MOCCA is a Multivariate (Optimal Constrained Control Algorithm developed specifically for non-square industrial control applications with practical difficulties such as interactions, time delays, constraints, modelling development, etc. MOCCA consists of an off-line simulation/translation module, for tuning the control parameters, and an on-line module that implements the designed control law.
An alternate means of constructing advanced control strategies is model based control. Here an empirical or phenomenological model of the process is used in conjunction with a user specified control law, or cost function, to calculate the required control action. It is possible to use the model to predict the output value over some specified time (prediction horizon) into the future. The error term to be minimized is an integral function over this time period, and not just a single value as it is with PID control. The control action over some specified time (control horizon) into the future is calculated in such a way as to minimize the error function.
Mechanics Of MOCCA
The MOCCA algorithm combines several features not normally encountered in a single loop PID type of control. These features are: multivariable control, extended horizon control, constrained control and feedforward control. The single input single output equation describing MOCCA is
for i =1 to P and Δu(k+i-j) = 0 for i-j > M. This equation simply states that the prediction into the future is the linear combination of the future control actions that will be taken (first line) and the past control actions (second line). MOCCA uses discrete step response data rather than a parametric model to predict the output trajectory.
The supervisory portion of MOCCA is used to generate the desired trajectory yd. For example it can accept a step set point change from the process operator and generate the signal trajectory yd using a filter that will transform the step into a first order system trajectory. In some situations this feature may be desirable in order to avoid a sudden large change in control actions. Higher level optimization (e.g. optimal set point selection in the economic sense) can also be included. The simplest supervisory system is that the desired trajectory is set to the current set point. This can be satisfactory for a large number of applications.
Application of Mocca at Hemlo Gold Mines Inc.
The amount of fine ore going into the primary ball mill was measured by a weightometer (WT) and controlled by a variable speed conveyor. A ratio controller adjusted the amount of water added to the primary ball mill in order to maintain a desired percent solid concentration. Pump box water addition was used to maintain level in the pump boxes.
For this control problem the manipulated variables were the tonnage set point and the primary mill discharge, primary cyclone feed and secondary cyclone feed pump box water addition rate set points. The measured variables of interest were the particle size and the primary mill discharge, primary cyclone feed and secondary cyclone feed pump box levels. The grinding water tank recycle water flow rate was measured as a feedforward signal.
The first step in implementing MOCCA is to obtain a good step response either directly from the plant or from a model of the plant. This requires that several parameters related to testing be selected appropriately. These parameters are the sampling period, the test duration and the amplitude of the input signal.
The number of input-output data points required to complete the test is determined by the lowest frequency of interest. The test duration should be at least four times the largest time constant i.e. the test duration should be at least as long as the settling time.
For the grinding circuit study the test duration was initially set to 2 hours but was subsequently reduced to hours. This reduction lowered the amount of calculations required in MOCCA and also reduced the number of past data points required in the MOCCA calculations.
The control horizon, M, is the number of future control actions that are calculated to reduce the predicted errors over the prediction horizon P. Increasing the value of M speeds up the response of the system, with possibly some oscillations as M is increased, and may eventually lead to an unstable system. The ratio M/P should be small if the objective is stability and robustness and closer to unity if performance is important.
Input weighting can be used to penalize the control action resulting in smaller changes in an input for a given change in error. For example, tonnage can be weighted so that it is subject to less fluctuations than the water flow rates. When applied to all the inputs it generally produces a more sluggish output response as the weighting is increased.
From these plots (and others not shown) it was concluded that:
- Weight on the primary or secondary cyclone feed pump box water addition had little effect on control as compared to the base case.
- Using a control horizon of 3 produced unstable results. A control horizon of 1 was therefore retained.
- No substantial benefit was obtained from weighting the water flows.
- As expected using a weight of 1 for the particle size did not produce as good a control of the particle size as for a weight of 10.
- A prediction horizon longer than 10 was desirable to avoid excessive control actions and to prevent oscillations.
- No explanation could be provided for the sharp peak in the primary cyclone feed pump box level.
For testing purposes, a step change in the particle size set point from 80 % -200 mesh to 83 % -200 mesh was performed for both the old particle size control (PID control) and MOCCA control.
Both MOCCA and PID control manipulated tonnage. In this test MOCCA reduced the tonnage immediately to a level near the steady state value. In contrast, the PID control waited before reducing the tonnage. It is believed that this was due to the fact that the particle size measurement was on an up swing when the set point change was introduced.
