André Pomerleau

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 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.

Simplified, ideal or inverted decoupling?

Abstract This paper presents a comparative study of simplified, ideal and inverted decoupling. The stability, robustness and implementation of the three decoupling methods are studied. The structured singular value (SSV) is used to carry out some comparisons. It is demonstrated that robust performance and robust stability of a nominally stable control system are equivalent for the three decoupling methods when the controllers are tuned to obtain identical nominal performance. A relation is derived between the presence of right-half plane (RHP) zeros of a process in series with its simplified decoupler and the instability of the ideal and inverted decouplers for the same process. This paper also describes a potential implementation problem related to the particular structure of the inverted decoupling. Finally, a recapitulative table of the main advantages and limitations of each decoupling method is presented.

PI settings for integrating processes based on ultimate cycle information

Presents simple proportional integral (PI) tuning formulas for integrating processes. They are based on the knowledge of the ultimate gain and the ultimate period. This information can be obtained by performing a classical ultimate cycle experiment or by using the relay feedback technique. Refined settings are proposed when the process gain is known. The tuning method is based on a maximum peak resonance specification. The results are compared to those obtained with the Ziegler-Nichols settings. Coherent performances are obtained over a wide range of linear integrating processes.

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.

Improved constrained cascade control for parallel processes

Abstract This paper addresses, first, the problem of constraint handling for a system with one input and multiple outputs, where one output must reach a given set point and the other outputs must lie between lower and an upper limits. Three algebraic solutions based on cascade control are outlined. One method employs the traditional cascade controllers, applied to serial transfer functions. The second uses cascade controllers applied to parallel transfer function processes. The latter method shows sensitivity to disturbance and tuning of inner loops. A third innovative method, called a pseudo-cascade controller, is introduced for parallel transfer functions. The new method allows independent tuning of the controllers, and requires no special anti-reset windup feature. An extension is also given for decoupled two-input processes. A simulated example and a distributed control design for an industrial application are given to illustrate the proposed methods.

Guide lines for the tuning and the evaluation of decentralized and decoupling controllers for processes with recirculation

This paper gives guidelines for the pairing, the time response specification, and the tuning for processes with recirculation when decentralized controllers are used. This selection is based on the condition number, which is an indicator of the process directionality, and on the generalized dynamic relative gain (GDRG), which is a measure of the interaction. Simple tuning rules are developed and results are compared to algebraic controllers with decouplers. Performances are evaluated for set-point changes as well as disturbance rejection using the generalized step response (GSR). The GSR gives a 3D graphic of the system response as a function of the input direction.

Adaptive predictive control of a grinding circuit

Abstract This paper deals with distributed adaptive generalized predictive control of a grinding circuit. This multivariable system is commonly used in mineral industries for size reduction. It is characterized by time varying dynamics owing to changes in ore properties and operating conditions. The fresh ore feed rate, the water addition rate, the circulating load and the product fineness are respectively selected as control and controlled variables. The parameters of two single input-single output discrete models are identified using a least-squares algorithm, taking into account the requirements for long-term adaptive control. Numerical results have been carried out using a simulator based on phenomenological models derived from mass balance considerations. The adaptive controller is compared to a fixed parameter controller. These results illustrate the self-tuning ability and the continuous adaptivity of the control strategy. They also highlight that adaptive control is particulary suitable for distributed control.

A procedure for the design and evaluation of decentralised and model-based predictive multivariable controllers for a pellet cooling process

The cooling zone of an induration furnace is a highly interactive multivariable process with strong nonlinearities and dissimilar dynamics. Linear controllers, implemented on a first-principles process model, are unable to properly control the unit in a wide operating range. This paper proposes a design procedure which considers relevant process characteristics, such as nonlinearity, interaction, directionality, and dynamics, for the synthesis of decentralised extended PIDs and model-based predictive controllers (MPCs). Linear controllers with variable transformations are used since the process model shows that a Hammerstein model can approximate the process nonlinear behaviour. The decentralised PIDs are tuned using efficient rules that take into account the process interaction. The performance of both control strategies is evaluated for set-point tracking, disturbance rejection, and robustness to modelling errors. Similar results are obtained for the gas temperature control, which is the most important process variable. Slightly better results are obtained with the MPC for the gas pressure, the fastest dynamic variable.

Adaptive control—practical aspects and application to a grinding circuit

This paper presents practical aspects and an application of the decentralized partial state reference model adaptive control (DPSRMAC) to a grinding circuit. This control algorithm belongs to the class of long-range predictive controllers. Having in mind the pole placement approach, the quadratic control objective is expressed in terms of input and output tracking errors. The regulation and servo performances can be specified independently. A robust parameter estimation algorithm is used for on-line identification of the single-input/single-output (SISO) models. Simulations have been carried out using a phenomenological model of a grinding circuit. Comparisons are made between the DPSRMAC and decentralized SISO extended PI controllers, showing the efficiency and robustness of the adaptive control algorithm.