초록 ▼

An apparatus and method is disclosed for solving optimization problems without the need to build mathematical models or rules. The inventive method combines the structure of a single-loop feedback control system and optimization search engine mechanisms. Running in real-time, a Model-Free Adaptive (

An apparatus and method is disclosed for solving optimization problems without the need to build mathematical models or rules. The inventive method combines the structure of a single-loop feedback control system and optimization search engine mechanisms. Running in real-time, a Model-Free Adaptive (MFA) optimizer can automatically search for the optimal operating point for a dynamic system when a parabolic relationship exists between the input and output. The MFA optimizer comprises a user-selected Min/Max setter to define the searching objective, a process acting-mode search engine to determine if the process is running in direct-acting or reverse-acting mode, a maximum search engine and a minimum search engine to find the maximum or minimum. This apparatus and method is useful in fuel-and-air ratio optimization for combustion processes, yield optimization for chemical or biological reactors, and operating efficiency optimization for coal or ore ball mills.

대표청구항 ▼

The invention claimed is: 1. An apparatus for automatically searching for the optimal operating point of a process, comprising: (a) a process having one variable input, a measured process variable which is a function of the output of said process, and a relationship between said input and said outp

The invention claimed is: 1. An apparatus for automatically searching for the optimal operating point of a process, comprising: (a) a process having one variable input, a measured process variable which is a function of the output of said process, and a relationship between said input and said output that includes an optimal operating point at which said process transitions from a direct-acting to a reverse-acting mode or vice versa, said process selected from the group of processes consisting of; (i) a metal production process in which said variable input is the temperature of the metal oven or furnace and said measured process variable is a metallic property; (ii) a coal gasification process in which said variable input is the vapor to coal ratio and said measured process variable is the measurement of trace elements within coal; (iii) an ore mining process in which said variable input is the ore to water ratio and said measured process variable is the ore yield; (iv) a liquid pumping process in which said variable input is the speed of variable frequency drives (VFD) and said measured process variable is the ratio of total power consumption to liquid flow rate: (b) a minimum or maximum setter providing a source of setpoint signals; and (c) an optimizer connected to said setpoint signal source and said process variable, said optimizer being arranged to so vary said input as to cause said process variable to reach said optimal operating point and stay near thereto for optimizing the efficiency of said process, said optimizer including: (i) an acting mode search engine arranged to detect the direct-acting or reverse-acting mode of said process; and (ii) a maximum search engine arranged to detect if said process variable has reached a maximum value, and/or a minimum search engine arranged to detect if the said process variable has reached a minimum value. 2. The apparatus of claim 1, in which said process is controlled by a control output of a single-input-single-output model-free adaptive controller as part of the said optimizer, said control output being applied to the input of said process, said controller including: (a) an error input representative of the difference between said measured process variable and a predetermined setpoint; (b) a model-free adaptive controller producing a control output u(t); (c) the output of said optimizer being in the form description="In-line Formulae" end="lead"Δu(t)=Δu(t), if |Δu(t)|≦OVLdescription="In-line Formulae" end="tail" description="In-line Formulae" end="lead"Δu(t)=SGN(Δu(t))OVL, if |Δu(t)|>OVLdescription="In-line Formulae" end="tail" or an equivalent thereof, in which Δu(t) is an increment or decrement of the optimizer output, SGN(.) denotes the sign function, SGN(Δu(t)) extracts the sign of Δu(t), and OVL>0 is a user-selected output velocity limit. 3. The apparatus of claim 1, in which said process is controlled by the control output of a single-input-single-output proportional-integral controller as part of the said optimizer, said control output being applied to the input of said process, said controller including: (a) an error input e(t) representative of the difference between said measured process variable and a predetermined setpoint; (b) the output of said optimizer being in the form description="In-line Formulae" end="lead"Δu=Kp {(e[2]-e[1])+(Ts /Ti)e[2]},description="In-line Formulae" end="tail" description="In-line Formulae" end="lead"Δu(t)=SGN(Δu(t))OVL, if|Δu(t)|>OVLdescription="In-line Formulae" end="tail" or an equivalent thereof, in which Δu(t) is an increment or decrement of the optimizer output, Ts is the sample interval, Kp is the proportional gain, Ti is the integral time, e[1] and e[2] are the time sampled error signals of e(t), e[2] is the current sample of e(t); SGN(.) denotes the sign function, SGN(Δu(t)) extracts the sign of Δu(t), and OVL>0 is a user-selected controller output velocity limit. 