## QuickStudy Technology

The QuickStudy model is a time series model and the identification algorithm is statistical. It uses conditional probability density functions to identify the coefficients most likely to model the real-time data.

Models can have varying levels of complexity up to 8th order in the statistical sense, i.e. up to 8 process constants for each manipulated or disturbance variable. The model can capture complex dynamics such as inverse response and integrating characteristics without special treatment. This model structure and identification method are not new. However, there are two capabilities of the QuickStudy implementation that distinguish it from other controllers.

First, the model is a delta model, i.e. the algorithm looks at changes in the measurements not the absolute values. This makes the QuickStudy controller insensitive to load changes and drift such as instrument drift, catalyst aging and exchanger fouling.

Second, the model is adaptive in closed loop without step testing. This property reduces implementation effort because models can be created on-line with the existing controls or off-line from existing historical data. No plant testing is required. This property also reduces long term maintenance effort because models can be refreshed while maintaining control. Note that this paragraph contains a very controversial claim. However it has been verified both in laboratory studies and in practice. The inventor of QuickStudy, Dr. Dennis Tobias, used a combination of basic mathematical treatment and practical constraints on algorithm execution to avoid the problem of numerical singularities in closed loop.

The model is used to provide predictions of the process variable based on recent samples. These predictions are used in a quadratic optimal control calculation that minimizes the integral square error over the control horizon.

The mathematical formulation is an infinite horizon so the controller has the property of “nominal stability”. It has also been shown to have practical stability in difficult applications such as jet engine control and exothermic reactor control. The controller output limits are “hard” constraints in the optimization.

Each Predictive Controller Setup (PCS) block contains the complete set of identification, prediction and control calculations. Individual blocks can be used to replace PID blocks or for complex feedforward problems. Decoupling and multivariable control strategies are implemented by cross linking inputs and outputs between the PCS blocks. In such a configuration, each PCS block is equivalent to a non-zero entry in a matrix controller.

The PCS calculations require approximately 20ms on the recommended computer platform. The maximum number of blocks in a single QuickStudy Adaptive Process Controller is 16 which requires 320ms for all calculations. In addition, data transfer requires approximately 500ms for a total of 820ms. Thus the fastest execution period for a PCS block is 1s.

Since APC is a model predictive controller, this is adequate for direct control of most process loops including pressure and flow. In fact the typical PCS configuration bypasses the PID block completely to avoid issues of PID tuning and internal signal filtering. Multiple APC’s can be linked to handle more complex problems.