Abstract: Disclosed are an articulated hydraulic machine supporting, control system and control method for same. The articulated hydraulic machine has an end effector for performing useful work. The control system is capable of controlling the end effector for automated movement along a preselected trajectory. The control system has a position error correction system to correct discrepancies between an actual end effector trajectory and a desired end effector trajectory. The correction system can employ one or more absolute position signals provided by one or more acceleration sensors supported by one or more movable machine elements. Good trajectory positioning and repeatability can be obtained. A two-joystick controller system is enabled, which can in some cases facilitate the operator's task and enhance their work quality and productivity.

Abstract: A system and method for controlling a process includes simulating the process and producing a simulated output of the process, developing a set of target values based on measured inputs from the process and based on the simulated output from the process simulator, and producing multiple control outputs configured to control the process based on the set of target values during each operational cycle of the process control system. The simulated outputs include one or more predicted future values up to the steady state of the process.

Abstract: Controller scaling and parameterization are described. Techniques that can be improved by employing the scaling and parameterization include, but are not limited to, controller design, tuning and optimization. The scaling and parameterization methods described here apply to transfer function based controllers, including PID controllers. The parameterization methods also applies to state feedback and state observer based controllers, as well as linear active disturbance rejection controllers.

Abstract: A technique is disclosed for reducing an error in a controlled variable via model predictive control. A predicted error in the controlled variable is determined for a forward-looking control horizon based upon measured or computed variables. The integral of the predicted error is computed. If the error or the integral exceed a tolerance for a determined time period, the model predictive control algorithm is modified to drive the error or the integral to within a tolerance. The modifications to the control algorithm may include changes to coefficients for terms based upon the error and/or the integral of the error.

Abstract: A method of detecting one or more failed current sensor and estimating a phase current for the failed current sensor on a three-phase machine is disclosed. The method may include detecting one or more failed current sensor by determining if an absolute value of a sum of the phase currents of the motor is below an open circuit value. The method may also include determining which phase currents are approximately zero, for each phase current associated with each phase of the motor, if the sum of the phase currents of the motor is not below the open circuit value. The method may further include estimating the phase current for the failed current sensor by determining the phase current value for the failed current sensor, that when added to the phase currents of the remaining current sensors, will make the sum of all the phase currents equal to approximately zero.

Abstract: A method and a system for controlling a crane drive unit so as to suppress sway of a load suspended by a rope of a crane, which sway occurs when the load has been transported from a first position to a second position, the control being made by operating a controller having a filter unit by using a feedforward control program.

Abstract: Process controllers, methods, and systems provide for frequency control to account for the effects of periodic disturbances in the feedback signal of closed loop control systems. The frequency components of the feedback signal are determined, including the magnitude and phase of each. Waveforms for each frequency component are generated with substantially the same magnitude and substantially the opposite phase of each frequency component. The waveforms are then summed to produce a compensating waveform that is summed within the output of the control system so that the effects of the periodic disturbances are cancelled from the control system output being provided to the system under control.

Abstract: A joint of a robot is controlled by a torque command. The joint has a position controller with a position feedback loop. The torque command is received for the joint, and a velocity feedforward command is determined for realizing the torque command using the position controller. The velocity feedforward command is sent to the position controller and the position feedback loop is canceled. The position feedback loop is canceled by sending a position command to the position controller, where the position command is an actual measured position of the joint. The position feedback loop is also canceled by setting the gain of the position feedback loop to zero.

Abstract: Disclosed is a controller having a processor and a control module adapted for periodic execution by the processor and configured to be responsive to a process variable to generate a control signal for a process. An iteration of the periodic execution of the control module involves implementation of a routine configured to generate a representation of a process response to the control signal. The routine is further configured to maintain the representation over multiple iterations of the periodic execution of the control module and until an update of the process variable is available. In some cases, the update of the process variable is made available via wireless transmission of the process signal. In those and other cases, the controller may be included within a process control system having a field device to transmit the process signal indicative of the process variable non-periodically based on whether the process variable has changed by more than a predetermined threshold.

Abstract: In a method for supplying a resource to an entity from a resource actuator, a plurality of physics-based models pertaining to the resource actuator and the entity are developed, a condition detected at the entity is received, feedback control on a resource demand of the entity employed based upon the detected condition, feed forward control on the resource demand of the entity is employed based upon the detected condition and the plurality of physics-based models, a constraint optimization problem having an objective function and at least one constraint using the plurality of physics-based models is formulated, a solution to the constraint optimization problem is determined, in which the solution provides the actuator setting, and the resource actuator is set to the actuator setting to supply the entity with the resource from the resource actuator.

