A filter based approach for stochastic performance monitoring of feedback control systems

ACKNOWLEDGEMENTS I would like to express my sincere thanks and gratefulness to Dr. Lakshminarayanan Samavedham for supervising my research activities. His consistent encouragement, especially during my unproductive times, coupled with valuable practical ideas motivated me throughout my Masters’ program. Under his friendly guidance, I have gained technical knowledge, self-confidence and maturity, which I feel is an important enhancement for me and keep on guiding me in my future endeavors. Further, I am also thankful to him for providing me an opportunity to be a tutor for PDC (Process Dynamics and Control) course, which was truly a fantastic learning experience for me. In addition to the technical stuff, I enjoyed non-technical discussions with him, filled with humor, in canteen, in cricket field, in departmental corridors and in group parties. I am indebted to him for improving me so much. I am also thankful to all the DACS group members for inspiring me in some way or the other. Kyaw’s passion for programming was inspiring enough to make me learn basics of GUI programming. Prabhat’s technical knowledge always helped me - in fact, ideas generated during this research work are influenced by his thesis work. Madhukar deserves special thanks, for helping me during my initial days in singapore and later for teaching me basics of Matlab. I always wondered how somebody can be so consistent and hardworking - I would like to be as steady as him in my future. I am also thankful to Dharmesh for giving me technical as well as non-technical advices. Ramprasad and May Su were wonderful batch mates - both of them helped me a lot. Finally, I like to thank our new group members Rohit and Balaji for their cooperation. Balaji’s company, during my thesis writing, has given me a tremendous amount of enthusiasm. i Pavan deserves special gratitude as he guided me throughout from the application stage to the joining stage to NUS. I am very much thankful to Murthy, Anand, Ganesh and Ramkrishna for providing me wonderful memories, especially tennis playing and swimming, as my flat mates. I feel lucky to have friends like Murthy and others. I will always relish the friendliness and affection I received from Arul, Mohan, Lalitha, Suresh, Raj, Biswajit, Shanthi, Ravi, Ashwin, Khare, Anju, Atreyyee, Pavan, Naveen, Manish, Manoj, Bhupendra, Vipul, Nirantar, Saurabh, Rahul, Sudhakar, Srinivas, Reddy and many more. I like to express a deep gratitude to my family, especially to my father, my mother and my brother, without their love and efforts I would have never made up to this point. My wife, Ritika, deserved special thanks for her love and support, help in thesis writing and patience during the many hours I spent in front of the computer. Finally, I like to acknowledge National University of Singapore for providing me financial support and excellent facilities during this study. Far better it is to dare mighty things, even though chequered by failure, than to dwell in that perpetual twilight that knows not victory or defeat …………………………………………………………… .……. Theodore Roosevelt ii TABLE OF CONTENTS Acknowledgements i Table of contents iii Summary vi Nomenclature viii List of Figures x List of Tables xi Chapter Introduction Chapter Review of Control Loop Performance Monitoring 2.1 Introduction 2.2 History of Control Loop Performance Monitoring 2.3 Minimum Variance Benchmark 11 2.3.1 Minimum Variance Estimation: SISO Case 11 2.3.2 15 Minimum Variance Estimation: MIMO Case 2.4 Limitations of MVC Benchmark 2.5 Control Loop Performance Monitoring: Present Status and Challenges Chapter Calculation of the PI Achievable Performance 22 23 25 3.1 Introduction 25 3.2 Existing methods for PI achievable performance calculation 26 3.2.1 ASDR technique 26 3.2.2 PI achievable performance calculation from closed loop data 28 3.3 A New filter based method for PI achievable performance calculation 29 iii 3.3.1 Central idea 29 3.3.2 Theoretical development 30 3.4 Case Studies 32 3.5 Conclusions 38 PI Achievable Performance Calculation: Multiloop Case 39 4.1 Introduction 39 4.2 PI achievable performance calculation for multiloop control Chapter systems 40 4.2.1 Multiloop control systems 40 4.2.2 Theoretical development 41 4.3 PI achievable performance calculation with alternate pairing 43 4.3.1 Pairing concerns in multiloop control systems 43 4.3.2 Methodology 46 4.4 PI achievable performance calculation with decouplers 47 4.4.1 Decouplers 47 4.4.2 Methodology 48 4.5 PI achievable performance calculation with a centralized control scheme 50 4.5.1 Centralized control 50 4.5.2 Theory 51 4.6 Case studies 52 4.7 Conclusions 66 Variance Tradeoff Issues in PI Achievable Performance Assessment 67 5.1 Introduction 67 5.2 LQG Benchmark 68 Chapter iv 5.3 PI achievable performance assessment: Variance Tradeoff Curve 69 5.3.1 Theoretical development: SISO case 70 5.3.2 70 Theoretical development: MIMO case 5.4 Case Studies 71 5.5 Conclusions 