Abstract: A method determines trajectories of redundant actuators of a machine including a first actuator and a second actuator. The method determines a first trajectory of the first actuator tracking a reference trajectory with an error tolerance, wherein the error tolerance is a function of a constraint of the second actuator, and determines a second trajectory of the second actuator based on a difference between the reference trajectory and the first trajectory.

Abstract: A method generates trajectories for motor controlled actuators subject to dynamics, acceleration and velocity constraints. The method solves a constrained optimal control problem with dynamics, acceleration, and velocity constraints. The motor control problem is formulated as an optimal control problem using an energy cost function which is based on numerical optimization results. A solution to the two-point boundary value problem (TBVP) for the unconstrained case of the optimal control problem is obtained. The energy efficient motor control trajectory generation solver is designed for real time energy efficient trajectory generation. The solver converts a difficult multi-point boundary value problem (MBVP) associated with the state and acceleration constrained optimal control problem into an iterative solution for the TBVPs with updated boundary conditions.

Abstract: A system and a method for controlling an operation of a vapor compression system are disclosed, such that a performance of the system measured in accordance with a metric of the performance is optimized. A control signal is modified with a modification signal including a perturbation signal having a first frequency, wherein the control signal controls at least one component of the vapor compression system. A metric signal representing a perturbation in the performance of the system caused by the modification signal is determined, wherein the metric signal has a second frequency substantially equal to the first frequency. The control signal is adjusted based on a function of a phase between the perturbation signal and the metric signal, such that the performance is optimized.

Abstract: A method controls a set of semi-active actuators arranged in an elevator system to minimize a vibration of an elevator car. The elevator system is represented with a model of a virtual elevator system having a single virtual semi-active actuator arranged to compensate a virtual disturbance. The virtual disturbance is determined using a motion profile of position of the elevator car during the operation and a disturbance profile of the virtual disturbance. A state of the elevator system is determined using the model of the virtual elevator system, the virtual disturbance and a signal indicative of a horizontal acceleration of the elevator car during the operation. Each actuator of the set of semi-active actuators is controlled based on the state of the elevator system and according to a control policy of the virtual semi-active actuator.

Abstract: A set of semi-active actuators is arranged in an elevator system to compensate a vibration of an elevator car. The actuators are controlled in accordance with the control policy based on a measured signal including values of the parameter measured during the operation of the elevator system. The control policy is determined, based on a model of the elevator system, wherein the control policy includes a state function representing an operation of the elevator system and a function of displacement representing an operation of the set of semi-active actuators. The state function is approximated, using the model of the elevator system, as a first function of a parameter representing the vibration. The function of displacement is approximated, using the model of the elevator system, as a second function of the parameter.

Abstract: A method and a system determine a position of at least one sway sensor in an elevator system for sensing a lateral motion of an elevator rope between a first boundary location and a second boundary location. An operation of the elevator system is simulated with a model of the elevator system to produce an actual shape of the elevator rope caused by the operation. At least one sway location is determined, such that an error between the actual shape of the elevator rope and an estimated shape of the elevator rope is minimized. The estimated shape of the elevator rope is determined by interpolation of the first boundary location, the second boundary location, and the sway location. The position of the sway sensor is determined, such that the sway sensor senses the lateral motion of the elevator rope at the sway location.

Abstract: A method solves a quadratic programming (QP) problem in real-time implementations of model predictive control for automation applications. The method can be implemented for fine-grained parallel solutions. Due to the extreme simplicity of the method, even serial implementations offer considerable speed advantages. The method solves the problem by formulating, over a predetermined time interval, an optimization problem with a quadratic cost function, and linear state and control constraints as a quadratic program for the application. Then, the quadratic program is solved by applying a parallel quadratic programming update law starting from a positive initial estimate to obtain control actions for the application.

Abstract: An operation of a system is controlled according to a control trajectory represented by a solution of a set of differential equations satisfying boundary conditions, wherein the set of differential equations includes ordered piecewise differential equations. The set of differential equations is parameterized to produce a first set of parameters representing values of the solution at switching times and a second set of parameters representing values of the switching times. The first and the second sets of parameters are determined alternately until the boundary conditions are satisfied to produce the solution; and the control trajectory is generated based on the solution to control the operation of the system.

Abstract: A hybrid controller for a mechanical system includes an actuator configured to position a load. A vibration attenuation controller produces a vibration attenuation control signal in response to an input signal for the mechanical system. A tracking controller configured produces a tracking control signal in response to the input signal. In response to an output signal from the mechanical system, either the vibration attenuation control signal or the tracking control signal is switched as a control signal for the mechanical system to reduce both vibration in the mechanical system and improve tracking the load.