Abstract: A two-stage model predictive control (MPC) controller uses a process model and two separate MPC control modules, including a feedforward MPC control module and a feedback MPC control module, to determine a set of control signals for use in controlling a process. The feedforward MPC control module uses the process model to determine a feedforward control component for each of a set of control signals and the feedback MPC control module uses the process model and one or more measured process outputs to determine a feedback control component for each of the set of control signals. The two-stage MPC controller combines the feedforward control components with the feedback control components to form the final control signals used to control the process.

Abstract: Processing a wafer using a double side grinder having a pair of grinding wheels. Warp data is obtained by a warp measurement device for measuring warp of a wafer as ground by the double side grinder. The warp data is received and a nanotopography of the wafer is predicted based on the received warp data. A grinding parameter is determined based on the predicted nanotopography of the wafer. Operation of the double side grinder is adjusted based on the determined grinding parameter.

Abstract: A method for controlling a process variable as it approaches a predetermined value (setpoint) so that the setpoint is not exceeded. The method employs a time domain polynomial equation in a feedback configuration and utilizes a controller that acts as an On/Off controller until the process variable approaches setpoint. As the process variable approaches setpoint, the controller acts as a fast responding analog controller thereby “tailoring” a control variable to precisely bring the process variable to the setpoint without exceeding or overshooting the setpoint.

Abstract: A repetitive controller scheme with negative feedback and feedforward introduces infinitely many poles on the imaginary axis located at the resonant peaks. The feedforward introduces zeros, which produce notches located in between two consecutive resonant peaks. The latter has the advantage of making the controllers more selective, in the sense that the original overlapping (appearing at the valleys) or interaction between consecutive resonant peaks is removed by the notches. This would allow, in principle, peaks of higher gains and slightly wider bandwidth, avoiding, at the same time, the excitation of harmonics located in between two consecutive peaks. A negative feedback compensator with feedforward is especially useful when only the compensation of odd harmonics is required, but not the even harmonics, like in many power electronic systems. In contrast, the positive feedback controller would try to reinject, and indeed amplify, any small noise, which has components on the even frequencies.

Abstract: One embodiment of the invention comprises a mass flow controller comprising a digital controller, a valve, and a sensor. The digital controller is adapted to implement a control loop having a proportional signal modifier in series with an integral signal modifier. The integral signal modifier is adapted to receive a combination signal and output an integrated signal. The valve is adapted to receive the integrated signal and adjust a valve opening in accordance with the integrated signal. The sensor is adapted to output a measured flow rate signal indicative of an actual fluid flow rate in the mass flow controller. The measured flow rate signal is received by the proportional signal modifier and used in conjunction with a setpoint signal to determine the error signal.

Abstract: A information processing apparatus 100 for processing an acquired value, which is a value acquired in regard to a state during a treatment, performed by a semiconductor manufacturing apparatus 200 for performing a treatment on a treatment target containing a semiconductor according to a set value, which is a value for setting a condition of a treatment, includes: a set value receiving portion 101 for receiving the set value; a state value receiving portion 102 for receiving the acquired value; a correction amount calculating portion 103 for calculating a correction amount of the acquired value, using a correction function indicating a relationship between the set value and the acquired value; a correcting portion 104 for correcting the acquired value received by the state value receiving portion 102, using the correction amount calculated by the correction amount calculating portion 103; and an output portion 105 for outputting a result of correction performed by the correcting portion 104.

Abstract: A production schedule creation device includes: a production simulator (100) simulating a production process expressing the production state and the production constraint of the production process; a mathematical expression holding device holding a mathematical model (110) created by acquiring information relating to creation of the production schedule in attention as a mathematical model expressing, in a mathematical expression, the production state and the production constraint of the production process; and an optimization calculation device (120) performing the optimization calculation by using a predetermined evaluation function for the mathematical model (110) and calculating a production instruction for the production simulator. The production instruction obtained by the optimization calculation device is supplied to the production simulator (100) so as to execute simulation. Thus, an optimum solution can be obtained by performing only one simulation.

