Rohit S. Patwardhan

Issues in performance diagnostics of model-based controllers ☆

Abstract The task of diagnosing poorly performing controllers is a challenging one. Process design, controller design, changing process conditions are amongst the common causes of poor performance. In this work, we quantify the effect of factors such as constraints, modelling uncertainty, disturbance uncertainty, process nonlinearity on the achieved closed loop performance. It is important to know the contribution of these factors on the achieved performance in order to attempt diagnosis. The results derived are applicable to the case of deterministic as well as stochastic inputs. Illustrative examples, both SISO and MIMO, are used to demonstrate the key results.

Brief Ripple-free conditions for lifted multirate control systems

Measurements in chemical processes are often unavailable at a uniform rate due to constraints on the sampling rates of process variables. Situations such as these and others give rise to a set of multirate signals comprising a multirate system. Control of multirate systems is appealing and challenging from a theoretical and practical point of view. Multirate control design in the lifting framework consists of lifting the system and subsequently designing a controller for the single-rate lifted system. In this work, it is shown that under certain conditions, intersample ripples arise in the outputs of closed-loop multirate systems. The process output can be guaranteed to be ripple-free if the controller satisfies certain constraints. Further, it is shown that the presence of an integrator in the plant aids in eliminating these intersample ripples. Experimental evaluations are presented in support of these theoretical results.

Performance evaluation of two industrial MPC controllers

This paper presents case studies of the performance evaluation of two industrial multivariate model predictive control (MPC) based controllers at the Mitsubishi chemical complex in Mizushima, Japan: (1) a 6-output, 6-input para-xylene (PX) production process with six measured disturbance variables that are used for feedforward control; and (2) a multivariate MPC controller for a 6-output, 5-input poly-propylene splitter column with two measured disturbances. A generalized predictive controller-based MPC algorithm has been implemented on the PX process. Data from the PX unit before and after the MPC implementation are analyzed to obtain and compare several different measures of multivariate controller performance. The second case study is concerned with performance assessment of a commercial MPC controller on a propylene splitter. A discussion on the diagnosis of poor performance for the second MPC application suggests significant model-plant-mismatch under varying load conditions and highlights the role of constraints.

Issues in multirate process control

Multirate systems are encountered when some signals of interest are sampled at a different rate than others. For example, in the process industry, composition measurements in distillation columns are typically sampled at a slower rate than temperatures and flow rates. In the context of closed-loop control, such multirate systems pose a challenging problem due to several reasons such as increased complexity in the design with tighter performance specifications. Lifting techniques provide a suitable framework for posing a multirate univariate/multivariate problem as a multivariable single-rate problem. We discuss the application of lifting techniques with respect to asymptotic setpoint tracking. Theoretical results are provided to show that there are constraints on the controller gains for step-type reference signals to ensure there are no intersample oscillations in the closed-loop system. Discrete lifting usually introduces non-uniform steady-state gains for the open-loop lifted model which could result in oscillatory continuous output signals for the closed-loop system. These results are supported by simulation results of a slow sampled and fast control system. Further, we provide a continuous-time interpretation to the design of multirate controllers while providing benchmarks for comparing the closed-loop performance of multi-rate and single rate systems in the LQR framework.

Brief The nature of data pre-filters in MPC relevant identification-open- and closed-loop issues

In this paper a model predictive control relevant identification (MRI) method is applied to a general class of linear PEM models and the effect of bias distribution on the multistep ahead predictions is studied. Good multistep ahead predictions are essential for model predictive controllers. Therefore, it is important to distribute the bias in such a way that it is compatible with the predictive control objective. This paper deals with the impact of MRI methods on the bias distribution and its effect on control loop performance.

BIAS DISTRIBUTION IN MPC RELEVANT IDENTIFICATION

Abstract In this paper a M odel Predictive Control R elevant I dentification (MRI) method is applied to a general class of PEM models and the effect of bias distribution on the multi step ahead predictions is studied. Good multi step ahead predictions are essential for model predictive controllers. Therefore it is important to distribute the bias in such a way that it is compatible with the predictive control objective. This paper deals with the analysis of use of MRI methods on the bias distribution and its effect on the control loop performance.

Model-Plant Mismatch Detection in MPC Applications using Partial Correlation Analysis

Abstract In model predictive control of processes, the process model plays an important role. The performance of the controller depends on the quality of the model and hence on the model-plant mismatch. Although model-plant mismatch is inevitable, it is highly desirable to minimize it. For processes with large number of inputs and outputs, re-identification of the model is a costly exercise as keeping a large number of inputs in a perturbed or excited state for a long time means loss of normal production time. Hence, it would be highly desirable to detect the precise location of the mismatch so that only a few inputs would have to be perturbed and only the degraded portion of the model updated. In this work, a methodology is proposed for the detection of mismatch from closed-loop operating data. The proposed methodology is based on the analysis of partial correlations between the model residuals and the manipulated variables. Its efficacy is demonstrated on two simulation case studies as well as its application to data from an industrial process.

Experiment design for MPC relevant identification

The bias and variance properties of identified models depend on various factors including the input spectrum. These properties of an estimated model have to be shaped in such a way that the resulting model is commensurate with the controller. This paper presents a few results on experiment design for Model Predictive Controllers. It is important to minimize multi step ahead predictions, as opposed to one step ahead prediction errors, if Model Predictive Controllers are used. An optimal weighting on the model error for multi step ahead prediction errors is derived. Using this weighting, optimal input spectra are derived for the open loop systems.

A Dynamic PLS Framework for Constrained Model Predictive Control

Abstract This paper demonstrates the constrained predictive control of linear multivariable systems based on models identified using a Dynamic Projection to Latent Structures (Partial Least Squares or PLS) algorithm. Though conventional control of systems using such models have been reported elsewhere (Kaspar and Ray (1992, 1993), Lakshminarayanan et al . (1996)), they are not suited for practical applications owing to their inability to handle constraints. A simple modification of the constraints provides a framework wherein the PLS based models can be incorporated in existing model based predictive control algorithms. The theory is supported using simulation as well as laboratory experiments.

Performance Assessment and Model Validation of Two Industrial MPC Controllers

Abstract This paper presents two case studies on the performance evaluation and model validation of two industrial multivariate model predictive control (MPC) based controllers at Suncor Energy Inc., Fort McMurray, Canada: (1) a 7 controlled variable (CV), 3 manipulated variables (MV) kerosene hydrotreating unit (KHU) with three measured disturbance variables that are used for feedforward control; and (2) an 8 CV, 4 MV naphtha hydrotreating unit (NHU) with 5 measured disturbances. The NHU and KHU controllers are implemented on the product stripping distillation towers. The first case study focuses on potential limits to control performance due to constraints and limits set at the time of controller commissioning. The root causes of sub-optimal performance of KHU are successfully isolated. Data from the NHU unit with MPC on and with MPC off are analyzed to obtain and compare several different measures of multivariate controller performance. Model quality assessment for the two MPCs are performed. A new model index is proposed to have a measure of simulation ability and prediction ability of a model. Open-loop identification of KHU and closed-loop identification of NHU are conducted using the asymptotic method (ASYM).