Daniel Hodouin

Development and evaluation of an auto-tuning and adaptive PID controller

Abstract This paper describes the design of a practical auto-tuning and adaptive single-input-single-output (SISO) PID controller (AAC). The AAC can control processes with stable and unstable zeros, processes with an integrator, unstable processes and standard aperiodic processes. It uses an explicit identification with a recursive parameter estimation of a second-order with delay model. The regulator tuning methods are based on an approximate minimization of the ITAE criterion by applying pole-zero cancellation, phase margin and maximum peak resonance specifications, with special considerations for delays, unstable zeros and poles. The data filtering, the identification, the tuning mechanism and the supervisory shell are described. Useful guidelines for PI and PID tuning for SISO processes are given. The AAC performances are compared using a benchmark test with commercial adaptive PID controllers: Foxboro 760C, Fisher DPR 910 and Leeds & Northrup Electromax V.

A hierarchical procedure for adjustment and material balancing of mineral processes data

Abstract In order to evaluate and model mineral processes, it is very useful to obtain consistent data in order to satisfy mass conservation. Since collected data are often redundant and erroneous due to natural disturbances, sampling errors, unreliable instrument readouts and laboratory analyses inaccuracies, they must be adjusted. The proposed procedure to minimize the weighted sum of squared residuals consists in a supervisory program working on a set of independent variables necessary to define overall ore flow rates. Within this algorithm, the variables are separated into two sets: the microscopic ones (particle size distributions, chemical assays...) and the macroscopic ones (flow rates, mass fraction of solids in pulp...), each set corresponding to a part of the sum of squares criterion to be minimized. The minimum of the microscopic part of this function can be found directly since the constraints are linear and the function quadratic. The macroscopic part is minimized using the standard Powell algorithm which is also used as supervisory algorithm. The material balance constraints are written using matrix formalism and flow-network description of the circuit. Three industrial application examples are given: a flotation circuit for which ten chemical elements were analyzed, a grinding circuit closed by DSM screens and a three-stages grinding circuit with rod, ball mills and hydrocyclones.

A survey of grinding circuit control methods: from decentralized PID controllers to multivariable predictive controllers

Abstract A conventional grinding circuit consisting of one open-loop rod mill and one closed-loop ball mill is essentially a two-input×two-output system, assuming that the classifier pump box level is controlled by a local loop. The inputs are the ore and water feed rates and the outputs are the product fineness and the circulating load. The design problem is to find a control algorithm and a tuning procedure which satisfy specified servo and regulatory robust performances. A first approach is to use decentralized PID controllers and systematic tuning methods which take into account loop interactions. Another technique consists of adding decouplers or pseudo-decouplers to the decentralized controllers. Finally, the design of a fully multivariable controller is a possible option. To face the problem of performance robustness related to change of process dynamics, two options are studied. A design criterion involving the minimization of a penalized quadratic function on a future trajectory can be used. A second alternative is to track process dynamics changes using adaptive process modelling. The paper will present a comparison of these various strategies, for a simulated grinding circuit. A benchmark test, involving a sequence of disturbances (grindability, feed size distribution, change of cyclone number…) and setpoint changes, is used to compare the performances of the controllers.

Constrained real-time optimization of a grinding circuit using steady-state linear programming supervisory control

This paper presents an application of real-time optimization (RTO) to a simulated ore grinding plant. The control and optimization methods are based on a dynamic linear model of the process. A linear programming (LP) method is used on-line to find the optimum controller set-point as a function of the process-operating constraints. The optimizer selects set-point values that maximize circuit throughput subject to constraints on circulating load, pump box level and hydrocyclone overflow and underflow densities. At the regulatory control level, performances of unconstrained and constrained multivariable predictive controllers are compared and discussed.

Reliability of material balance calculations a sensitivity approach

Abstract Material balance packages are used to estimate unmeasured variables and upgrade the measured ones in mineral processing plants. The reliability of such estimates strongly depends on the data structure. Their variance-covariance matrix is here derived to evaluate the reliability of estimated flowrates, dilutions, particle size distributions and chemical assays. A relationship is shown to relate estimates reliability to the degree of redundancy of data. An illustration is given for a flotation plant.

Adaptive control : state of the art and an application to a grinding process

Abstract Adaptive control is finding its way into real-life situations, mainly as a result of considerable advances in microelectronics and the understanding of adaptive control theory. Several adaptive control algorithms are now available and many industrial applications have been performed in the field of chemical engineering and more recently in the field of particulate processes. This paper gives an overview of discrete adaptive controllers. It presents qualitatively the underlying control design and discusses the recursive least-squares estimation algorithm with requirements for long-term parameter tracking. Particular emphasis is put on the design assumptions and several adaptive control applications in the particulate process field are given. Results concerning the adaptive control of a simulated grinding circuit are detailed.

The estimation of rate and breakage distribution parameters from batch grinding data for a complex pyritic ore using a back-calculation method

Abstract Using the back-calculation approach, simultaneous estimation of rate and breakage distribution parameters has been carried out for a complex pyritic ore from the batch ball mill size distribution data. The ore showed several deviations from the normal grinding behavior: (i) the slope of the Gaudin-Schumann plots in the fine size range varied with the feed size and the grinding time, (ii) the first-order plots showed marked curvature in the initial period of grinding, (iii) the rate parameters did not conform to the relationship S i = Ax α i , even in the fine size range, and (iv) the breakage distribution parameters exhibited a high degree of non-normalizability. The main problem encountered was the choice of a suitable functional form for the breakage distribution function. This paper illustrates the limitations of the two existing functional forms and several other functional forms used in this work, and emphasizes the need for having a more general and practical functional form for the breakage distribution function.

A recursive node imbalance method incorporating a model of flowrate dynamics for on-line material balance of complex flowsheets

A method is proposed to perform on-line material balance of mineral processing circuits using on-stream assays and flowrate measurements. The method, based on a least-squares recursive procedure, is derived from the node imbalance method developed for steady-state mass balance, and incorporates additional equations to represent the dynamic evolution of the flowrates. The method is illustrated for a simulated separation unit and for a simulated flotation circuit.

Simulation of a SX–EW pilot plant

Abstract Solvent extraction followed by electrowinning (SX–EW) is an economical option for the processing of low-grade and oxidized copper ore. Phenomenological models were developed to simulate the copper SX and the EW processes. The two models were linked together to make a SX–EW simulator. The simulator is used to predict the operation of the Mines Gaspe pilot plant put in operation in 1996. Results confirm the potential of the simulation that would subsequently be used for student training, process optimisation and to assess the performance of control strategies.

State of the art in copper hydrometallurgic processes control

Abstract A review of the state of art and trends in automation and control of hydrometallurgic processes is presented. Besides the great expansion of hydrometallurgic processes world-wide, there are a number of unsolved problems related to lack of instrumentation, lack of process knowledge, odd operating practices, and in general, lack of use of data management and processing. In general, process control of local objectives are frequently achieved, however, application of mature and new techniques, successfully adopted in other mineral processing plants, are seldom reported. In the near future it is expected that intelligent techniques will be incorporated to solve a large variety of problems.