Patent Application: US-84004001-A

Abstract:
a ripple suppressor / compensator useful in the general area of motion control and applicable to a wide range of servomechanisms exhibiting a force ripple characteristics , including the permanent magnet linear motors . an adaptive feed - forward control signal is generated which compensates for the ripple force , thus allowing for more precise tracking performance to be achieved .

Description:
referring to fig1 and 2 , block diagrams are provided of two control systems for a permanent magnet linear motor . the fig1 system is a prior art system employing feedback and feed - forward control , whereas the fig2 system is an illustrative embodiment of the present invention and employs adaptive feed - forward control ( afc ) as well as feed - forward control ( ffc ), and feedback control ( fbc ) which in this example is a proportional / integral / derivation ( pid ) controller . traditionally , where systems required an output state to be accurately controlled , adjusted and maintained at a predetermined value , feedback control systems were employed to continually adjust input to the system being controlled in order to maintain the required output . typically , such feedback systems measured an output parameter 16 known as he measured variable or plant variable and compared it with a desired value 11 of that variable to calculate an error signal 18 . it is common in single loop feedback systems to employ proportional / integral / derivative ( pid ) controllers 19 ( also known as 3 - term controllers ) which have as their input , the error signal ( e ) 18 and have as their output a control signal ( u pid ) 20 given by : u pid = - k i  e + k 2  ∫ e   t + k 3   e  t where k 1 , k 2 & amp ; k 3 are constants chosen for the particular plant . the principle of feed - forward control is that if the characteristics of the device to be controlled are modelled , the model may be used to predict the input required to obtain a desired change in output . by applying a demand signal 11 , representing the desired system output to the input of the feed - forward controller 12 , a component 13 is added to the pid controller output 20 to produce signal 14 of the device 15 being controlled such that , assuming perfect modelling , the output 16 should be caused to change to the desired output . unfortunately , it is rarely possible to perfectly model a physical device , and therefore , feed - forward control cannot replace the traditional feedback control systems , but , merely supplement them . feed - forward control , can however , significantly improve system response by quickly adjusting the plant input for rapidly changing demand signals . to achieve similar response with a traditional feedback controller , would require high loop gains and would increase the possibility of instability . with non - linear systems , these problems are even more evident and the advantages of feed - forward control even greater , however , it is often not possible to model non - linear systems with sufficient accuracy , particularly when the non - linear response characteristic of the plant being controlled is a function of manufacturing tolerances of the plant . to deal with these shortcomings of conventional feed - forward control , it is now proposed to employ a form of adaptive feed - forward control which broadly models the non - linear characteristics of the plant being controlled , but includes an adaptive function that continuously adjusts the feed - forward parameters . in fig2 the system input 11 is fed to the adaptive feed - forward controller ( afc ) 21 as is the error signal 18 and the afc 21 processes these inputs to produce its own control signal component ( u afc ) 22 which is added to the other control signals 13 , 20 to produce the plant input 24 . in the case of a pmlp , the non - linear characteristic is primarily due to the force ripple phenomenon described previously . in the preferred embodiment the force ripple phenomenon is viewed and modelled as a response to a virtual input to the pmlm described in the form of a periodic sinusoidal signal : u ripple = a ( x ) sin ( ω x + ø )= a 1 ( x ) sin ( ω x )+ a 2 ( x ) cos ( ω x ), ( 1 ) is the pole pitch of the magnet structure . ø is the phase specification providing a reference point to the sinusoidal function . a ( x ), a 1 ( x ) pand a 2 ( x ) are functions of the displacement x of the translator of the linear motor . a dither signal is thus designed correspondingly to eradicate this virtual force as : u afc = α 1 ( x ( t )) sin ( ω x )+ α 2 ( x ( t )) cos ( ω x ). ( 2 ) α 1 *( x )=− a 1 ( x ), α 2 *( x )=− a 2 ( x ). ( 3 ) feed - forward compensation schemes are well known to be sensitive to modelling errors which inevitably result in significant remnant ripples . an adaptive approach is thus adopted so that α 1 and α 2 will be continuously adapted based on desired trajectories and prevailing tracking errors . a = [ a 1  ( x ) a 2  ( x ) ] , θ = [ sin  ( ω   x ) cos   ( ω   x ) ] , a * = [ - a 1  ( x ) - a 2  ( x ) ] . ( 4 ) ( 5 ) falls within the standard framework of adaptive control theory . possible update laws for the adaptive parameters will therefore be : where g & gt ; 0 is an arbitrary adaptation gain , e = x d − x is the tracking error where x d is the desired position trajectory . differentiating ( 13 ) and ( 14 ) with respect to time , the following equations are obtained α & amp ; 1 ( t )=− gex & amp ; d sin ( ω x ), ( 8 ) α & amp ; z ( t )=− gex & amp ; d cos ( ω x ), ( 9 ) in other words , the adaptive update laws ( 8 ) and ( 9 ) can be applied as an adjustment mechanism such that α 1 ( t ) and α 2 ( t ) in ( 2 ) converge to their true values . as described above , the physical implementation of the ripple suppression / compensation apparatus is preferably by means of a microprocessor / digital - computer using known techniques to implement various aspects of the above described function . however , as will be appreciated by those of ordinary skills in the art , analog electronic circuits may be used to fulfil many parts of this purpose . for the preferred digital implementation of the control apparatus , an interface between the ( digital ) controller apparatus and the analog ( input ) measurements and actuator ( output ) signals uses analog - to - digital and digital - to - analog converters , respectively , in the same manner as used by conventional digital controllers . accordingly , the present disclosure omits description of such converters . similarly , the functions of the ripple suppressor / compensator are implemented as a software program ( stored in a programmable read only memory of the microprocessor / digital - computer , for example ) for processing the stored data representing the converted input and output signals . the input parameter set , time functions and other data variables are held in the random access memory of the microprocessor / digital computer . the software used for this purpose by the present invention is the same as in other digitally implemented controllers and , accordingly , a detailed description thereof is omitted . in this experimental example , a linear drive tubular linear motor ( ld3810 ) was employed . the test bed system was equipped with a renishaw optical encoder with an effective resolution of 1 tm . the dspace control environment and rapid prototyping system was used , employing the ds1102 board . x d ( τ )= 10 6 [ x 0 +( x 0 − x f )( 15τ 4 − 6τ 5 − 10τ 3 )], ( 10 ) x & amp ; d ( τ )= 10 6 ( x 0 − x f )( 60τ 3 − 30τ 4 − 30τ 2 ), ( 11 ) where 10 6 is used to normalize the system units to μm . x d and x & amp ; d denote the desired position and velocity trajectories , x 0 = 0 and x f = 0 . 21 m denote the initial and final positions , respectively . τ = t /( t f − t 0 ), where t 0 = 2 seconds and t f = 5 seconds are the initial time and final time of the trajectory . as with feedback control , the gain ( g ) chosen for the adaptive feed - forward controller will be a trade off between lower values which give reliable performance and higher values which give faster tracking . the optimum value will depend on factors related to the configuration and use of the system and is usually adjusted by trial and error . values in the range of 0 - 1 and preferably in the order of 0 . 2 have been found to be useful with the particular system described above . the experimental results are shown in fig3 showing a maximum tracking error of around 5 tm . to further illustrate the effectiveness of the adaptive dither , the control results without the dither signal are shown in fig4 . it will be appreciated by persons skilled in the art that numerous variations and / or modifications may be made to the invention as shown in the specific embodiments without departing from the spirit or scope of the invention as broadly described . the present embodiments are , therefore , to be considered in all respects as illustrative and not restrictive . 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