjected to actuator bandwidth frequency and saturation limitations.

Feedback control of actuation‐constrained moving structure carrying Timoshenko beam

This paper provides an effective systematic procedure for the efficient treatment of worm gearboxes for industrial-grade cases. The accurate and general dynamic model of the worm gearbox is analyti...

Algorithm for the torque sensorless worm gearbox servo application based on kinetic motion/friction realization:

The multivariable modeling of a servo actuating system consisting of multi-field multi-armature direct current (MFMADC) machine is extracted and a novel discrete time nonlinear algorithm is proposed for the corresponding system. The proposed control algorithm demonstrates robustness against modeling uncertainty and by utilizing its novel mathematical structure, decouples the dynamical interactions of the connected motors. The main contribution of this paper is the proposition of a new decoupling control algorithm that in which, the driving (commanding) voltages of the connected driving motors are extracted separately and independently using the Lyapunov principle in discrete time. In fact, the obtained coupled stabilizing convex inequalities of the controlling voltages, resulting from the evaluation of the Lyapunov functions, are analytically decoupled using elementary matrix operations. Consequently, each motor now has the capability to perform its controlling task (position control or torque control) with asymptotic stability and robustness against uncertainty. To assess the performance of the proposed controlling algorithm and its verification, a MFMADC machine is attached to a harmonic drive reducer (HDR) whose flex spline and circular spline are fabricated using viscoelastic polyesters PLA and thermoplastic PLA, respectively. A number of experiments are conducted where in the first test, the MFMADC is controlled in only-position mode while in the second test, the MFMADC is controlled in simultaneous position-torque control mode. Comparative assessments confirm that the MFMADC technology is needed when a high precision tracking of position, under high frequency disturbances, is desired.

Input-decoupled discrete-time sliding mode control algorithm for servo multi-field multi-armature DC machine.

The main objective of this paper is to present a non-predictive method in the design of nonlinear multi-input multi-output (MIMO) control systems with the presence of constraints that are determinant in practical conditions, namely, the frequency bandwidth limitation of the actuation system and saturation boundaries in control commands. If these constraints are applied in the non-predictive control design problem, it is not possible to simultaneously satisfy Lyapunov stability and actuation constraints, analytically. Instead of model-predictive-based algorithms, which in most cases are computationally expensive, this paper proposes an algorithm based on synthetic Lyapunov stability. In this technique, by defining an intelligent filter applied to the system desired trajectories, defining intelligent proximity coefficients in decoupled inequalities resulting from Lyapunov stability, and determining the admissible boundaries of control commands, a space of regulatory parameters is generated. By appropriately adjusting these parameters based on statistical analysis conducted on the overall dynamics of the system, the Lyapunov stability is guaranteed, and the mentioned control constraints are not violated. In summary, the proposed control algorithm includes the formulation of discrete-time dynamics of sliding functions, the presentation of the procedure of defining and adjusting the control algorithm parameters with the proposed synthetic stability criterion, and the calculation of control inputs based on constraints imposed on the problem. Finally, the algorithm is applied to a cart moving in the X-Y plane, including two rigid cooperative arms that are carrying a load. The most important features of synthetic Lyapunov stability compared to the model predictive-based method are its small computational load and its acceptable performance in satisfying both the Lyapunov stability conditions and determinant control constraints in more realistic situations. 

Synthetic Lyapunov stabilization technique for designing actuation-constrained multi-input multi-output control systems

The multivariable modeling of a servo actuating system consisting of multi-field multi-armature direct current (MFMADC) machine is extracted and a novel discrete time nonlinear algorithm is proposed for the corresponding system. The proposed control algorithm demonstrates robustness against modeling uncertainty and by utilizing its novel mathematical structure, decouples the dynamical interactions of the connected motors. The main contribution of this paper is the proposition of a new decoupling control algorithm that in which, the driving (commanding) voltages of the connected driving motors are extracted separately and independently using the Lyapunov principle in discrete time. In fact, the obtained coupled stabilizing convex inequalities of the controlling voltages, resulting from the evaluation of the Lyapunov functions, are analytically decoupled using elementary matrix operations. Consequently, each motor now has the capability to perform its controlling task (position control or torque control) with asymptotic stability and robustness against uncertainty. To assess the performance of the proposed controlling algorithm and its verification, a MFMADC machine is attached to a harmonic drive reducer (HDR) whose flex spline and circular spline are fabricated using viscoelastic polyesters PLA and thermoplastic PLA, respectively. A number of experiments are conducted where in the first test, the MFMADC is controlled in only-position mode while in the second test, the MFMADC is controlled in simultaneous position-torque control mode. Comparative assessments confirm that the MFMADC technology is needed when a high precision tracking of position, under high frequency disturbances, is desired. • Offering a New Affordable Solution for Precision Servo Applications of PMDC Machines. • Proposing a New Nonlinear Decoupling Control for Simultaneous Position-Torque Control. • Analytical Robust Stability of Feedback System versus Broad-Band Impedance Disturbance. • Applicability of Proposed High-Precision Servo Actuator Using Regular Micro-Processors. 

M. Farzannasab

Papers

Switching position-torque control system for increasing servo PMDC positioning precision in presence of intense external disturbance loading