4. The apparatus of claim 1, in which said process is controlled by a controller as part of the said optimizer, which is subject to a user-selected output step limit OSL, the output of said optimizer being in the form description="In-line Formulae" end="lead"Δu(t)=OSL,description="In-line Formulae" end="tail" or an equivalent thereof, in which Δu(t) is an increment or decrement of the optimizer output, and OSL>0 is said user-selected output step limit. 5. A method of searching, through the use of an optimizer, for the optimal operating point of a process having one variable input, a measured process variable which is a function of the output of said process, and a relationship between said input and said output that includes an optimal operating point at which said process transitions from a direct-acting to a reverse-acting mode or vice versa, said process selected from the group of processes consisting of: (i) a metal production process in which said variable input is the temperature of the metal oven or furnace and said measured process variable is a metallic property; (ii) a coal gasification process in which said variable input is the vapor to coal ratio and said measured process variable is the measurement of trace elements within coal; (iii) an ore mining process in which said variable input is the ore to water ratio and said measured process variable is the ore yield; (iv) a liquid pumping process in which said variable input is the speed of variable frequency drives (VFD) and said measured process variable is the ratio of total power consumption to liquid flow rate; (v) a combustion process in which said variable input is the air flow or fuel to air ratio and said measured process variable is the combustion temperature or generated energy; (vi) a chemical reactor process in which said variable input is the ratio of two material inflows to the reactor and said measured process variable is the product outflow or yield; (vii) an ore ball mill process in which said variable input is the ratio of ore to metal balls of the ball mill and said measured process variable is the crushed ore yield; (viii) a wind turbine process in which said variable input is the generator speed of the wind turbine and said measured process variable is the generated power; said method comprising the steps of; (a) providing initialization steps; (b) selecting a search for a maximum or a minimum operating point; (c) running a process acting mode search engine routine to determine if the process is running in a direct-acting mode or reverse-acting mode; (d) determining if the optimizer is searching for a minimum or maximum based on the selected search; (e) running a minimum search engine routine if a minimum search has been selected; (f) running a maximum search engine routine if a maximum search has been selected; and (g) maintaining said operating point for a controllable period of time for optimizing the efficiency of said process. 6. The method of claim 5 in which said process acting mode search engine comprises a direct-acting counter, a reverse-acting counter, a direct-acting flag, and a reverse-acting flag; and the steps of: (a) providing initialization steps including tasks to clear all counters, and set all default flags and parameters; (b) increasing the output of said optimizer by a computed increment; (c) waiting for a user-selected period of time; (d) determining if the measured process variable has increased; (e) if the measured process variable has increased, incrementing said direct-acting counter by 1, clearing said reverse-acting counter, and determining if the count of said direct-acting counter is bigger than a predetermined number; (f) if the measured process variable has decreased, incrementing said reverse-acting counter by 1, clearing said direct-acting counter, and determining if the count of said reverse-acting counter is bigger than a predetermined number; (g) if the count of said direct-acting counter is bigger than a predetermined number, setting said direct-acting flag to ON, and exiting the acting mode search engine routine; (h) if the count of the direct-acting counter is not bigger than a predetermined number, going back to step b); (i) if the count of said reverse-acting counter is bigger than a predetermined number, setting said reverse-acting flag to ON, and exiting said acting mode search engine routine; and (j) if the count of said reverse-acting counter is not bigger than a predetermined number, going back to step b). 