System and method for controlling ramp imbalances in model predictive controllers
The temporary relaxation of constraints permits the efficient and cost-effective operation of certain process models. Ramp imbalances are controlled using soft-landing constraints. Such soft-landing constraints permit a smooth return to a ramp limit which permits continued operation of a system, such as a petrochemical system that includes several inflows and outflows, as opposed to a forced shut-down of the system. A ramp imbalance may be controlled by determining imbalance ramp rates and imbalance set-point ramp rates and using those constraints to resolve the dynamic control problem of a process model.
1. A method for controlling ramp imbalances in a model predictive controller by allowing temporary relaxation of ramp imbalance constraints when within limits to better control a petrochemical process, comprising:
determining user specified settings comprising minimum/maximum allowed ramp rates (δ in min −δ in max ), time to balance (t bal ), and set-point recovery rate (δ r );
determining a change (Δ) in current ramp imbalance induced by changes in one or more external disturbance affecting one or more ramp variables;
modifying low (y lo,sp ) and high (y hi,sp ) set-point limits in accordance with y lo,sp =y lo,sp +min(t bal Δ,0) and y hi,sp =y hi,sp +max(0,t bal Δ);
determining soft-landing ramp limit time constants (T lo and T hi ) based on ramp limits (y lo and y hi ) and the user-defined minimum/maximum allowed ramp rates in accordance with T lo =max(T min ,(y lo −y)/δ in min ) and T hi =max(T min ,(y hi −y)/δ in max ) where y is a current ramp and T min is a minimum time constant that determines how fast the ramp rate may be driven to zero;
determining soft-land set-point limit time constants (T lo,sp and T hi,sp ) in accordance with T lo,sp =max(T min ,(y lo,sp −y)/δ in min ) and T hi,sp =max(T min ,(y hi,sp −y)/δ in max );
determining imbalance ramp rate constraints (δ min,ss and δ max,ss ) in accordance with δ min,ss =(y lo −y)/max(T lo ,h) and δ max,ss =(y hi −y)/max(T hi ,h) where h is the dynamic control horizon;
determining imbalance set-point ramp rate constraints (δ min,sp,ss and δ max,sp,ss ) in accordance with δ min,sp,ss =(y lo,sp −y)/max(T lo,sp ,h) and δ max,sp,ss =(y hi,sp −y)/max(T hi,sp ,h);
resolving static control process problem by imposing the determined imbalance ramp rate constraints (δ min,ss and δ max,ss ) at a priority higher than the ramp limits (y lo and y hi ) and imposing the determined imbalance set-point ramp rate constraints (δ min,sp,ss and δ max,sp,ss ) at a priority higher than the ramp set point limits (y lo,sp and y hi,sp );
updating constraints for the ramp limits (y lo and y hi ) in accordance with y lo ≤y k +T lo δ k and y k +T hi δ k ≤y hi where k is a prediction time and δ k is a ramp rate at the prediction time;
updating constraints for the set-point limit trajectories in accordance with y lo,sp,k ≤y k +T lo,sp δ k and y k +T hi,sp δ k ≤y hi,sp,k where set-point limit trajectories (y lo,sp,k and y hi,sp,k ) are defined as y lo,sp,k =min(y lo,sp +kδ r ,y sp ) and y hi,sp,k =max(y sp y hi,sp −kδ r );
resolving a dynamic control process problem using said updates; and
controlling the ramp imbalances in the model predictive controller by said ramp imbalance constraints to better control the petrochemical process.
2. A system comprising:
one or more processors for processing information;
a memory communicatively coupled to the one or mom processors; and
one or more modules that comprise instructions stored in the memory, the instructions, when executed by the processor, operable to perform calculations of a static control problem and a dynamic control problem comprising:
determining user specified settings comprising minimum/maximum allowed ramp rates (δ in min −δ in max ), time to balance ramp (t bal ), and set-point recovery rate (δ r );
determining a change (Δ) in a current ramp imbalance induced by changes in one or more external disturbances affecting one or more ramp variables;
modifying low (y lo,sp ) and high (y hi,sp ) set-point limits in accordance with y lo,sp =y lo,sp +min(t bal Δ,0) and y hi,sp =y hi,sp +max(0,t bal Δ);
determining soft-landing ramp limit time constants (T lo and T hi ) based on ramp limits (y lo and y hi ) and the user-defined minimum/maximum allowed ramp rates in accordance with T lo =max(T min ,(y lo −y)/δ in min ) and T hi =max(T min ,(y hi −y)/δ in max ) where y is a current ramp and T min is a minimum time constant that determines how fast the ramp rate may be driven to zero;
determining soft-land set-point limit time constants (T lo,sp and T hi,sp ) in accordance with T lo,sp =max(T min ,(y lo,sp −y)/δ in min ) and T hi,sp =max(T min ,(y hi,sp −y)/δ in max );
determining imbalance ramp rate constraints (δ min,ss and δ max,ss ) in accordance with δ min,ss =(y lo −y)/max(T lo ,h) and δ max,ss =(y hi −y)/max(T hi ,h) where h is the dynamic control horizon;
determining imbalance set-point ramp rate constraints (δ min,sp,ss and δ max,sp,ss ) in accordance with δ min,sp,ss =(y lo,sp −y)/max(T lo,sp ,h) and δ max,sp,ss =(y hi,sp −y)/max(T hi,sp ,h);
resolving static control process problem by imposing the determined imbalance ramp rate constraints (δ min,ss and δ max,ss ) at a priority higher than the ramp limits (y lo and y hi ) and imposing the determined imbalance set-point ramp rate constraints (δ min,sp,ss and δ max,sp,ss ) at a priority higher than the ramp set point limits (y lo,sp and y hi,sp );
updating constraints for the ramp limits (y lo and y hi ) in accordance with y lo ≤y k +T lo δ k and y k +T hi δ k ≤y hi where k is a prediction time and δ k is a ramp rate at the prediction time;
updating constraints for the set-point limit trajectories in accordance with y lo,sp,k ≤y k +T lo,sp δ k and T hi,sp δ k ≤y hi,sp,k where set-point limit trajectories (y lo,sp,k and y hi,sp,k ) are defined as y lo,sp,k =min(y lo,sp +kδ k y sp ) and y hi,sp,k =max(y sp y hi,sp −kδ r );
resolving a dynamic control process problem using said updates; and
controlling the ramp imbalances in the model predictive controller by said ramp imbalance constraints to better control the petrochemical process.