G. Agranovich

Backlash compensation for motion system with elastic transmission

Control of mechanical system with backlash is a topic well studied by many control practitioners. This interest has been motivated by the fact that backlash is one of the most important nonlinearities, that primary limit the performance of speed and position loop in industrial motion system, such as robotics, automation and many other motion systems. This research deals with backlash in two-mass system, which well represents the majority of such systems. In this research backlash is treated as torque disturbance, which enter the system at the location of the backlash. Then a disturbance observer (DOB) is constructed in order to estimate and compensate the disturbance in an inner feedback loop fusion, such that the outer controller will used to control “backlash-free” system. Also the issue of torsional vibrations is investigated. Such vibrations are often generated because of the elastic shaft connected between the two masses (usually motor and load inertias). The torsional torque disturbance is estimated and compensated by using the disturbance observer in the same manner as the backlash.

Average Modeling and Performance Analysis of Voltage Sensorless Active Supercapacitor Balancer With Peak Current Protection

In this paper, average modeling and analysis of a dual-supercapacitor bank, actively balanced by a bidirectional buck-boost converter, is presented. In such a system, natural balancing is achieved when the converter is operated in open loop with 50% duty cycle, eliminating the need for measuring the voltage of each storage device. Nevertheless, excessive currents arise even for slight voltage misbalance because of the highly underdamped nature of the system. In order to remedy this drawback, bidirectional pulse-by-pulse inductor current limitation is introduced, which is equivalent to adding a peak-current-mode-like control loop to the system. Since the duty cycle never exceeds 50%, compensation ramp is not required to maintain stability. On the other hand, while the uncontrolled system dynamics is linear, introducing the current limit mechanism turns the closed-loop dynamics into a nonlinear one, burdening the analysis task and thus calling for suitable average model to perform fast simulations for system analysis. Therefore, dynamical equations of the system are developed in order to derive the switching-cycle-averaged model and reveal the tradeoff between current limit level, balancing time and efficiency for the worst case of imbalance. Simulations and experiments support the presented findings.

Optimal control synthesis for the constrained bilinear biquadratic regulator problem

Optimal process control with control constraints is a challenging task related to many real-life problems. In this paper, a single input continuous time constrained linear quadratic regulator problem, is defined and fully solved. The constraints include both bilinear inequality constraints and customary control force bounds. As a first step, the problem is reformulated as an equivalent constrained bilinear biquadratic optimal control problem. Next, Krotov’s method is used to solve it. To this end, a sequence of improving functions suitable to the problem’s new formulation is constructed and the corresponding successive algorithm is derived. The required computational steps are arranged as an algorithm and proof outlines for the convergence and optimality of the solution are given. The efficiency of the suggested method is demonstrated by numerical example.

Optimal Control of a Constrained Bilinear Dynamic System

In this paper, an optimal feedback, for a free vibrating semi-active controlled plant, is derived. The problem is represented as a constrained optimal control problem of a single input, free vibrating bilinear system, and a quadratic performance index. It is solved by using Krotov’s method and to this end, a novel sequence of Krotov functions that suits the addressed problem, is derived. The solution is arranged as an algorithm, which requires solving the states equation and a differential Lyapunov equation in each iteration. An outline of the proof for the algorithm convergence is provided. Emphasis is given on semi-active control design for stable free vibrating plants with a single control input. It is shown that a control force, derived by the proposed technique, obeys the physical constraint related with semi-active actuator force without the need of any arbitrary signal clipping. The control efficiency is demonstrated with a numerical example.

Active voltage sensorless supercapacitor bank balancer with peak current protection

In this paper, average modeling of a dual-supercapacitor bank, actively balanced by a bidirectional buck-boost converter is presented. In such a system, natural balancing is achieved when the converter is operated in open loop with 50% duty cycle, eliminating the need for measuring the voltage of each storage device. Nevertheless, excessive currents arise even for slight voltage misbalance because of the highly underdamped nature of the system. In order to remedy this drawback, bidirectional pulse-by-pulse inductor current limitation is introduced, which is equivalent to adding a peak-current-mode-like control loop to the system. Since the duty cycle never exceeds 50%, compensation ramp is not required to maintain stability. On the other hand, while the uncontrolled system dynamics is linear, introducing the current limit mechanism turns the closed loop dynamics into a nonlinear one, burdening the analysis task and thus calling for suitable average model to perform fast simulations for system analysis. Dynamical equations of the system are developed in order to derive the switching-cycle-averaged model. Simulations support the presented findings.

Efficient Newton method for optimal viscous dampers design

Passive control is a known method for vibrations damping in many mechanical systems, including civil structures. The simplicity and reliability of passive damping devices makes them a worthy candidate in many practical problems. However, despite of its practical simplicity, the optimal design of passive controller is quite hard computational problem. In this work, an enhanced optimal viscous passive dampers design method is proposed. The optimization is done with relation to performance index consists of ||H||2 system norm and quadratic gains norm. An algorithm is suggested for the look after a candidate optimum. It is based on Newtons optimization method with a new and effective calculation method for the Hessian matrix. Numerical tests of the suggested method shows a very fast convergence rate with relation to known ones.

Using canonical models for LQR and H-infinity control of structures

According to the seismic modal approach, optimal modal control design should derive a control signal affecting only the dominant modal coordinates. However, existence of an optimal state feedback, affecting only a selected set of modes, is questionable. This study proves the existence of optimal modal feedback for the case of infinite horizon LQR and H∞ control methods. It defines a modal state space model by using a new state-space similarity transformation and solves the corresponding algebraic Riccatis equation. The solution is based on the selection of LQR weighting and H∞ output matrices. A modal design method is formulated and the spillover effect for the controlled structure is introduced.