This study investigates the effectiveness of the non-smooth semi-active control algorithm on suppressing the vibration performance of a building structure subjected to seismic waves. According to the Lyapunov stabilit...This study investigates the effectiveness of the non-smooth semi-active control algorithm on suppressing the vibration performance of a building structure subjected to seismic waves. According to the Lyapunov stability theory, it has bene proven that the non-smooth semi-active control algorithm can achieve a finite-time stability of the vibration relative to the isolation layer of a building structure. Through numerical simulation of two buildings with different parameters subjected to the input of a seismic wave, the vibration conditions of passive control, LQR semi-active control and non-smooth semiactive control are compared and analyzed. The simulation results show that the non-smooth semi-active control algorithm has a better robustness and effectiveness in restraining the impact of earthquakes on the structure.展开更多
A novel non-smooth controller of the second order double integrator system with a bounded disturbance is proposed,which stability is proved and which disturbance rejection capability is analyzed by MATLAB simulation e...A novel non-smooth controller of the second order double integrator system with a bounded disturbance is proposed,which stability is proved and which disturbance rejection capability is analyzed by MATLAB simulation experiments. The novel non-smooth output feedback controller and tracking differentiator are applied to control the azimuth servo systemof the small floating satellite antenna. The MATLAB simulation and hardware in the loop simulation experiments are conducted. The experiment results validate that the non-smooth output feedback controller with stronger surge and sudden disturbance rejection capability can realize the stable azimuth servo control of the small floating antenna to ensure the communication between the target satellite and the antenna with high quality.展开更多
This paper is concerned with a systematic method of smooth switching linear parameter- varying （LPV） controllers design for a morphing aircraft with a variable wing sweep angle. The morphing aircraft is modeled as a...This paper is concerned with a systematic method of smooth switching linear parameter- varying （LPV） controllers design for a morphing aircraft with a variable wing sweep angle. The morphing aircraft is modeled as an LPV system, whose scheduling parameter is the variation rate of the wing sweep angle. By dividing the scheduling parameter set into subsets with overlaps, output feedback controllers which consider smooth switching are designed and the controllers in over- lapped subsets are interpolated from two adjacent subsets. A switching law without constraint on the average dwell time is obtained which makes the conclusion less conservative. Furthermore, a systematic algorithm is developed to improve the efficiency of the controllers design process. The parameter set is divided into the fewest subsets on the premise that the closed-loop system has a desired performance. Simulation results demonstrate the effectiveness of this approach.展开更多
In real machining, the tool paths are composed of a series of short line segments, which constitute groups of sharp corners correspondingly leading to geometry discontinuity in tangent. As a result, high acceleration ...In real machining, the tool paths are composed of a series of short line segments, which constitute groups of sharp corners correspondingly leading to geometry discontinuity in tangent. As a result, high acceleration with high fluctuation usually occurs. If these kinds of tool paths are directly used for machining, the feedrate and quality will be greatly reduced. Thus, generating continuous tool paths is strongly desired. This paper presents a new error-controllable method for generating continuous tool path. Different from the traditional method focusing on fitting the cutter locations, the proposed method realizes globally smoothing the tool path in an error-controllable way. Concretely, it does the smoothing by approaching the newly produced curve to the linear tool path by taking the tolerance requirement as a constraint. That is, the error between the desired tool path and the G01 commands are taken as a boundary condition to ensure the finally smoothed curve being within the given tolerance. Besides, to improve the smoothing ability in case of small corner angle, an improved local smoothing method is also proposed by symmetrically assigning the control points to the two adjacent linear segments with the constrains of tolerance and G3 continuity. Experiments on an open five-axis machine are developed to verify the advantages of the proposed methods.展开更多
The fluctuation of active power output of wind farm has many negative impacts on large-scale wind power integration into power grid. In this paper, flywheel energy storage system (FESS) was connected to AC side of the...The fluctuation of active power output of wind farm has many negative impacts on large-scale wind power integration into power grid. In this paper, flywheel energy storage system (FESS) was connected to AC side of the doubly-fed induction generator (DFIG) wind farm to realize smooth control of wind power output. Based on improved wind power prediction algorithm and wind speed-power curve modeling, a new smooth control strategy with the FESS was proposed. The requirement of power system dispatch for wind power prediction and flywheel rotor speed limit were taken into consideration during the process. While smoothing the wind power fluctuation, FESS can track short-term planned output of wind farm. It was demonstrated by quantitative analysis of simulation results that the proposed control strategy can smooth the active power fluctuation of wind farm effectively and thereby improve power quality of the power grid.展开更多