79 Chapter Conclusions and Recommendations 81 6.1 Conclusions 81 6.2 Recommendations 83 Bibliography 85 Appendix-A 92 Appendix-B 93 Appendix-C 94 v SUMMARY The chemical industry has long recognized process control as a key enabling technology to improve its safety record and ensure its economic viability. In today’s quality conscious market environment, product variability must be kept to as minimum levels as possible in order to generate sustained economic benefits for the shareholders. Chemical process industries rely on instrumentation and control technologies to meet these needs. Consequently, there is a demand for good performance of the control loops in a plant (typically consisting of several thousand control loops) on a continuous basis. Over the past decade, academia and industry have focused on the topic of control loop benchmarking and monitoring. Great strides have been made in the assessment of control loop performance using the minimum variance controller as the benchmark. In a scenario where more than 95% of process controllers belong to the PID family, this yardstick is unrealistic. The performance index of an industrial controller must really be based on the best performance obtainable from this class of controllers (controllers of reduced/restricted complexity). This work deals with the performance assessment and enhancement of regulatory level PI controllers for SISO as well as MIMO (multiloop) control configurations. The benchmark employed is the best performance achievable with PI controllers. For realistic benchmarking of PI control loops, a filter based method is introduced for the calculation of best achievable performance by a PI controller. In this filter based framework, the variance tradeoff between output variance and the variance of the manipulated variable is also considered. The benchmark standard and the vi consideration of variance tradeoffs make this work very relevant for the chemical process industry. Industrial process control systems are configured as multiloop feedback controllers. Therefore, the scope of our work was extended to the domain of multiloop control systems. A methodology that facilitates the calculation of best PI achievable performance and the optimal multiloop PI settings for stochastic disturbance rejection is provided in this thesis. Often, multiloop performance is not acceptable even with the properly tuned controllers due to interactions. To enhance multiloop performance, advanced control strategies are often employed. The most important questions that comes to mind, before any kind of restructuring of control system, is whether the new control strategy will offer significant benefits than the current strategy and if the extent of performance enhancement can be quantified beforehand (i.e. before making the change in the actual system). The filter based approach proposed here has been extended to answer questions such as: (a) performance enhancement possible with the alternate pairing scheme (b) benefits that will accrue through the employment of decouplers and (c) the performance achievable with the use of multivariable controller (as opposed to a multiloop controller). Further, tradeoff curve between output variance and control effort is generated for all the above stated control strategies. The methods proposed here permit a critical analysis of the current system and leads to the selection of the best control strategy for the process. The developed theory is validated with realistic simulation examples. vii NOMENCLATURE at :White noise sequence d :Time delay (SISO); Delay order (MIMO) D :Interactor matrix F :First (d-1) parameters of closed loop impulse response sequence FCOR :Filtering and Correlation analysis G :Closed loop servo process transfer function (matrix for MIMO systems) G* :Decoupled closed loop servo transfer function J :Index of linear quadratic objective function (cost function) LQG :Linear Quadratic Gaussian MIMO :Multiple input multiple output MVC :Minimum variance control N :Open loop disturbance transfer function Q :Controller transfer function (matrix for MIMO systems) Q* :New controller, Optimal controller (matrix for MIMO systems) R :Input weighting matrix SISO :Single input single output T :Open loop process transfer function (matrix for MIMO systems) T* ~ T :Decoupled open loop transfer function ut :Process input for SISO u t* :New input series (corresponding to Q * ) Ut :Process input vector U t* :New input vector (corresponding to Q * ) W :Output weighting matrix yt :Process output for SISO y t* :New output series (corresponding to Q * ) Yt :Process output vector Yt* :New output vector (corresponding to Q * ) :Delay free process transfer function (matrix for MIMO systems) viii ~ Yt :Interactor filtered process output σ a2 :White noise variance σ mv :Minimum variance σ y2 :Variance of process output η ( d ) :Closed loop performance index Σy :Output covariance matrix Σ mv : Output covariance matrix under Minimum variance control ix LIST OF FIGURES Figure 2.1: White noise