Method of controlling an actuator system and aircraft using same
A method of operating an under-actuated actuator system including a plurality of actuators ( 3 ), preferably for operating a multiactuator aerial vehicle ( 1 ), wherein the actuators ( 3 ) are individual propulsion units of the multiactuator aerial vehicle ( 1 ), each actuator having a maximum physical capacity u max , the method including: controlling the actuators ( 3 ) by with an actual control input u∈ k computed from an allocation equation u=D −1 u p , wherein D −1 is an inverse allocation matrix and u p ∈ m is a pseudo control input defined by a system dynamics equation m(x){umlaut over (x)}+c(x,{dot over (x)})+g(x)+G(x)u p =f ext , wherein x∈ n is an n-dimensional configuration vector of the system, m(x)∈ n×n is a state dependent generalized moment of inertia, c(x,{dot over (x)})∈ n are state dependent Coriolis force, g(x)∈ n are gravitational forces and f ext ∈ n are external forces and torques, and G(x)∈ n×m is a control input matrix which contains the information of under-actuation. The system is under-actuated if Rank (G(x))<n or both under-actuated and overly determined in case of k>m>n and Rank (G(x)D)<n, with k,m,n∈ ; using state feedback control to recurrently compute a desired pseudo control input u p from the system dynamics equation. If at least one component of the desired pseudo control input u p is greater than a corresponding maximum pseudo control input u p max that can be generated based on the actuator maximum physical capacity u max and based on positions (or characteristics and configurations) of the actuators within the system, prioritizing at least one of the components of u p over the other components of u p ; and a) by using a prioritizing algorithm, solving the allocation equation for the at least one prioritized component of u p before solving the allocation equation for the remaining components of u p ; or b) during state feedback control, adjusting a limiting value of the at least one prioritized component of u p by an amount, while keeping respective limiting values of the remaining components of u p essentially constant.
1. A method of operating an under-actuated actuator system comprising a plurality of actuators ( 3 ), wherein said actuators ( 3 ) comprise individual propulsion units of a multiactuator aerial vehicle ( 1 ), each one of the actuators having a maximum physical capacity u max , the method comprising:
controlling the actuators ( 3 ) with an actual control input u∈ k computed from an allocation equation
u=D −1 u p ,
wherein D −1 is an inverse allocation matrix and u p ∈ m is a pseudo control input defined by a system dynamics equation
M ( x ) {umlaut over (x)}+c ( x,{dot over (x)} )+ g ( x )+ G ( x ) u p =f ext ,
wherein x∈ n is an n-dimensional configuration vector of the system, M(x)∈ n×n is a state dependent generalized moment of inertia, c(x,{dot over (x)}) E n are state dependent Coriolis forces, g(x)∈ n are gravitational forces,f ext ∈ n are external forces and torques, and G(x)∈ n×n is a control input matrix which contains information of under-actuation, where the system is said to be under-actuated if Rank (G(x))<n or both under-actuated and overly determined in case of k>m>n and Rank (G(x)D)<n, with k,m,n ∈ ;
using a feedback control to recurrently compute a desired pseudo control input u p from said system dynamics equation;
if at least one component of said desired pseudo control input u p is greater than a corresponding maximum pseudo control input u p max that can be generated based on said actuator maximum physical capacity u max and based on positions or configuration of the actuators ( 3 ) within the system, or if the actuator system comes to a control volume limit, u p >u p max , without individual ones of the actuators reaching their own limits u max , such as if all actuators ( 3 ) are close to their respective limits u max , prioritizing at least one of the components of u p over the other of the components of u p ; and
a) by use of a prioritizing algorithm, solving said allocation equation for said at least one prioritized component of u p before solving said allocation equation for the remaining components of u p ; or
b) during state feedback control, adjusting a limiting value of said at least one prioritized component of u p by an amount, while keeping respective limiting values of the remaining components of u p essentially constant.
2. The method of claim 1 , wherein
in case of b), adjusting said limiting value of said at least one prioritized component of u p by an amount comprises reducing said limiting value.
3. The method of claim 1 , wherein
in case of a), at least one of the components of u p is pre-selected, and solving said allocation equation comprises solving said allocation equation for said at least one pre-selected component of u p before solving said allocation equation for the other components of u p .