Driven by the ever increasing demand in function integration,more and more next generation high value-added products,such as head-up displays,solar concentrators and intra-ocular-lens,etc.,are designed to possess free...Driven by the ever increasing demand in function integration,more and more next generation high value-added products,such as head-up displays,solar concentrators and intra-ocular-lens,etc.,are designed to possess freeform(i.e.,non-rotational symmetric)surfaces.The toolpath,composed of high density of short linear and circular segments,is generally used in computer numerical control(CNC)systems to machine those products.However,the discontinuity between toolpath segments leads to high-frequency fluctuation of feedrate and acceleration,which will decrease the machining efficiency and product surface finish.Driven by the ever-increasing need for high-speed high-precision machining of those products,many novel toolpath interpolation and smoothing approaches have been proposed in both academia and industry,aiming to alleviate the issues caused by the conventional toolpath representation and interpolation methods.This paper provides a comprehensive review of the state-of-the-art toolpath interpolation and smoothing approaches with systematic classifications.The advantages and disadvantages of these approaches are discussed.Possible future research directions are also offered.展开更多
Micro-grid smooth switchover between different operation modes is important for steady operation and reliable power supply of micro-grid. In order to reduce the transient fluctuation of voltage and frequency during sw...Micro-grid smooth switchover between different operation modes is important for steady operation and reliable power supply of micro-grid. In order to reduce the transient fluctuation of voltage and frequency during switchover, this paper proposed a new switchover method based on controller state following. When transferring to island mode, the control method for inverter of storage device changed from PQ control to V/f control. Before switchover, the output of V/f controller is always following the output of PQ controller. So that the sudden change of output is avoided at the moment of switchover. A micro-grid model with photovoltaic and battery is built on DIgSILENT Power Factory simulation software, to simulate micro-grid switchover from grid-connected mode to island mode. Results show this method can effectively suppress the transient fluctuation of voltage and frequency, and reduce the influence of transient process on power grid. This conclusion has important practical significance on micro-grid smooth switchover from grid-con- nected mode to island mode.展开更多
A novel type of control law was adopted to reduce the vertical acceleration of a fast ferry as well as the motion sickness incidence suffered by the passengers onboard by means of a submerged T-foil.Considering the sy...A novel type of control law was adopted to reduce the vertical acceleration of a fast ferry as well as the motion sickness incidence suffered by the passengers onboard by means of a submerged T-foil.Considering the system changing characteristics under high disturbances,a model-free approach was adopted.In addition,an upgraded proportional-derivative(PD)controller with correction terms resulting from a fast-online estimation of the system dynamics was designed.The overall controller,known as intelligent PD(i-PD)controller,was tested,and the obtained results were compared with those of a classic PD controller.The controllers were also tested in a changing environment and at different operating velocities.The results confirmed the effectiveness of the i-PD controller to smooth the motions with low computational cost control schemes.Furthermore,thanks to ability of the i-PD controller to continually update the estimated dynamics of the system,it showed a better reduction in both vertical motions and the seasickness level of the passengers with the needed robustness under external disturbances and system changing parameters.展开更多
A model reference adaptive control(MRAC)with smooth switching scheme was proposed for piecewise linear systems,and the method was utilized in turbofan engine control to avoid the discontinuity of control input.In this...A model reference adaptive control(MRAC)with smooth switching scheme was proposed for piecewise linear systems,and the method was utilized in turbofan engine control to avoid the discontinuity of control input.In this scheme,each sub-region of the operating envelope had its own MRAC controller,and smooth indicator function based smooth switching scheme was introduced to switch multiple controllers smoothly at the boundary of adjacent sub-regions.The Lyapunov stability analysis indicated that the proposed smooth switching scheme can guarantee the convergence of the closed-loop system during the controllers switching.The tracking error system was converted into a switched system to analyze the global stability of the closed-loop system.The advantage of the method was that the chattering of system output and instability caused by asynchronous switching can be eliminated.The simulation illustrates the effectiveness of the proposed control scheme in comparison with the existing MRAC controller with gain scheduling for turbofan engine.展开更多
The aircraft engine multi-loop control system is described and the switching control theory is introduced to solve the regulating and protecting control problems in this paper. The aircraft engine multi-loop control s...The aircraft engine multi-loop control system is described and the switching control theory is introduced to solve the regulating and protecting control problems in this paper. The aircraft engine multi-loop control system is firstly described and the control problems are formulated. Secondly, the theory of the smooth switching control is devoted and a new extended scheme for the smooth switching of a switched control system is introduced. Then, for the key technologies of aero-engines switching control, a design algorithm is presented which can determine which candidate controller should be put in feedback with the plant to achieve a desired performance and the procedure to design the aircraft engine multi-loop control system is detailed. The switching performance objectives and the switching scheme are given and a family of PID controllers and compensators is designed. The simulation shows that using the switching control design method can not only improve the dynamic performance of the aircraft engine control system and reduce the switching times, but also guarantee the stability in some peculiar occasions.展开更多