driven closed loop system 12 Figure 3.1: Experimental data for example 33 Figure 3.2: Results with optimal controller for example 33 Figure 3.3: Experimental data for example 35 Figure 3.4: Results with optimal controller for example 35 Figure 3.5: Experimental data for example 37 Figure 3.6: Results with optimal controller for example 37 Figure 4.1: Stochastic disturbance rejection with various control strategies for example 57 Figure 4.2: Set point tracking with various control strategies for example 59 Figure 4.3: Closed loop experimental data for example 60 Figure 4.4: Stochastic disturbance rejection with various control strategies for example 64 Figure 4.5: Set point tracking with various control strategies for example 65 Figure 5.1: An example of a variance tradeoff curve 68 Figure 5.2: Variance tradeoff curve for example 72 Figure 5.3: Comparison of tradeoff curve obtained from exact G and identified G for example 73 Figure 5.4: Variance tradeoff curve for example 74 Figure 5.5: Comparison of tradeoff curve obtained from exact G and identified G for example 75 Figure 5.6: Variance tradeoff curve for example 76 Figure 5.7: Comparison of tradeoff curve obtained from exact G and identified G for example 77 Figure 5.8: Comparison of tradeoff curve for various control strategies for example 4, obtained with exact G 78 x obtained after trying a lot of initial guesses, but still these solutions may not be the globally optimal solutions. Figure 5.8 provides some important insights when comparing various potential control strategies for the given process. For instance, if control action is constrained, decouplers provide the worst performance. Decouplers can provide better performance with respect to output variance but at the cost of higher control effort. The reason for this is the change in the process i.e. diagonalizing of the original process, which probably needs higher control effort for this example. Further, if the initial performance is seen with reference to the tradeoff curves for diagonal setting, off-diagonal setting and multivariable controller setting, one can observe improper utilization of control effort. The initial control effort is much more than what is required to achieve the maximum performance (lowest variance in output) with a PI controller. To be more precise, we can say that the initial controller is highly ill-tuned. Figure 5.8 also shows that the off-diagonal strategy is the best control strategy, if the control effort variance is restricted to a value close to 1. Although, these predictions are made with the knowledge of exact G , the same theory can be equally productive with properly identified closed loop model. 5.5 Conclusions A new benchmark that provides a solution for the drawbacks of the MVC benchmark has been proposed. The proposed benchmark considers both controller structure limitation and variation in input for assessment of controller’s performance. Further, the proposed method gives a very important insight by comparing the present control action with the control action desired to reach PI achievable performance. As evident 79 from example 3, the analysis based on this method can be very helpful in enhancing the loop performance with the use of proper control effort. The MIMO extension of the proposed method is found to be extremely useful in comparing various control strategies as shown in example 4. With the help of the proposed method, tradeoff curves can be generated for various control strategies. A critical analysis based on the developed method can be done for various control strategies, which in turn helps in making decisions for restructuring control systems. From a practical point of view, this method demands a global optimization tool and a very good process model G. Improvements in system identification techniques and optimization methods will help to meet these requirements. 80 CHAPTER CONCLUSIONS AND RECOMMENDATIONS 6.1 Conclusions A novel filter based method is developed to deal with the various aspects related to single as well as multiloop PI control loop performance monitoring. The goal is to maximize the performance of the control system in regulating stochastic disturbances. This work deals with the two main limitations of the minimum variance benchmark. The minimum variance benchmark doesn’t take into account the limits to control performance imposed by curbs on the controller structure. Secondly, it doesn’t consider the control effort needed to achieve the minimum variance bound. In this study, these limitations of MVC are resolved with the use of the new filter based method. The controller structure limitation is solved earlier by Ko and Edgar (1998) and Agrawal and Lakshminarayanan (2003) with the estimation of PI achievable performance, a MVC based benchmark with controller structure restricted to PI type. Both of the above mentioned works use the process model as well as noise model information for the estimation of PI achievable performance. With the help of the proposed filter based method, the