7. The method of claim 5 in which the maximum search engine comprises a direct-acting flag, a maximum counter, and a maximum flag; and the steps of: (a) providing initialization steps including tasks to clear all counters, and set all default flags and parameters; (b) determining if said process is direct-acting; (c) increasing the output of said optimizer by a computed increment if said process is direct-acting; (d) decreasing the output of said optimizer by a computed decrement if said process is not direct-acting; (e) waiting for a user-selected period of time; (f) determining if the measured process variable has increased; (g) if the measured process variable has increased, setting said maximum counter to 0 and going back to step b); (h) if the measured process variable has not increased, saving the current maximum value, and incrementing said maximum counter by 1; (i) determining if the count of the maximum counter is bigger than a predetermined number; (j) if the count of the maximum counter is not bigger than a predetermined number, going back to step b); and (k) if the count of the maximum counter is bigger than a predetermined number, setting said maximum flag to ON, saving the current value of optimizer output, and exiting the maximum search engine routine. 8. The method of claim 5 in which the minimum search engine comprises a direct-acting flag, a minimum counter, and a minimum flag; and the steps of: (a) providing initialization steps including tasks to clear all counters, and set all default flags and parameters; (b) determining if said process is direct-acting; (c) increasing the output of said optimizer by a computed increment if said process is direct-acting; (d) decreasing the output of said optimizer by a computed decrement if said process is not direct-acting; (e) waiting for a user-selected period of time; (f) determining if the measured process variable has decreased; (g) if the measured process variable has decreased, setting said minimum counter to 0 and going back to step b); (h) if the measured process variable has not decreased, saving the current minimum value, and incrementing said minimum counter by 1; (i) determining if the count of the minimum counter is bigger than a predetermined number; (j) if the count of the minimum counter is not bigger than a predetermined number, going back to step b); and (k) if the count of the minimum counter is bigger than a predetermined number, setting said minimum flag to ON, saving the current value of optimizer output, and exiting the minimum search engine routine. 9. The method of claim 5, which the said controllable period of time is 0. 10. The method of claims 6, 7, or 8, in which the said user-selected period of time is the process delay time between its input and output. 11. The method of claims 6, 7 or 8, in which the said predetermined number is 2. 12. The apparatus of claim 1, in which the said minimum or maximum setter produces: (a) a setpoint value equivalent to the high limit of the said output, if the optimizer is to search for a maximum; or (b) a setpoint value equivalent to the low limit of the said output, if the optimizer is to search for a minimum. 13. The apparatus of claim 1, in which the signal of the measured process variable is filtered by a filter mechanism to remove noises. 14. The apparatus of claim 1 in which said optimizer is a computer program embodied in a digital medium. 15. One or more processor readable storage devices having processor readable code embodied on said processor readable storage devices, said processor readable code for programming one or more processors to perform a method of searching, through the use of an optimizer, for the optimal operating point of a process having one variable input, a measured process variable which is a function of the output of said process, and a relationship between said input and said output that includes an optimal operating point at which said process transitions from a direct-acting to a reverse-acting mode or vice versa, said process selected from the group of processes consisting of: (i) a metal production process in which said variable input is the temperature of the metal oven or furnace and said measured process variable is a metallic property; (ii) a coal gasification process in which said variable input is the vapor to coal ratio and said measured process variable is the measurement of trace elements within coal; (iii) an ore mining process in which said variable input is the ore to water ratio and said measured process variable is the ore yield; (iv) a liquid pumping process in which said variable input is the speed of variable frequency drives (VFD) and said measured process variable is the ratio of total power consumption to liquid flow rate; (v) a combustion process in which said variable input is the air flow or fuel to air ratio and said measured process variable is the combustion temperature or generated energy; (vi) a chemical reactor process in which said variable input is the ratio of two material inflows to the reactor and said measured process variable is the product outflow or yield; (vii) an ore ball mill process in which said variable input is the ratio of ore to metal balls of the ball mill and said measured process variable is the crushed ore yield; (viii) a wind turbine process in which said variable input is the generator speed of the wind turbine and said measured process variable is the generated power; said method comprising the steps of: (a) providing initialization steps; (b) selecting a search for a maximum or a minimum operating point; (c) running a process acting mode search engine routine to determine if the process is running in a direct-acting mode or reverse-acting mode; (d) determining if the optimizer is searching for a minimum or maximum based on the selected search; (e) running a minimum search engine routine if a minimum search has been selected; (f) running a maximum search engine routine if a maximum search has been selected; and (g) maintaining said operating point for a controllable period of time for optimizing the efficiency of said process. 