Horizon-based control has become an established method for use with difficult industrial process control applications. Moving horizon methods efficiently use process models to effectively control multi-variable systems and process constraints. It has been shown that model predictive control can benefit from the use of state estimation. Various methods using horizon-based estimation show that accurate estimates can be developed for process systems. The work presented in this paper demonstrate the integrated use of horizon-based estimation and control on two complex systems: an experimental four-tank system and a mini-plant simulation system.
There are many advantages in the use of a moving horizon formulation for both disturbance estimation and process control. The methods are very similar, in that at every time step an optimization problem is solved using a finite amount of measurement data and a model of the process. The estimation procedure attempts to solve for the past disturbances that best reconcile the given historical data. The control problem uses the process model to solve for the optimal control moves for the system. Horizon-based formulations allow for the addition of mathematical constraints to the optimization problem. Horizon-based formulations can also readily handle multivariable systems.
The estimation formulation currently used takes advantage of step response models to capture the influence of unmeasured disturbances on the modeled process outputs. Assuming that a limited number of disturbances are present over a single optimization window, propositional logic constraints can be added to the optimization formulation. These constraints include binary decision variable representing the presence or absence of a disturbance. Depending upon the objective function chosen, this results in either a Mixed Integer Linear Program (MILP) or a Mixed Integer Quadratic Program (MIQP). The disturbance estimate can potentially be used to improve controller response. Also, the use of an explicit estimation scheme which detects and isolates disturbances allows for the added potential for supervisory correction of disturbances, if possible.
The proposed architecture requires that the two optimization problems be solved at each sampling time: one to reconcile past disturbance effects on measurements and one to predict optimal control moves for a known future trajectory. In addition to the optimization problems to be solved, a separate application must handle data moving to and from the process in question, whether it is a high fidelity simulated model or an actual physical process. Currently, the most difficult computational problem is the estimation process. The use of a mixed integer formulation results in problems that can be difficult to solve in real-time. By taking advantage of prior solutions, exploiting the formulation structure, and distributing the computational load to multiple machines, the estimation problem can be handled in a timely manner. This allows the use of accurate disturbance estimates when solving the control problem.
Two case studies are considered for application of moving horizon estimation and control. A four-tank experimental laboratory apparatus (similar to the system presented in [11]) is considered. This multivariable system can exhibit a multivariable right-half or left-half plane zero, depending upon the valve settings for a given operating condition. This system is automated by a Bailey DCS system running Freelance using a Dynamic Data Exchange (DDE) interface to connect to MATLAB and SIMULINK. The system has two manipulated variables, two measured variables (both controlled), six unmeasured disturbances, and time constants on the order of 45 seconds. A high fidelity simulation of a CO2 absorption/desorption process is also considered, as modeled by [4]. The simulation and modeling is carried out using Aspen Dynamics and Aspen Custom Modeler with a DDE interface to MATLAB. This system has one manipulated variable, ten measured variables (one controlled), sixteen unmeasured disturbances, and time constants on the order of 800 seconds.