PI achievable performance calculation problem is solved with the knowledge of process model alone. To deal with the second inadequacy, control effort is integrated in the benchmarking exercise by generating a tradeoff curve between output variance and control effort (input variance). Using this 81 tradeoff curve, the possible enhancement in the PI control loop performance with the same control effort can be estimated. The filter based approach has also been extended to the MIMO domain. Along with the estimation of PI achievable performance calculation for multiloop systems, requisite theory is developed for some of the interesting performance monitoring issues related to multiloop control systems such as 1. PI achievable performance estimation with the alternate pairing arrangement. 2. Estimation of the performance enhancement that would result with the use of decouplers. 3. Estimation of improvements in the performance if multivariable PI control is employed. Finally, the tradeoff curve between output variance and control effort are generated for multiloop systems for various control strategies. It includes tradeoff curves for alternate pairing scheme, for decouplers and for a multivariable controller - all these are generated “in silico” without implementing any of them on the real physical process. This method provides a very good comparison of various control strategies, alongwith the probable benefits that would result by implementing them. These tools will be very useful for the control engineer to make decisions about the best regulatory level control strategy for any process. All the above stated work is done with only the knowledge of the closed loop servo model of the process. Initially, the methodology is demonstrated using exact 82 information about the closed loop servo model. Later, identified models obtained from the set point experimentation are used for all the analysis. Understandably, the methods perform less then perfectly as the quality of the model deteriorates – this underscores the need for sound process experimentation, good identification tools and robust optimization strategies. 6.2 Recommendations For Future Work This research work can be viewed as a combination of three streams - control loop performance monitoring, system identification and optimization. Though the theory developed in this work is solely for performance monitoring, its usage for practical industrial problems is highly dependent on system identification and optimization. As evident from the theory developed, process model is an essential requirement for all the analysis. Further, it has been shown in the case studies that we are unable to identify a suitable model, in particular in the examples with integrating noise. Hence the most important recommendation of this thesis is for the advancement in the identification methodologies. This method can serve very well to the needs of the industry, if identification strategies are improved. The second major recommendation is the need for a global optimization tool. As optimization is a vital ingredient, a completely valid analysis can be done if a global optimization tool is available. Hence, the development and use of a global optimization tool is also important for control loop performance monitoring and related decision making tasks. 83 Future research, with reference to control loop performance monitoring, could focus on using the uncertainty associated with the identified models to determine statistical bounds on the CLPI estimates and tradeoff curves. The work done so far in this area (including this work) lacks the statistical aspects one would associate with any data based estimation procedures. So, this may be a good investigation for future researchers to dwell upon. 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As objective function contains term with poles to the power of greater than 10, the poles greater than 1, will be penalized while poles less than zero will not be affected much due to the definition of objective function. 6. This optimization scheme will yield a guess which result in the filter with all the poles of less than one magnitude, which means a stable guess for alternate pairing arrangement without the knowledge of open loop model T . 92 APPENDIX B Algorithm for calculation of Decoupled closed loop model ( G * )Q for initial controller, from the closed loop servo model G . 1. We know G = ( I + TQ )−1TQ , & we want to calculate ( G* )Q = ( I + T * Q )−1T * Q 2. The first step is calculation of ( TQ ) from G , using the following equation TQ = G( I − G )−1 Eqn – B.1 3. Since T * = diagonal( T ) , we can write the following equation T * Q = diagonal ( TQ ) Eqn – B.2 4. Once T * Q is known, ( G * )Q can be calculated as ( G* )Q = ( I + T * Q )−1T * Q Eqn – B.3 5. Hence using closed loop model G , decoupled closed loop model ( G * )Q can be calculated using the above algorithm. 