Abstract: A method of creating and using an adaptive DMC type or other MPC controller includes using a model switching technique to periodically determine a process model, such as a parameterized process model, for a process loop on-line during operation of the process. The method then uses the process model to generate an MPC control model and creates and downloads an MPC controller algorithm to an MPC controller based on the new control model while the MPC controller is operating on-line. This technique, which is generally applicable to single-loop MPC controllers and is particularly useful in MPC controllers with a control horizon of one or two, enables an MPC controller to be adapted during the normal operation of the process, so as to change the process model on which the MPC controller is based to thereby account for process changes.

Abstract: The invention comprises apparatuses and methods for providing the capability to stabilize and control a non-minimum phase, nonlinear plant with unmodeled dynamics and/or parametric uncertainty through the use of adaptive output feedback. A disclosed apparatus can comprise a reference model unit for generating a reference model output signal ym The apparatus can comprise a combining unit that combines and differences a plant output signal y of a non-minimum phase plant for which not all of the states can be sensed, and a plant output signal y, to generate an output error signal {tilde over (y)}. The apparatus can further comprise an adaptive control unit for generating an adaptive control signal uad used to control the plant.

Abstract: A system and method are provided for controlling temperature of a batch fermenter in a biofuel production process. A nonlinear predictive integrating temperature model for a batch fermentation process is provided that is a function of fermenter level. An objective for the batch fermentation process specifying a target fermenter temperature for the batch fermentation process is received, as is process information for the batch fermentation process, including fermenter level and fermenter temperature. The nonlinear predictive integrating temperature model is executed in accordance with the objective using the process information as input to determine target values for manipulated variables for controlling fermenter temperature of the batch fermentation process. The fermenter temperature for the batch fermentation process is controlled in accordance with the target values to produce biofuel in accordance with the objective, to substantially optimize the end of batch biofuel yield.

Abstract: An electric power steering apparatus includes a driving target value setting unit for setting a driving target value of an electric motor; a steering acceleration detecting unit for detecting or estimating a steering acceleration; a correction amount computing unit for computing a control correction amount in accordance with the steering acceleration; a vehicle acceleration detecting unit for detecting an acceleration of a motor vehicle; an acceleration adaptive gain setting unit for setting a gain in accordance with an acceleration of a motor vehicle; a multiplication unit for determining a gain adjusted control correction amount by multiplying the control correction amount with the acceleration adaptive gain; a correcting unit for correcting the driving target value on the basis of the gain adjusted control correction amount; and motor driving units for driving the electric motor on the basis of the corrected driving target value.

Abstract: A method of dynamic model predictive control is presented in which both steady state optimization and dynamic moves calculation of the manipulated variables are determined together as part of one optimization solution (211). The method combines steady state optimization and dynamic move calculation such that the steady state optimal targets are determined consistent with the dynamic moves and the resulting dynamic response of the process so that the controlled variables do not violate their low/high limits in both steady state and dynamically. The method utilizes what is described as high limit dynamic violation variables and low limit dynamic violation variables corresponding to each of the controlled variables.

Abstract: A method of controlling a power generating unit or other process equipment with a slow reaction time includes creating a feedforward control signal to selectively include a fast response rate component or a slow response rate component based on the average rate at which a load demand set point signal has changed during a particular previous period of time. The method then uses the developed feedforward control signal to control the power generating equipment or other slowly reacting process equipment. In particular, a control method switches between introducing a fast or a slow response component within a feedforward control signal based on whether the change in the load demand set point over a particular period of time in the past (e.g., an average rate of change of the load demand set point signal) is greater than or less than a predetermined threshold. This method is capable of providing a relatively fast control action even if the expected load demand set point change is in a small range.

Abstract: A method of obtaining improved feedforward data for a feedforward control system to move a component through a setpoint profile is presented. The setpoint profile includes a plurality of target states of the component each to be substantially attained at one of a corresponding sequence of target times. The method includes moving the component with the feedforward control system according to the setpoint profile using a first set of feedforward data; measuring a state of the component at a plurality of times during the movement; comparing the measured states with corresponding target states defined by the setpoint profile to obtain a set of errors; filtering the set of errors with a non-linear filter; generating improved feedforward data based on the filtered errors, the improved feedforward data being usable by the feedforward control system to move the component more accurately through the setpoint profile.