The sliding mode controller of mobile welding robot is established in this paper through applying the method of variable structure control with sliding mode into the control of the mobile welding robot. The traditiona...The sliding mode controller of mobile welding robot is established in this paper through applying the method of variable structure control with sliding mode into the control of the mobile welding robot. The traditional switching function smooth method is improved by combining the smoothed switching function with the time-varying control gain. It is shown that the proposed sliding mode controller is robust to bounded external disturbances. Experimental results demonstrate that sliding mode controller algorithm can be used into seam tracking and the tracking system is stable with bounded uncertain disturbance. In the seam tracking process, the robot moves steadily without any obvious chattering.展开更多
In order to study the bending behavior of aluminum alloy 7050 thick plate during snake hot rolling, several coupled thermo-mechanical finite element(FE) models were established. Effects of different initial thicknesse...In order to study the bending behavior of aluminum alloy 7050 thick plate during snake hot rolling, several coupled thermo-mechanical finite element(FE) models were established. Effects of different initial thicknesses, pass reductions, speed ratios and offset distances on the bending value of the plate were analyzed. ‘Quasi smooth plate' and optimum offset distance were defined and quasi smooth plate could be acquired by adjusting offset distance, and then bending control equation was fitted. The results show that bending value of the plate as well as the extent of the increase grows with the increase of pass reduction and decrease of initial thickness; the bending value firstly increases and then keeps steady with the ascending speed ratio; the bending value can be reduced by enlarging the offset distance. The optimum offset distance varies for different rolling parameters and it is augmented with the increase of pass reduction and speed ratio and the decrease of initial thickness. A proper offset distance for different rolling parameters can be calculated by the bending control equation and this equation can be a guidance to acquire a quasi smooth plate. The FEM results agree well with experimental results.展开更多
Due to the characteristics of intermittent photovoltaic power generation and power fluctuations in distributed photovoltaic power generation,photovoltaic grid-connected systems are usually equipped with energy storage...Due to the characteristics of intermittent photovoltaic power generation and power fluctuations in distributed photovoltaic power generation,photovoltaic grid-connected systems are usually equipped with energy storage units.Most of the structures combined with energy storage are used as the DC side.At the same time,virtual synchronous generators have been widely used in distributed power generation due to their inertial damping and frequency and voltage regulation.For the PV-storage grid-connected system based on virtual synchronous generators,the existing control strategy has unclear function allocation,fluctuations in photovoltaic inverter output power,and high requirements for coordinated control of PV arrays,energy storage units,and photovoltaic inverters,which make the control strategy more complicated.In order to solve the above problems,a control strategy for PV-storage grid-connected system based on a virtual synchronous generator is proposed.In this strategy,the energy storage unit implements maximum power point tracking,and the photovoltaic inverter implements a virtual synchronous generator algorithm,so that the functions implemented by each part of the system are clear,which reduces the requirements for coordinated control.At the same time,the smooth power command is used to suppress the fluctuation of the output power of the photovoltaic inverter.The simulation validates the effectiveness of the proposed method from three aspects:grid-connected operating conditions,frequency-modulated operating conditions,and illumination sudden-drop operating condition.Compared with the existing control strategies,the proposed method simplifies the control strategies and stabilizes the photovoltaic inverter fluctuation in the output power of the inverter.展开更多
The necessary continuity of the second order derivative or curvature of the cam profile has been analyzed. In order to guarantee the smoothness of the cam radius data, a proper method with which it could be possible t...The necessary continuity of the second order derivative or curvature of the cam profile has been analyzed. In order to guarantee the smoothness of the cam radius data, a proper method with which it could be possible to revise directly the first and the second order difference coefficients as well as the slope has been proposed. This method, applicable to different cam mechanisms by using a unified formula of correction, possesses the characteristics of simplicity, intuition and precision. Meanwhile, a cubic spline function for fitting the cam profile has also been described.展开更多
基金National Natural Science Foundation(NNSF)of China under Grant No.51478132Guangzhou City College Scientific Research Project under Grant No.120163017
文摘This study investigates the effectiveness of the non-smooth semi-active control algorithm on suppressing the vibration performance of a building structure subjected to seismic waves. According to the Lyapunov stability theory, it has bene proven that the non-smooth semi-active control algorithm can achieve a finite-time stability of the vibration relative to the isolation layer of a building structure. Through numerical simulation of two buildings with different parameters subjected to the input of a seismic wave, the vibration conditions of passive control, LQR semi-active control and non-smooth semiactive control are compared and analyzed. The simulation results show that the non-smooth semi-active control algorithm has a better robustness and effectiveness in restraining the impact of earthquakes on the structure.