93 APPENDIX C Mranal Jain received his B.Tech degree (May 2002) in Chemical Engineering from the National Institute of Technology, Warangal, India (formerly known as Regional Engineering College, Warangal). In July 2002, he joined the M.Eng Program in the Chemical & Environmental Engineering Department at the National University of Singapore. He wishes to pursue doctoral studies soon & intends to take up research and teaching as his career. 94 [...]... Stanfelj et al (1993) used cross correlation analysis for feed forward plus feedback control systems to diagnose the root cause of a poor performance Later Desborough and Harris (1993), and Vishnubhotla et al (1997) used analysis of variance (ANOVA) for performance assessment of feed forward plus feedback control systems of SISO processes MVC based performance monitoring was extended to multivariable... series analysis to extract the controller invariant part of variance from the routine operating data and used this minimum variance as a benchmark for control loop performance assessment This contribution by Harris was significant as it marked a new direction in this area and initiated considerable academic research and industrial applications especially in the pulp, paper, chemical and petrochemical industries... (1994) recommended use of PI achievable performance as a benchmark Ko and Edgar (1998) developed ASDR technique to determine PI achievable performance calculation using known open loop process model and routine data Later, Agrawal and Lakshminarayanan (2003) proposed a method to obtain PI achievable performance using closed loop experimental data The PI achievable performance benchmark is discussed in... overview of the research in the area of control loop performance monitoring based on MVC can be found in Harris et al (1999), Hoo et al (2003) and Qin (1998) Huang and Shah (1999) provide a through treatment of this area 2.3 Minimum Variance Benchmark The most fundamental limitation to the controller’s performance is delay, which characterizes the control invariant part of output variance This control invariant... performances cannot be achieved simultaneously There are certain advantages and disadvantages associated with both approaches In this study, our focus is on stochastic performance monitoring as we are primarily concerned with the control loops in the regulatory layer Apart from the performance assessment based on the MVC benchmark, few other approaches are also reported in literature Kendra and Cinar (1997)... minimum variance controller Hence, using MVC benchmark for performance monitoring of PI controllers is not only inappropriate but also misleading as it may lead to inaccurate diagnosis of the factors causing low performance For instance, it may happen that a PI controller is performing up to its potential i.e giving maximum performance that can be achieved with a PI controller, 1 A shorter version of this... industrially relevant methodology to estimate this performance index was developed by Agrawal and Lakshminarayanan (2003) The PI achievable performance is covered extensively in chapter 3 All the work discussed above is concerned with the stochastic performance monitoring, as they deal with the assessment of control loop performance under unmeasured, stochastic disturbances Few researchers have also addressed... insufficient for deterministic performance monitoring Also, they initiated a need for benchmark that takes PI structure of controller into consideration, as MVC based variance is not achievable by PI/PID controllers when delay is significant or if the disturbance is non-stationary Later, a more realistic performance measure called the 9 PI achievable performance was introduced by Ko and Edgar (1998) and an industrially... use of frequency domain techniques for performance monitoring Tyler and Morari (1995) developed a performance monitoring method based on likelihood ratios Rengaswamy et al (2001) proposed QSA (qualitative shape analysis) formalism for detecting and diagnosing different kind of oscillations in control loops MVC based benchmark is useful as a first check in performance monitoring For higher level performance. .. by Huang et al (199 7a) They proposed a filtering and correlation (FCOR) algorithm for MIMO performance assessment Harris et al (1996) also extended MVC for MIMO performance assessment based on the estimation of interactor matrix The issue of estimation of time delay from closed loop operating data, which is mandatory for MVC based assessment, was addressed by Lynch and Dumont (1996) Estimation of the . diagnose the root cause of a poor performance. Later Desborough and Harris (1993), and Vishnubhotla et al. (1997) used analysis of variance (ANOVA) for performance assessment of feed forward. based method is introduced for the calculation of best achievable performance by a PI controller. In this filter based framework, the variance tradeoff between output variance and the variance. benchmarks and different controller objectives. At the end of this chapter, a suitable benchmark, PI achievable performance, is identified after comparing advantages and disadvantages of each