16. The one or more processor readable storage devices of claim 15 in which said process acting mode search engine comprises a direct-acting counter, a reverse-acting counter, a direct-acting flag, and a reverse-acting flag; and the steps of: (a) providing initialization steps including tasks to clear all counters, and set all default flags and parameters; (b) increasing the output of said optimizer by a computed increment; (c) waiting for a user-selected period of time; (d) determining if the measured process variable has increased; (e) if the measured process variable has increased, incrementing said direct-acting counter by 1, clearing said reverse-acting counter, and determining if the count of said direct-acting counter is bigger than a predetermined number; (f) if the measured process variable has decreased, incrementing said reverse-acting counter by 1, clearing said direct-acting counter, and determining if the count of said reverse-acting counter is bigger than a predetermined number; (g) if the count of said direct-acting counter is bigger than a predetermined number, setting said direct-acting flag to ON, and exiting the acting mode search engine routine; (h) if the count of the direct-acting counter is not bigger than a predetermined number, going back to step (b); (i) if the count of said reverse-acting counter is bigger than a predetermined number, setting said reverse-acting flag to ON, and exiting said acting mode search engine routine; and (j) if the count of said reverse-acting counter is not bigger than a predetermined number, going back to step (b). 17. The one or more processor readable storage devices of claim 15 in which the maximum search engine comprises a direct-acting flag, a maximum counter, and a maximum flag; and the steps of: (a) providing initialization steps including tasks to clear all counters, and set all default flags and parameters; (b) determining if said process is direct-acting; (c) increasing the output of said optimizer by a computed increment if said process is direct-acting; (d) decreasing the output of said optimizer by a computed decrement if said process is not direct-acting; (e) waiting for a user-selected period of time; (f) determining if the measured process variable has increased; (g) if the measured process variable has increased, setting said maximum counter to 0 and going back to step (b); (h) if the measured process variable has not increased, saving the current maximum value, and incrementing said maximum counter by 1; (i) determining if the count of the maximum counter is bigger than a predetermined number; (j) if the count of the maximum counter is not bigger than a predetermined number, going back to step (b); and (k) if the count of the maximum counter is bigger than a predetermined number, setting said maximum flag to ON, saving the current value of optimizer output, and exiting the maximum search engine routine. 18. The one or more processor readable storage devices of claim 15 in which the minimum search engine comprises a direct-acting flag, a minimum counter, and a minimum flag; and the steps of: (a) providing initialization steps including tasks to clear all counters, and set all default flags and parameters; (b) determining if said process is direct-acting; (c) increasing the output of said optimizer by a computed increment if said process is direct-acting; (d) decreasing the output of said optimizer by a computed decrement if said process is not direct-acting; (e) waiting for a user-selected period of time; (f) determining if the measured process variable has decreased; (g) if the measured process variable has decreased, setting said minimum counter to 0 and going back to step (b); (h) if the measured process variable has not decreased, saving the current minimum value, and incrementing said minimum counter by 1; (i) determining if the count of the minimum counter is bigger than a predetermined number; (j) if the count of the minimum counter is not bigger than a predetermined number, going back to step (b); and (k) if the count of the minimum counter is bigger than a predetermined number, setting said minimum flag to ON, saving the current value of optimizer output, and exiting the minimum search engine routine. 19. The one or more processor readable storage devices of claim 15, in which the said controllable period of time is 0. 20. The one or more processor readable storage devices of claims 16, 17, or 18, in which the said user-selected period of time is the process delay time between its input and output. 21. The one or more processor readable storage devices of claims 16, 17 or 18, in which the said predetermined number is 2. 