Abstract: The present invention discloses a feedback and feedforward process control system, comprising the steps: 1.) Determining an output variable that is highly correlated with the controlled variable, the variation of which is mainly influenced by upstream processes rather than current process, 2.) Processing a semiconductor wafer with a first set of parameters, 3.) Measuring the output variable that is highly correlated with the controlled variable after the semiconductor wafer is processed, 4.) Developing a predictive feedforward signal based on the output variable, 5.) Measuring the controlled variable after the semiconductor wafer is processed to be used as feedback signal, and 6.) Determining a second set of parameters based on feedback and feedforward signals.

Abstract: A method in one embodiment comprises scanning a zone in an active mode at a first power level for identifying presence of a tag; and scanning portions of the zone in a passive mode at a second power level for again identifying presence of the tag. A system in another embodiment comprises an interrogator for scanning a zone in an active mode at a first power level for identifying presence of a tag; wherein the interrogator also scans portions of the zone for again identifying presence of the tag. A method in another embodiment comprises scanning zones of an area in an active mode for identifying the zone in which the tag is located; and scanning portions of the zone in which the tag is located in a passive mode for identifying the portion of the zone in which the tag is located.

Abstract: A remote maintenance system 1 is provided with a linear motor apparatus 2, a motor driver 3 for controlling a motor of the linear motion apparatus 2, and a user terminal 4. The motor driver 3 includes a memory which stores parameters relating to motor control. The user terminal 4 acquires the parameters from the motor driver 3, and sends the parameters to a maintenance server 5. Then, the user terminal 4 receives the parameters adjusted by the maintenance servers from the maintenance server 5, and writes the parameter into the memory of the motor driver 3. Thus, the parameters of the linear motion apparatus can be adjusted from remote locations at a high precision.

Abstract: A controller includes a feedforward module to produce a feedforward component azr, where a is a high frequency gain, a proportional module is to produce a proportional component Kpvz, where Kpv is a proportional gain, and an integral or lag module with state resetting to produce an integral or lag component. The feedforward component azr, the proportional component Kpvz, and the integral component Kivzc are combined as an input u for the system to be controlled.

Abstract: An appliance control system is described for controlling a plurality of appliances. The system includes a control station located remotely from the appliances and having a control unit for controlling the plurality of appliances, at least one client station being associated with at least one of the plurality of appliances and being adapted for allowing a user to make requests to the control station for using the at least one of the plurality of appliances, actuators connected to the control station and the at least one of the plurality of appliances for receiving control signals from the control station and controlling the at least one of the plurality of appliances, and sensors connected to the water appliance and the control station for recording information about the at least one of the plurality of appliances and providing the information to the control station.

Abstract: A method of setting control data by an active vibration isolation control system includes the steps of selecting, when a frequency of a pulse signal actually detected is superior to a predetermined frequency, appropriate control data selected from among predetermined data maps incorporating control data capable of securing, in accordance with various vehicle driving conditions respectively, a control condition in which operation of the vibrator is preferably controlled, calculating a deviation between the appropriate control data commensurate with the actual vehicle driving condition at the time of controlling and actually detected data representing vibration subjected to a vehicle specific position, the actually detected data obtained in terms of a same physics amount as a physics amount of the control data, and modifying the appropriate control data on the basis of the calculated deviation.

Abstract: In a feedback control apparatus comprising a controller, a control object to be controlled by the controller, and an observer for inputting a control output from the control object and an output of the controller and setting an output of a control object model to be a feedback signal, the observer includes an observer compensator for inputting a difference between the control output and an output of an element model and inputs, to the control object model, a sum of an output of the observer compensator and the output of the controller. Consequently, a control system having an excellent response performance can be constituted and a stable observer can easily be constituted.

Abstract: A flow control system comprises a flow sensor, a valve controller, a signal processor, a control processor and an interface. The flow sensor generates a sensor signal characterizing a flow rate. The valve controller controls the flow rate as a function of a control output. The signal processor converts the sensor signal into a flow signal characterizing the flow rate as a function of time, and the control processor generates the control output as a function of a setpoint and the flow signals. The interface receives an input representative of the setpoint, transmits a flow output representative of the flow signals, and transmits a diagnostic output directly indicative of an operational condition of the flow control system.

