MPC Weighting Coefficient Setting for Servo Control With Integrator
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
In model prediction control for servo control, determining optimal weighting coefficients is challenging due to a lack of direct relationship with the time response of the control target, requiring numerous trial-and-errors, and existing methods cannot effectively handle servo control scenarios.
Innovation Solution
A method is introduced to set weighting coefficients for model prediction control by linearizing the prediction model near the terminal end and using ILQ design, incorporating a virtual integrator and Riccati equation to calculate state feedback and integral gains, allowing immediate determination of coefficients based on desired time responses.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If model prediction control is used for servo control, then tracking performance is improved, but determining optimal weighting coefficients becomes difficult requiring numerous trial-and-errors
Solution Approach 1:
The patent transforms the difficult-to-determine weighting coefficients into easily adjustable time response parameters (rise time, settling time, overshoot). By establishing mathematical relationships between these parameters and the weighting coefficients through linearization and ILQ design, users can directly specify desired time response characteristics without trial-and-error tuning of the original weighting coefficients.
Solution Approach 2:
The patent introduces time response parameters as an intermediary between the user's control objectives and the model prediction control weighting coefficients. These intermediate parameters serve as a bridge, translating user-friendly time response specifications into the actual control parameters needed for optimal tracking performance.
2Reliability
If existing weighting coefficient determination methods are used, then some control performance is achieved, but they cannot effectively handle servo control scenarios with integrators
Solution Approach 1:
The patent segments the servo control problem into two parts: the original control target system and an added virtual integrator. By linearizing the prediction model near the terminal end and separately designing the state feedback gain and integral gain through ILQ design, the method creates a unified control approach that handles both the original system dynamics and the integrator behavior, enabling effective servo control with zero steady-state error.
3Manufacturing precision
If weighting coefficients are set through trial-and-error, then optimal tracking may be achieved, but time consumption and operational complexity increase
Solution Approach 1:
The patent performs preliminary design of the weighting coefficients based on desired time response specifications before actual control implementation. By using linearization and ILQ design to pre-calculate the optimal weighting coefficients from time response requirements, the system eliminates the need for time-consuming trial-and-error adjustments during deployment, significantly reducing parameter setting time while maintaining high tracking accuracy.
Data Source
AI summary
A setting method according to the present invention determines a desired time response in an optimum servo control structure corresponding to a servo control structure of a control target, calculates a predetermined gain corresponding to the desired time response, and calculates a first weighting coefficient Qf, a second weighting coefficient Q, and a third weighting coefficient R of a predetermined Riccati equation according to the Riccati equation on the basis of the predetermined gain. The first weighting coefficient Qf, the second weighting coefficient Q, and the third weighting coefficient R are set as a weighting coefficient corresponding to a terminal cost, a weighting coefficient corresponding to a state quantity cost, and a weighting coefficient corresponding to a control input cost, respectively, in a predetermined evaluation function for model prediction control.