22. An apparatus for automatically searching for the optimal operating point of a combustion process, comprising: (a) a combustion process having one variable input, a measured process variable which is a function of the output of said process, and a relationship between said input and said output that includes an optimal operating point at which said combustion process transitions from a direct-acting to a reverse-acting mode or vice versa; in which said variable input is the air flow or fuel to air ratio and said measured process variable is the combustion temperature or generated energy; (b) a minimum or maximum setter providing a source of setpoint signals; and (c) an optimizer connected to said setpoint signal source and said process variable, said optimizer being arranged to so vary said input as to cause said process variable to reach said optimal operating point and stay near thereto for optimizing the efficiency of said combustion process, said optimizer including: (i) an acting mode search engine arranged to detect the direct-acting or reverse-acting mode of said combustion process; and (ii) a maximum search engine arranged to detect if said process variable has reached a maximum value, and/or a minimum search engine arranged to detect if the said process variable has reached a minimum value. 23. The apparatus of claim 22, in which said combustion process is controlled by a control output of a single-input-single-output model-free adaptive controller as part of the said optimizer, said control output being applied to the input of said combustion process, said controller including; (a) an error input representative of the difference between said measured process variable and a predetermined setpoint; (b) a model-free adaptive controller producing a control output u(t); (c) the output of said optimizer being in the form description="In-line Formulae" end="lead"Δu(t)=Δu(t), if |Δu(t) |≦OVLdescription="In-line Formulae" end="tail" description="In-line Formulae" end="lead"Δu(t)=SGN(Δu(t))OVL, if |Δu(t)|>OVLdescription="In-line Formulae" end="tail" or an equivalent thereof, in which Δu(t) is an increment or decrement of the optimizer output, SGN(.) denotes the sign function, SGN(Δu(t)) extracts the sign of Δu(t), and OVL>0 is a user-selected output velocity limit. 24. The apparatus of claim 22, in which said combustion process is controlled by the control output of a single-input-single-output proportional-integral controller as part of the said optimizer, said control output being applied to the input of said combustion process, said controller including: (a) an error input e(t) representative of the difference between said measured process variable and a predetermined setpoint; (b) the output of said optimizer being in the form description="In-line Formulae" end="lead"Δu=Kp {(e[2]-e[1])+(Ts/ Ti )e[2]},description="In-line Formulae" end="tail" description="In-line Formulae" end="lead"Δu(t)=SGN(Δu(t))OVL, if |Δu(t)|>OVLdescription="In-line Formulae" end="tail" or an equivalent thereof, in which Δu(t) is an increment or decrement of the optimizer output, Ts is the sample interval, Kp is the proportional gain, Ti is the integral time, e[1] and e[2] are the time sampled error signals of e(t), e[2] is the current sample of e(t); SGN(.) denotes the sign function, SGN(Δu(t)) extracts the sign of Δu(t), and OVL>0 is a user-selected controller output velocity limit. 25. The apparatus of claim 22, in which said combustion process is controlled by a controller as part of the said optimizer, which is subject to a user-selected output step limit OSL, the output of said optimizer being in the form description="In-line Formulae" end="lead"Δu(t)=OSL,description="In-line Formulae" end="tail" or an equivalent thereof, in which Δu(t) is an increment or decrement of the optimizer output, and OSL>0 is said user-selected output step limit. 26. An apparatus for automatically searching for the optimal operating point of a chemical reactor process, comprising: (a) a chemical reactor process having one variable input, a measured process variable which is a function of the output of said process, and a relationship between said input and said output that includes an optimal operating point at which said chemical reactor process transitions from a direct-acting to a reverse-acting mode or vice versa; in which said variable input is the ratio of two material inflows to the reactor and said measured process variable is the product outflow or yield; (b) a minimum or maximum setter providing a source of setpoint signals; and (c) an optimizer connected to said setpoint signal source and said process variable, said optimizer being arranged to so vary said input as to cause said process variable to reach said optimal operating point and stay near thereto for optimizing the efficiency of said chemical reactor process, said optimizer including: (i) an acting mode search engine arranged to detect the direct-acting or reverse-acting mode of said chemical reactor process; and (ii) a maximum search engine arranged to detect if said process variable has reached a maximum value, and/or a minimum search engine arranged to detect if the said process variable has reached a minimum value. 