4. The method of claim 3 , wherein
in case of a plurality of pre-selected ones of the components of u p , solving said allocation equation for said pre-selected components of u p comprises solving said allocation equation for said plurality of pre-selected components of u p at a same time as solving said allocation equation for said other components of u p .
5. The method of claim 4 , wherein
solving said allocation equation at the same time is performed if said at least one component of said desired u p which is greater than said corresponding maximum pseudo control input u p max is a pre-selected component of u p .
6. The method of claim 5 , wherein,
if said at least one component of said desired u p which is greater than said corresponding maximum pseudo control input u p max is not a pre-selected component of u p , at least one physical threshold value is defined and compared to a current value of a corresponding state variable of the system; and wherein an order of solving said allocation equation for the other components of u p is determined based on a result of said comparison.
7. The method of claim 1 , wherein,
u p =[u t τ x τ y τ z ] T ∈ 4 , where u t is a collective thrust, and τ * are body-fixed frame control torques around the body axes, which are *={x,y,z}, τ x being a roll torque, τ y being a pitch torque, and τ z being a yaw torque.
8. The method of claim 7 , wherein
the roll torque τ x and the pitch torque τ y are pre-selected, and solving said allocation equation comprises solving said allocation equation for said at least one pre-selected component of u p before solving said allocation equation for the other components of u p .
9. The method of claim 8 , wherein
the yaw torque τ z and the collective thrust u t are considered as other components of u p .
10. The method of claim 9 , wherein
if said at least one component of said desired u p which is greater than said corresponding maximum pseudo control input u p max is not a pre-selected component of u p , at least one physical threshold value is defined and compared to a current value of a corresponding state variable of the system; and wherein an order of solving said allocation equation for the other components of u p is determined based on a result of said comparison, and the yaw torque τ z is prioritized over collective thrust u t , if a translational velocity v of the multiactuator aerial vehicle ( 1 ) is greater than a first threshold value v t and if an altitude z of the multiactuator aerial vehicle ( 1 ) is greater than a second threshold value z t .
11. The method of claim 10 , wherein
the collective thrust u t is prioritized over the yaw torque T z , if the translational velocity v of the multiactuator aerial vehicle ( 1 ) is less than or equal to a first threshold value v t and if an altitude z of the multiactuator aerial vehicle ( 1 ) is less than or equal to a second threshold value z t .
12. An aircraft ( 1 ), comprising:
a flight control unit ( 2 ) including a feedback control unit ( 2 a ) and an allocation unit ( 2 b ),
an actuator system comprising a plurality of actuators ( 3 ), wherein said actuators ( 3 ) comprise individual propulsion units of the aircraft ( 1 ), said actuators ( 3 ), during operation, are adapted to receive, from the flight control unit ( 2 ), a control input u∈ k , k∈ , said control input u is determined by at least one computer algorithm performed on said flight control unit ( 2 ),
wherein the flight control unit ( 2 ), by at least one of: the feedback control unit ( 2 a ) or the at least one computer algorithm, is adapted to perform the method according to claim 1 ; and
the respective control input u is adapted to be supplied by the flight control unit to said actuators ( 3 ).
13. The aircraft ( 1 ) of claim 12 , further comprising:
at least one of: sensor units ( 4 ), estimation units, or output units in operative connection with said feedback control unit ( 2 a ) for providing sensor data (SD), estimation data, or output data, respectively, representative of a physical and operational state of the aircraft ( 1 ) to said feedback control unit ( 2 a ), and the flight control unit ( 2 ) is configured to determine said desired pseudo control input u p from said sensor data (SD), estimation data or output data, respectively.
14. The aircraft ( 1 ) of claim 13 , further comprising:
the at least one of sensor units ( 4 ), estimation units or output units are in operative connection with said allocation unit ( 2 b ) for providing the sensor data (SD), estimation data or output data, respectively, representative of the physical and operational state of the aircraft ( 1 ) to said allocation unit, wherein the least one flight control unit ( 2 ) is configured to determine said actual control input u from said desired pseudo control input u p and from said sensor data (SD), estimation data or output data, respectively.
15. The aircraft ( 1 ) of claim 14 , wherein
said feedback control unit ( 2 a ) and said allocation unit ( 2 b ) are operatively connected and said feedback control unit ( 2 a ) is adapted to provide said desired pseudo control input u p to said allocation unit ( 2 b ), said allocation unit ( 2 b ) is adapted to solve allocation equation u=D −1 u p and to output control input u to said actuators ( 3 ).