Energy efficient motion control system

• US 8,816,627 B2
• Filed: 11/10/2011
• Issued: 08/26/2014
• Est. Priority Date: 11/10/2011
• Status: Active Grant

• Current Assignee: Mitsubishi Electric Research Laboratories, Inc. (Mitsubishi Electric Corporation)
• Original Assignee: Mitsubishi Electric Corporation, Mitsubishi Electric Research Laboratories, Inc. (Mitsubishi Electric Corporation)
• Inventors: Wang, Yebin, Ueda, Koichiro, Bortoff, Scott A.
• Primary Examiner(s): Ro, Bentsu
• Application Number:
  US13/294,049
• Publication Number:
  US 20130119916A1
• Time in Patent Office: 1,020 Days
• Field of Search: 318/565, 318/671, 318/490, 318/492, 318/558
• US Class Current: 318/565
• CPC Class Codes: B25J 9/1664 characterised by motion, path, trajectory planning
• CPC Class Codes: G05B 13/042 in which a parameter or coefficient is automatically adjusted to optimise the performance
• CPC Class Codes: G05B 2219/39361 Minimize time-energy cost
• CPC Class Codes: G05B 2219/40517 Constraint motion planning, variational dynamic programming
• CPC Class Codes: G05B 2219/41427 Feedforward of position

Abstract

A control signal for controlling an operation of a motion control system suitable for positioning a load is generated using determining a cost function based on a model of energy consumption of the system and a function of a tracking time; and minimizing the cost function subject to constraints to determine a trajectory of the control signal. The control signal is generated based on the trajectory and a current state of the system, wherein the steps of the method are performed by a processor.

Claims

1. A method for generating a control signal for controlling an operation of a motion control system suitable for positioning a load, comprising the steps of:

determining a cost function based on a model of energy consumption of the system and a function of a tracking time, determining the model according to

P(x,u)=Ru²+K_tux₂,

wherein P(x, u) is the energy consumption of the system, x is a state of the motor, u is a control input to the motor, R is a resistance of windings of the motor, x₂ is a second component of the state of the motor x representing an angular velocity of the motor, and K_t is a torque constant of the motor;

minimizing the cost function subject to constraints to determine a trajectory of the control signal; and

generating the control signal based on the trajectory and a current state of the system, wherein the steps of the method are performed by a processor.

2. The method of claim 1, further comprising:

determining the model based on the energy consumption of components of the system.

3. The method of claim 1, further comprising:

determining the model based on at least one of a copper loss at a motor of the system, an iron loss at the motor of the system, a switching loss of an amplifier of the system, and a mechanical work required for positioning the load, or combination thereof.

4. The method of claim 1, further comprising:

determining the model according to

P(x,u)=Ru²+{K_ex₂²u²+K_h|x₂∥

u^γ

|}+K_s|u|+K_tux₂,

wherein P(x, u) is the energy consumption of the system, x is a state of the motor, u is a control input to the motor, R is a resistance of windings of the motor, x₂ is a second component of the state of the motor x representing an angular velocity of the motor, K_e is a constant coefficient of an eddy current of the motor, K_h is a constant coefficient of hysteresis losses in the motor, K_s is a constant coefficient of the switching loss at an amplifier, γ

is the Steinmetz constant, and K_t is a torque constant of the motor.

5. The method of claim 4, further comprising:

determining the model according to

6. The method of claim 5, further comprising:

determining the cost function according to

E=∫

₀^TQ(x(t),u(t))dt

wherein T is the tracking time.

7. The method of claim 5, further comprising:

determining the cost function according to

E=∫

₀^tf(ε

+Q(x(t),u(t)))dt,

wherein t_f is an unspecified tracking time, and ε

is a preference constant.

8. The method of claim 1, wherein the constraints includes one or combination of an acceleration constraint of a motor, a velocity constraint of the motor, an input current constraint of the motor, a dynamic constraint of the motor, the tracking time, an initial state of the motor, and a final state of the motor.

9. The method of claim 1, further comprising:

determining a Hamiltonian based on the cost function and the constraints;

determining a set of conditions minimizing the Hamiltonian; and

determining the trajectory that satisfies the set of conditions.

10. The method of claim 9, further comprising:

formulating a resultant multi-point boundary value problem based on the set of conditions; and

solving the problem to produce the trajectory.

11. The method of claim 9, wherein the minimizing comprises:

defining a Hamiltonian based on the cost function and the constraints, wherein the Hamiltonian includes a first Hamiltonian for a positive control signal and a positive energy consumption, a second Hamiltonian for a negative control signal and the positive energy consumption, and a third Hamiltonian for the negative control signal and the negative energy consumption;

determining a first sot of conditions for a first sub-trajectory, such that the first Hamiltonian is minimized;

determining a second set of conditions for a second sub-trajectory, such that the second Hamiltonian is minimized;

determining a third set of conditions for a third sub-trajectory, such that the third Hamiltonian is minimized; and

determining the set of conditions based on the first, the second, and the third set of conditions.

12. The method of claim 11, further comprising:

determining nonlinear algebraic equations (NAE) satisfying the set of conditions, such that the NAE defines the control signal at a current point of the tracking time;

determining boundary conditions, wherein the boundary conditions include terminal conditions, and entry conditions for each of the first, the second, and the third sub-trajectory;

determining nonlinear ordinary differential equations (ODE) satisfying the boundary conditions, such that the ODE defines a state and a costate of the system at the current point of the tracking time; and

solving the ODE and the NAE alternately over the tracking time until the boundary conditions are satisfied to produce the trajectory.

13. The method of claim 12, wherein the NAE includes linear algebraic equations.

14. The method of claim 1, further comprising:

determining a preliminary trajectory; and

selecting the preliminary trajectory as the trajectory, if a gradient of the cost function with respect to the preliminary trajectory is less than a threshold.

15. The method of claim 14, further comprising:

determining a finite dimensional optimization problem that minimizes the cost function subject to the constraint; and

determining the trajectory by solving the problem.

16. The method of claim 15, further comprising:

performing a discretization of decision variables, the cost function, and the constraints;

approximating an infinite dimensional optimization problem with the finite dimensional optimization problem;

generating a preliminary trajectory;

determining a gradient of the cost function with respect to the preliminary trajectory;

determining the trajectory based on the preliminary trajectory, if the gradient is less than a threshold; and

otherwise;

updating the preliminary trajectory based on the gradient and the constraints; and

repeating the determining the gradient and the determining the trajectory.