27. The apparatus of claim 26, in which said chemical reactor process is controlled by a control output of a single-input-single-output model-free adaptive controller as part of the said optimizer, said control output being applied to the input of said chemical reactor process, said controller including: (a) an error input representative of the difference between said measured process variable and a predetermined setpoint; (b) a model-free adaptive controller producing a control output u(t); (c) the output of said optimizer being in the form description="In-line Formulae" end="lead"Δu(t)=Δu(t), if|Δu(t)≦OVLdescription="In-line Formulae" end="tail" description="In-line Formulae" end="lead"Δu(t)=SGN(Δu(t))OVL, if |Δu(t) >OVLdescription="In-line Formulae" end="tail" or an equivalent thereof, in which Δu(t) is an increment or decrement of the optimizer output, SGN(.) denotes the sign function, SGN(Δu(t)) extracts the sign of Δu(t), and OVL>0 is a user-selected output velocity limit. 28. The apparatus of claim 26, in which said chemical reactor process is controlled by the control output of a single-input-single-output proportional-integral controller as part of the said optimizer, said control output being applied to the input of said chemical reactor process, said controller including: (a) an error input e(t) representative of the difference between said measured process variable and a predetermined setpoint; (b) the output of said optimizer being in the form description="In-line Formulae" end="lead"Δu=Kp{(e[2]-e[1])+(T s /Ti)e[2]},description="In-line Formulae" end="tail" description="In-line Formulae" end="lead"Δu(t)=SGN(Δu(t))OVL, if|Δu(t)|>OVLdescription="In-line Formulae" end="tail" or an equivalent thereof, in which Δu(t) is an increment or decrement of the optimizer output, Ts is the sample interval, Kp is the proportional gain, Ti is the integral time, e[1] and e[2] are the time sampled error signals of e(t), e[2] is the current sample of e(t); SGN(.) denotes the sign function, SGN(Δu(t)) extracts the sign of Δu(t), and OVL>0 is a user-selected controller output velocity limit. 29. The apparatus of claim 26, in which said chemical reactor process is controlled by a controller as part of the said optimizer, which is subject to a user-selected output step limit OSL, the output of said optimizer being in the form description="In-line Formulae" end="lead"Δu(t)=OSL,description="In-line Formulae" end="tail" or an equivalent thereof, in which Δu(t) is an increment or decrement of the optimizer output, and OSL>0 is said user-selected output step limit. 30. An apparatus for automatically searching for the optimal operating point of an ore ball mill process, comprising: (a) an ore ball mill process having one variable input, a measured process variable which is a function of the output of said process, and a relationship between said input and said output that includes an optimal operating point at which said ore ball mill process transitions from a direct-acting to a reverse-acting mode or vice versa; in which said variable input is the ratio of ore to metal balls of the ball mill and said measured process variable is the crushed ore yield; (b) a minimum or maximum setter providing a source of setpoint signals; and (c) an optimizer connected to said setpoint signal source and said process variable, said optimizer being arranged to so vary said input as to cause said process variable to reach said optimal operating point and stay near thereto for optimizing the efficiency of said ore ball mill process, said optimizer including: (i) an acting mode search engine arranged to detect the direct-acting or reverse-acting mode of said ore ball mill process; and (ii) a maximum search engine arranged to detect if said process variable has reached a maximum value, and/or a minimum search engine arranged to detect if the said process variable has reached a minimum value. 31. The apparatus of claim 30, in which said ore ball mill process is controlled by a control output of a single-input-single-output model-free adaptive controller as part of the said optimizer, said control output being applied to the input of said ore ball mill process, said controller including: (a) an error input representative of the difference between said measured process variable and a predetermined setpoint; (b) a model-free adaptive controller producing a control output u(t); (c) the output of said optimizer being in the form description="In-line Formulae" end="lead"Δu(t)=Δu(t), if |Δu(t)|≦OVLdescription="In-line Formulae" end="tail" description="In-line Formulae" end="lead"Δu(t)=SGN(Δu(t))OVL, if |Δu(t)|>OVLdescription="In-line Formulae" end="tail" or an equivalent thereof, in which Δu(t) is an increment or decrement of the optimizer output, SGN(.) denotes the sign function, SGN(Δu(t)) extracts the sign of Δu(t), and OVL>0 is a user-selected output velocity limit. 