基金Supported by Academic Innovation Project of Beijing(201106149)
文摘A novel non-smooth controller of the second order double integrator system with a bounded disturbance is proposed,which stability is proved and which disturbance rejection capability is analyzed by MATLAB simulation experiments. The novel non-smooth output feedback controller and tracking differentiator are applied to control the azimuth servo systemof the small floating satellite antenna. The MATLAB simulation and hardware in the loop simulation experiments are conducted. The experiment results validate that the non-smooth output feedback controller with stronger surge and sudden disturbance rejection capability can realize the stable azimuth servo control of the small floating antenna to ensure the communication between the target satellite and the antenna with high quality.
基金supported by the National Natural Science Foundation of China(Nos.61273083 and 61374012)
文摘This paper is concerned with a systematic method of smooth switching linear parameter- varying （LPV） controllers design for a morphing aircraft with a variable wing sweep angle. The morphing aircraft is modeled as an LPV system, whose scheduling parameter is the variation rate of the wing sweep angle. By dividing the scheduling parameter set into subsets with overlaps, output feedback controllers which consider smooth switching are designed and the controllers in over- lapped subsets are interpolated from two adjacent subsets. A switching law without constraint on the average dwell time is obtained which makes the conclusion less conservative. Furthermore, a systematic algorithm is developed to improve the efficiency of the controllers design process. The parameter set is divided into the fewest subsets on the premise that the closed-loop system has a desired performance. Simulation results demonstrate the effectiveness of this approach.
基金supported by the National Natural Science Foundation of China under Grant Nos.51675440 and 11620101002National Key Research and Development Program of China under Grant No.2017YFB1102800the Fundamental Research Funds for the Central Universities under Grant No.3102018gxc025
文摘In real machining, the tool paths are composed of a series of short line segments, which constitute groups of sharp corners correspondingly leading to geometry discontinuity in tangent. As a result, high acceleration with high fluctuation usually occurs. If these kinds of tool paths are directly used for machining, the feedrate and quality will be greatly reduced. Thus, generating continuous tool paths is strongly desired. This paper presents a new error-controllable method for generating continuous tool path. Different from the traditional method focusing on fitting the cutter locations, the proposed method realizes globally smoothing the tool path in an error-controllable way. Concretely, it does the smoothing by approaching the newly produced curve to the linear tool path by taking the tolerance requirement as a constraint. That is, the error between the desired tool path and the G01 commands are taken as a boundary condition to ensure the finally smoothed curve being within the given tolerance. Besides, to improve the smoothing ability in case of small corner angle, an improved local smoothing method is also proposed by symmetrically assigning the control points to the two adjacent linear segments with the constrains of tolerance and G3 continuity. Experiments on an open five-axis machine are developed to verify the advantages of the proposed methods.