Abstract: Methods and apparatus are described for control of friction at the nanoscale. A method of controlling frictional dynamics of a plurality of particles using non-Lipschitzian control includes determining an attribute of the plurality of particles; calculating an attribute deviation by subtracting the attribute of the plurality of particles from a target attribute; calculating a non-Lipschitzian feedback control term by raising the attribute deviation to a fractionary power ?=(2m+1)/(2n+1) where n=1, 2, 3 . . . and m=0, 1, 2, 3 . . . , with m strictly less than n and then multiplying by a control amplitude; and imposing the non-Lipschitzian feedback control term globally on each of the plurality of particles; imposing causes a subsequent magnitude of the attribute deviation to be reduced.

Abstract: A position/force control device includes position detectors on a master 1 side and on a slave 3 side. Reaction force estimation observers 2 and 4 estimate reaction force based on outputs of the position detectors. A position control part 5 generates acceleration signals apm, aps for controlling positions on the master side and on the slave side on the basis of the position signals outputted by the position detectors. The operation force control part 6 generates acceleration signals afm, afs for controlling forces applied to the master side and to the slave side based upon the outputs from reaction force estimation observers 2 and 4. The acceleration composition part 7 composes the two sets of acceleration signals apm, aps, and afm, afs, and outputs the driving signals for the master side and the slave side.

Abstract: A method for controlling a power system control area according to a first and a second control performance standard, wherein operation of the control area determines area control parameter values.

Abstract: Various methods and systems for the parametric control of a process include representing the process with a process model used to generate future predictions of a process variable. In one embodiment, the process exhibits integrating behavior that is represented by a non-integrating process model. In another embodiment, an inverse of the model is filtered using a filter that includes a lead time constant that is selected to minimize a steady state error of the predicted process variable. In yet another embodiment, an array of output model values is revised or reindexed in response to a change in a time-varying parameter related to the process.

Abstract: Systems, methods and computer-executable code stored on computer readable media for synchronizing the evolving state of a dynamic object in a shared virtual environment among a plurality of geographically separated computers connected in a communications network including data communications links introducing time delays in the propagation of data between said computers. The synchronization scheme utilizes an advanced feedback controller to compensate for the state error between sites, comprised of a linear compensator and a Smith predictor based internal model, to determine correct control forces creating a smooth input while maintaining high levels of responsiveness and consistency. A recovery filter for restoring the natural motion of the virtual object distorted by synchronization control is also described.

Abstract: A feedback controller performs a feedback control based on an error between a target position and an actual position of a head. A model controller obtains a control command, a model position to be output as a command for the target position to the feedback controller, and a model velocity for the head to follow a target velocity, by using a preset control equation model, and obtains the control command and the model position with the target position as an input, based on a differential value of the target velocity corresponding to a remaining distance from the model position to the target position.

Abstract: A system for controlling a plant process wherein the plant is over-actuated with N+1 actuators and provides N performance variables is disclosed. The system includes an outer-loop controller operable to compare N performance variable values from the plant with a reference set point and provide a desired virtual control input to an inner-loop controller. The inner-loop controller receives the desired virtual control input from the outer-loop controller and provides real control inputs to the at least N+1 actuators. The N+1 actuators receive the real control inputs and subsequently provide an actual virtual control input to the plant. Upon receiving the actual virtual control input from the N+1 actuators the plant is operable to produce N updated performance variable values in an optimized manner.

Abstract: This document describes a correction signal usable to correct an effect of a disturbance signal on a controlled system or apparatus. In one case this document describes ways in which to diminish a future change to an output signal based on determining that a disturbance signal consistently precedes the future change.

Abstract: An integrated digital controller for controlling power electronic devices and method of its use, comprises an analog-to-digital converting scanner module for scanning analog data inputs and used to create digital data correlated with the analog inputs, a loop control module operative to receive the digital data ad used for controlling at least one control loop, and a pulse sequence generator (PSG) module used for generating a variety of fast, configurable, event-driven pulse sequences in cooperation with the PSG and scanner modules. The controller comprises optionally a CPU for managing various tasks and coordinate between the modules, means to create the events, and means for configuration and reconfiguration on-the-fly. The controller is preferably integrated in a semiconductor chip.

Abstract: Disclosed are methods and devices for controlling a process with a control signal. Iterations of a control routine are implemented to generate the control signal, and when an indication of a response to the control signal is unavailable, a feedback contribution to the control signal is maintained over one or more of the iterations of the control routine. The feedback contribution is then modified upon receiving the response indication, in which the feedback contribution is determined in accordance with an elapsed time between the received response indication and a previous communication of the response indication.