32. The apparatus of claim 30, in which said ore ball mill process is controlled by the control output of a single-input-single-output proportional-integral controller as part of the said optimizer, said control output being applied to the input of said ore ball mill process, said controller including: (a) an error input e(t) representative of the difference between said measured process variable and a predetermined setpoint; (b) the output of said optimizer being in the form description="In-line Formulae" end="lead"Δu=Kp{(e[2]-e[1])+(T s /Ti)e[2]},description="In-line Formulae" end="tail" description="In-line Formulae" end="lead"Δu(t)=SGN(Δu(t))OVL, if|Δu(t)|>OVLdescription="In-line Formulae" end="tail" or an equivalent thereof, in which Δu(t) is an increment or decrement of the optimizer output, Ts is the sample interval, Kp is the proportional gain, Ti is the integral time, e[1] and e[2] are the time sampled error signals of e(t), e[2]is the current sample of e(t); SGN(.) denotes the sign function, SGN(Δu(t)) extracts the sign of Δu(t), and OVL>0 is a user-selected controller output velocity limit. 33. The apparatus of claim 30, in which said ore ball mill process is controlled by a controller as part of the said optimizer, which is subject to a user-selected output step limit OSL, the output of said optimizer being in the form description="In-line Formulae" end="lead"Δu(t)=OSL,description="In-line Formulae" end="tail" or an equivalent thereof, in which Δu(t) is an increment or decrement of the optimizer output, and OSL>0 is said user-selected output step limit. 34. An apparatus for automatically searching for the optimal operating point of a wind turbine process, comprising: (a) a wind turbine process having one variable input, a measured process variable which is a function of the output of said process, and a relationship between said input and said output that includes an optimal operating point at which said wind turbine process transitions from a direct-acting to a reverse-acting mode or vice versa; in which said variable input is the generator speed of the wind turbine and said measured process variable is the generated power; (b) a minimum or maximum setter providing a source of setpoint signals; and (c) an optimizer connected to said setpoint signal source and said process variable, said optimizer being arranged to so vary said input as to cause said process variable to reach said optimal operating point and stay near thereto for optimizing the efficiency of said wind turbine process, said optimizer including: (i) an acting mode search engine arranged to detect the direct-acting or reverse-acting mode of said wind turbine process; and (ii) a maximum search engine arranged to detect if said process variable has reached a maximum value, and/or a minimum search engine arranged to detect if the said process variable has reached a minimum value. 35. The apparatus of claim 34, in which said wind turbine process is controlled by a control output of a single-input-single-output model-free adaptive controller as part of the said optimizer, said control output being applied to the input of said wind turbine process, said controller including: (a) an error input representative of the difference between said measured process variable and a predetermined setpoint; (b) a model-free adaptive controller producing a control output u(t); (c) the output of said optimizer being in the form description="In-line Formulae" end="lead"Δu(t)=Δu(t), if|Δu(t)|≦OVLdescription="In-line Formulae" end="tail" description="In-line Formulae" end="lead"Δu (t)=SGN(Δu(t))OVL, if|Δu(t)|>OVLdescription="In-line Formulae" end="tail" or an equivalent thereof, in which Δu(t) is an increment or decrement of the optimizer output, SGN(.) denotes the sign function, SGN(Δu(t)) extracts the sign of Δu(t), and OVL>0 is a user-selected output velocity limit. 36. The apparatus of claim 34, in which said wind turbine process is controlled by the control output of a single-input-single-output proportional-integral controller as part of the said optimizer, said control output being applied to the input of said wind turbine process, said controller including: (a) an error input e(t) representative of the difference between said measured process variable and a predetermined setpoint; (b) the output of said optimizer being in the form description="In-line Formulae" end="lead"Δu=Kp{(e[2]e[1])+(T s /Ti)e[2]},description="In-line Formulae" end="tail" description="In-line Formulae" end="lead"Δu(t)=SGN(Δu(t))OVL, if|Δu(t)|>OVLdescription="In-line Formulae" end="tail" or an equivalent thereof, in which Δu(t) is an increment or decrement of the optimizer output, Ts is the sample interval, Kp is the proportional gain, Ti is the integral time, e[1] and e[2] are the time sampled error signals of e(t), e[2] is the current sample of e(t); SGN(.) denotes the sign function, SGN(Δu(t)) extracts the sign of Δu(t), and OVL>0 is a user-selected controller output velocity limit. 37. The apparatus of claim 34, in which said wind turbine process is controlled by a controller as part of the said optimizer, which is subject to a user-selected output step limit OSL, the output of said optimizer being in the form description="In-line Formulae" end="lead"Δu(t)=OSL,description="In-line Formulae" end="tail" or an equivalent thereof, in which Δu(t) is an increment or decrement of the optimizer output, and OSL>0 is said user-selected output step limit. or an equivalent thereof, in which Au(t) is an increment or decrement of the optimizer output, SGN(.) denotes the sign function, SGN(Au(t)) extracts the sign of Au(t), and OVL>0 is a user-selected output velocity limit.