文摘The fluctuation of active power output of wind farm has many negative impacts on large-scale wind power integration into power grid. In this paper, flywheel energy storage system (FESS) was connected to AC side of the doubly-fed induction generator (DFIG) wind farm to realize smooth control of wind power output. Based on improved wind power prediction algorithm and wind speed-power curve modeling, a new smooth control strategy with the FESS was proposed. The requirement of power system dispatch for wind power prediction and flywheel rotor speed limit were taken into consideration during the process. While smoothing the wind power fluctuation, FESS can track short-term planned output of wind farm. It was demonstrated by quantitative analysis of simulation results that the proposed control strategy can smooth the active power fluctuation of wind farm effectively and thereby improve power quality of the power grid.
基金the support from the UK Engineering and Physical Sciences Research Council (EPSRC) under the program (No. EP/K018345/1)the International Cooperation Program of China (No. 2015DFA70630)
文摘Driven by the ever increasing demand in function integration,more and more next generation high value-added products,such as head-up displays,solar concentrators and intra-ocular-lens,etc.,are designed to possess freeform(i.e.,non-rotational symmetric)surfaces.The toolpath,composed of high density of short linear and circular segments,is generally used in computer numerical control(CNC)systems to machine those products.However,the discontinuity between toolpath segments leads to high-frequency fluctuation of feedrate and acceleration,which will decrease the machining efficiency and product surface finish.Driven by the ever-increasing need for high-speed high-precision machining of those products,many novel toolpath interpolation and smoothing approaches have been proposed in both academia and industry,aiming to alleviate the issues caused by the conventional toolpath representation and interpolation methods.This paper provides a comprehensive review of the state-of-the-art toolpath interpolation and smoothing approaches with systematic classifications.The advantages and disadvantages of these approaches are discussed.Possible future research directions are also offered.
文摘Micro-grid smooth switchover between different operation modes is important for steady operation and reliable power supply of micro-grid. In order to reduce the transient fluctuation of voltage and frequency during switchover, this paper proposed a new switchover method based on controller state following. When transferring to island mode, the control method for inverter of storage device changed from PQ control to V/f control. Before switchover, the output of V/f controller is always following the output of PQ controller. So that the sudden change of output is avoided at the moment of switchover. A micro-grid model with photovoltaic and battery is built on DIgSILENT Power Factory simulation software, to simulate micro-grid switchover from grid-connected mode to island mode. Results show this method can effectively suppress the transient fluctuation of voltage and frequency, and reduce the influence of transient process on power grid. This conclusion has important practical significance on micro-grid smooth switchover from grid-con- nected mode to island mode.
文摘A novel type of control law was adopted to reduce the vertical acceleration of a fast ferry as well as the motion sickness incidence suffered by the passengers onboard by means of a submerged T-foil.Considering the system changing characteristics under high disturbances,a model-free approach was adopted.In addition,an upgraded proportional-derivative(PD)controller with correction terms resulting from a fast-online estimation of the system dynamics was designed.The overall controller,known as intelligent PD(i-PD)controller,was tested,and the obtained results were compared with those of a classic PD controller.The controllers were also tested in a changing environment and at different operating velocities.The results confirmed the effectiveness of the i-PD controller to smooth the motions with low computational cost control schemes.Furthermore,thanks to ability of the i-PD controller to continually update the estimated dynamics of the system,it showed a better reduction in both vertical motions and the seasickness level of the passengers with the needed robustness under external disturbances and system changing parameters.
文摘A model reference adaptive control(MRAC)with smooth switching scheme was proposed for piecewise linear systems,and the method was utilized in turbofan engine control to avoid the discontinuity of control input.In this scheme,each sub-region of the operating envelope had its own MRAC controller,and smooth indicator function based smooth switching scheme was introduced to switch multiple controllers smoothly at the boundary of adjacent sub-regions.The Lyapunov stability analysis indicated that the proposed smooth switching scheme can guarantee the convergence of the closed-loop system during the controllers switching.The tracking error system was converted into a switched system to analyze the global stability of the closed-loop system.The advantage of the method was that the chattering of system output and instability caused by asynchronous switching can be eliminated.The simulation illustrates the effectiveness of the proposed control scheme in comparison with the existing MRAC controller with gain scheduling for turbofan engine.
