André Desbiens

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.

Extended Kalman Filter for State Estimation and Trajectory Prediction of a Moving Object Detected by an Unmanned Aerial Vehicle

The development of effective target tracking and collision avoidance algorithms is essential to the success of unmanned aerial vehicle (UAV) missions. In a dynamic environment, path planning for UAVs is often based on predicted obstacle and target motion. In this paper, an extended Kalman filter (EKF) is first used to estimate the states of a moving object detected by a UAV from its measured position in space. The optimal object trajectory is then predicted from the estimated object states and using the motion model defined for Kalman filtering. Finally, the quality of the predicted trajectory is evaluated by computing the variance of the prediction error. Simulation results are presented to demonstrate the effectiveness of the proposed approach.

UAV collision avoidance using cooperative predictive control

This article describes the use of predictive control for the decentralized cooperative control of unmanned aerial vehicles in an unfamiliar three-dimensional environment. It is assumed that each vehicle is equipped with an autopilot and a trajectory control unit. The autopilot insures the stability of the vehicle. The setpoints of the autopilot are calculated by the trajectory control unit, thus forming a cascade control structure. The trajectory control unit relies on a predictive control algorithm to calculate the optimal commands (autopilot setpoints) such that the vehicle will reach fixed targets at known positions while avoiding static obstacles that are detected en route. The advantage in using predictive control is that it offers great flexibility in the objective function to optimize while respecting constraints such as command limits, limits on the displacement that a vehicle can carry out, and the constraints that allow obstacle avoidance. The principle proposed in order to avoid static obstacles (that are assumed ellipsoid) is to verify that the predicted vehicle trajectory does not intersect these obstacles. With the objective to increase performance, cooperation between vehicles must also be privileged. Thus, if some vehicles are within the communication range, they can share the position and shape of the obstacles they have detected. Simulations illustrate the method and higlight the benefits of cooperation.

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.

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.

Long-range predictive control of a rougher flotation unit

Abstract This work deals with the long-range predictive control of a flotation circuit simulated using a phenomenological model. As in the generalized predictive control approach, the control strategy is based on a multistep cost function minimization subject to the constraint that, over a certain control horizon, the future control increments are equal to zero. A linear discrete input-output model is used to represent the complex dynamics of the flotation circuit. The control variables are the air feed rate and the collector feedrate to ore feedrate ratio. A robust identification scheme is used for parameter estimation purposes. Simulation results highlight the performance of this long-range predictive control algorithm.

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.

Control of a Hovering Mini Fixed Wing Aerial Vehicle

This paper describes an approach for designing a stabilizing control strategy of a mini fixed wing aerial vehicle in hovering mode. This flight mode gives the ability to navigate inside a constrained environment. An inertial measurement unit is used to measure the attitude. The increased mass due to the on-board sensor poses a greater challenge to developing a functional autonomous vehicle than previous studies that employed o-board sensors for attitude sensing. Linear transfer functions are proposed for attitude with slow transits modeling. The design is achieved with a frequency domain method involving the Nichols chart. The control of a hovering vehicle requires ecient tuning methods capable of insuring robustness to account for model errors. Simulation and flight test results are presented to show the performance obtained with the proposed tuning method.