Abstract: A robust digital controller is equipped with a high degree of approximation and is able to incorporate a novel two-degree-of-freedom robust digital control system without substantially considering the magnitude of the control inputs and there is provided its designing device. A control compensating means is configured as an integral type control system in which a discrete transfer function Wry (z) between a target value r and a controlled variable y is approximated to a higher-approximate quadratic approximate model transfer function Wm (z) and an arithmetic processing can be performed within the digital controller based on the model transfer function Wm (z). Further, the designing device automatically calculates parameters constituting the control system. Consequently, a robust digital controller can be easily realized that is equipped with a high degree of approximation as compared with a conventional approximate digital control system for realizing a first-order model and is robust against output noises.

Abstract: An environment control device, an environment control method, an environment control program, and a computer-readable recording medium containing the environment control program for enabling the user to actually have a comfortable feeling in a reliable manner and further to maintain such a comfortable state, are provided. A biological information measuring portion acquires time-series data of the biological information of the user. A chaos analysis portion calculates a parameter about the biological information through chaos analysis of the time-series data acquired by the biological information measuring portion. A state inferring portion infers a comfortable feeling of the user on the basis of the parameter calculated by the chaos analysis portion. A device control portion controls generation of a stimulus to be given to the user on the basis of the result of inference made by the state inferring portion.

Abstract: An adaptive control device includes an identifier and a feedforward controller. The identifier estimates an unknown coefficient in a discrete-time transfer function model of a controlled object to identify the discrete-time transfer function model. Estimation is performed based on a manipulated variable supplied to the controlled object and a controlled variable of the controlled object to the given manipulated variable. When estimating each coefficient of the discrete-time transfer function model, the identifier estimates a single unknown coefficient in numerator in non-expanded form of the numerator.

Abstract: An adaptive cascade proportional-integral-derivative controller produces a fixed controller output including a fixed proportional-integral-derivative and a fixed feedforward controller command, and an adaptive controller output including an adaptive cascade PID and an adaptive feedforward command all from a reference command. The fixed controller output and the adaptive controller output are added to produce a control command for a controlled system, which provides a measure of an output and a rate of change of the output as feedback for the controller.

Abstract: An adaptive parallel proportional-integral-derivative controller produces a fixed controller output including a fixed proportional-integral-derivative and a fixed feedforward controller command, and an adaptive controller output including an adaptive parallel PID and an adaptive feedforward command all from a reference command. The fixed controller output and the adaptive controller output are added to produce a control command for a controlled system, which provides a measure of an output and a rate of change of the output as feedback for the controller.

Abstract: A method is provided wherein a lithographic projection apparatus is used to print a series of test patterns on a test substrate to measure printed critical dimension as function of exposure dose setting and focus setting. A full-substrate analysis of measured critical dimension data is modeled by a response model of critical dimension. The response model includes an additive term which expresses a spatial variability of the response with respect to the surface of the test substrate. The method further includes fitting the model by fitting model parameters using measured critical dimension data, and controlling critical dimension using the fitted model.

Abstract: Disclosed is a controller having a processor and a control module adapted for periodic execution by the processor and configured to be responsive to a process variable to generate a control signal for a process. An iteration of the periodic execution of the control module involves implementation of a routine configured to generate a representation of a process response to the control signal. The routine is further configured to maintain the representation over multiple iterations of the periodic execution of the control module and until an update of the process variable is available. In some cases, the update of the process variable is made available via wireless transmission of the process signal. In those and other cases, the controller may be included within a process control system having a field device to transmit the process signal indicative of the process variable non-periodically based on whether the process variable has changed by more than a predetermined threshold.

Abstract: A lithographic apparatus includes a movable object and a control system to control the position of the movable object. The control system includes a position measurement system configured to measure the position of the movable object, a comparative unit configured to generate a servo error signal by subtracting a position signal representative of an actual position of the movable object from a reference signal, a control unit configured to generate a first control signal based on the servo error signal, a feed-forward unit configured to generate a feed-forward signal based on the reference signal, an addition unit configured to generate a second control signal by adding the first control signal and the feed-forward signal, and an actuator unit configured to actuate the movable object. A gain of the feed-forward unit is dependent on the position of the movable object.