基金supported by the National Natural Science Foundation of China (Grant No. 61104146/F030203)Innovation Plan of Aero Engine Complex System Safety by the Ministry of Education Chang Jiang Scholars of China (Grant No. IRT0905)
文摘The aircraft engine multi-loop control system is described and the switching control theory is introduced to solve the regulating and protecting control problems in this paper. The aircraft engine multi-loop control system is firstly described and the control problems are formulated. Secondly, the theory of the smooth switching control is devoted and a new extended scheme for the smooth switching of a switched control system is introduced. Then, for the key technologies of aero-engines switching control, a design algorithm is presented which can determine which candidate controller should be put in feedback with the plant to achieve a desired performance and the procedure to design the aircraft engine multi-loop control system is detailed. The switching performance objectives and the switching scheme are given and a family of PID controllers and compensators is designed. The simulation shows that using the switching control design method can not only improve the dynamic performance of the aircraft engine control system and reduce the switching times, but also guarantee the stability in some peculiar occasions.
文摘The sliding mode controller of mobile welding robot is established in this paper through applying the method of variable structure control with sliding mode into the control of the mobile welding robot. The traditional switching function smooth method is improved by combining the smoothed switching function with the time-varying control gain. It is shown that the proposed sliding mode controller is robust to bounded external disturbances. Experimental results demonstrate that sliding mode controller algorithm can be used into seam tracking and the tracking system is stable with bounded uncertain disturbance. In the seam tracking process, the robot moves steadily without any obvious chattering.
基金Projects(2012CB619505,2010CB731703)supported by the National Basic Research Program of ChinaProject(CX2013B065)supported by Hunan Provincial Innovation Foundation for Postgraduate,China+1 种基金Project(51405520)supported by the National Natural Science Foundation of ChinaProject(zzyjkt2013-06B)supported by the State Key Laboratory of High Performance Complex Manufacturing(Central South University),China
文摘In order to study the bending behavior of aluminum alloy 7050 thick plate during snake hot rolling, several coupled thermo-mechanical finite element(FE) models were established. Effects of different initial thicknesses, pass reductions, speed ratios and offset distances on the bending value of the plate were analyzed. ‘Quasi smooth plate' and optimum offset distance were defined and quasi smooth plate could be acquired by adjusting offset distance, and then bending control equation was fitted. The results show that bending value of the plate as well as the extent of the increase grows with the increase of pass reduction and decrease of initial thickness; the bending value firstly increases and then keeps steady with the ascending speed ratio; the bending value can be reduced by enlarging the offset distance. The optimum offset distance varies for different rolling parameters and it is augmented with the increase of pass reduction and speed ratio and the decrease of initial thickness. A proper offset distance for different rolling parameters can be calculated by the bending control equation and this equation can be a guidance to acquire a quasi smooth plate. The FEM results agree well with experimental results.
基金supported by National Natural Science Foundation of China Key program(51937003)。
文摘Due to the characteristics of intermittent photovoltaic power generation and power fluctuations in distributed photovoltaic power generation,photovoltaic grid-connected systems are usually equipped with energy storage units.Most of the structures combined with energy storage are used as the DC side.At the same time,virtual synchronous generators have been widely used in distributed power generation due to their inertial damping and frequency and voltage regulation.For the PV-storage grid-connected system based on virtual synchronous generators,the existing control strategy has unclear function allocation,fluctuations in photovoltaic inverter output power,and high requirements for coordinated control of PV arrays,energy storage units,and photovoltaic inverters,which make the control strategy more complicated.In order to solve the above problems,a control strategy for PV-storage grid-connected system based on a virtual synchronous generator is proposed.In this strategy,the energy storage unit implements maximum power point tracking,and the photovoltaic inverter implements a virtual synchronous generator algorithm,so that the functions implemented by each part of the system are clear,which reduces the requirements for coordinated control.At the same time,the smooth power command is used to suppress the fluctuation of the output power of the photovoltaic inverter.The simulation validates the effectiveness of the proposed method from three aspects:grid-connected operating conditions,frequency-modulated operating conditions,and illumination sudden-drop operating condition.Compared with the existing control strategies,the proposed method simplifies the control strategies and stabilizes the photovoltaic inverter fluctuation in the output power of the inverter.
文摘The necessary continuity of the second order derivative or curvature of the cam profile has been analyzed. In order to guarantee the smoothness of the cam radius data, a proper method with which it could be possible to revise directly the first and the second order difference coefficients as well as the slope has been proposed. This method, applicable to different cam mechanisms by using a unified formula of correction, possesses the characteristics of simplicity, intuition and precision. Meanwhile, a cubic spline function for fitting the cam profile has also been described.