Abstract: A method controls redundant actuators of a machine based on a reference trajectory. The method determines a cost function representing operations of the redundant actuators and minimizes the cost function subject to constraints to produce a sequence of commands for each actuator. The redundant actuators are controlled according to the sequences of commands.

Abstract: A method determines a sway of an elevator rope during an operation of an elevator system. The method includes acquiring at least one measurement of a motion of the elevator rope during the operation of the elevator system; and determining the sway of the elevator rope connecting an elevator car and a pulley based on an interpolation between boundaries of the elevator rope based on the measurement of the motion.

Abstract: An elevator including a car is arranged in a shaft. A set of compensator cables are attached to a bottom of the car and engaged with a compensator drum. A set of hoist cables are attached to a top of the car and engaged with a hoist drum to move the car vertically in the shaft, wherein the set of compensator cables and the set of hoist cables are configured to only move the car vertically.

Abstract: A control signal for controlling an operation of a motion control system suitable for positioning a load is generated using determining a cost function based on a model of energy consumption of the system and a function of a tracking time; and minimizing the cost function subject to constraints to determine a trajectory of the control signal. The control signal is generated based on the trajectory and a current state of the system, wherein the steps of the method are performed by a processor.

Abstract: A laser cutting machine includes a platform and a motion system. The motion system includes a first prismatic joint facilitating a first motion of the platform along a first direction and a second prismatic joint facilitating a second motion of the platform along a second direction. A galvano arranged on the platform, such that a motion of the platform causes a motion of the galvano, the galvano including a first mirror, wherein a third motion of the first mirror positions the laser beam along a third direction, and a second minor, wherein a fourth motion of the second mirror positions the laser beam along a fourth direction. A control module controls concurrently the motion system and the galvano, such that a position of the laser beam on the workpiece is a vector sum of the first motion, the second motion, the third motion, and the fourth motion.

Abstract: A hybrid controller for a mechanical system includes an actuator configured to position a load. A vibration attenuation controller produces a vibration attenuation control signal in response to an input signal for the mechanical system. A tracking controller configured produces a tracking control signal in response to the input signal. In response to an output signal from the mechanical system, either the vibration attenuation control signal or the tracking control signal is switched as a control signal for the mechanical system to reduce both vibration in the mechanical system and improve tracking the load.

Abstract: A method generates trajectories for motor controlled actuators subject to dynamics, acceleration and velocity constraints. The method solves a constrained optimal control problem with dynamics, acceleration, and velocity constraints. The motor control problem is formulated as an optimal control problem using an energy cost function which is based on numerical optimization results. A solution to the two-point boundary value problem (TBVP) for the unconstrained case of the optimal control problem is obtained. The energy efficient motor control trajectory generation solver is designed for real time energy efficient trajectory generation. The solver converts a difficult multi-point boundary value problem (MBVP) associated with the state and acceleration constrained optimal control problem into an iterative solution for the TBVPs with updated boundary conditions.

Abstract: Vibration in a mechanical system driven by a motor connected to a load is reduced by providing an angular position and an angular velocity of the motor to a linear feedback term and to a nonlinear feedback term. Outputs of the linear feedback term and the nonlinear feed term, and an optimal feedforward term determined off-line are summed to produce a summed signal, which is fed back to control a torque of the motor.

Abstract: A method solves a quadratic programming (QP) problem in real-time implementations of model predictive control for automation applications. The method can be implemented for fine-grained parallel solutions. Due to the extreme simplicity of the method, even serial implementations offer considerable speed advantages. The method solves the problem by formulating, over a predetermined time interval, an optimization problem with a quadratic cost function, and linear state and control constraints as a quadratic program for the application. Then, the quadratic program is solved by applying a parallel quadratic programming update law starting from a positive initial estimate to obtain control actions for the application.

Abstract: A system and a method for controlling an operation of a vapor compression system are disclosed, such that a performance of the system measured in accordance with a metric of the performance is optimized. A control signal is modified with a modification signal including a perturbation signal having a first frequency, wherein the control signal controls at least one component of the vapor compression system. A metric signal representing a perturbation in the performance of the system caused by the modification signal is determined, wherein the metric signal has a second frequency substantially equal to the first frequency. The control signal is adjusted based on a function of a phase between the perturbation signal and the metric signal, such that the performance is optimized.