Model predictive control (MPC) schemes such as MOCCA, DMC, MAC, MPHC, and IMC use discrete step (or impulse) response data rather than a parametric model. They predict the future output trajectory of the process &(k + I], i = 1, . . . , PI, then the controller calculates the required control action {Au(k + I], i = 0, 1, . . . , M -i } so that the difference between the predicted trajectory and user-specified (setpoint) trajectory is minimized. This paper shows how the step (impulse) response model can be put into state space form thus reducing computation time and permitting the use of state space theorems and techniques with any of the above-mentioned MPC schemes. A series of experimental runs on a simple pilot plant shows that a Kalman filter based on the proposed state space model gives better performance that direct use of the step response data for prediction. IntroductionIn this paper, the generic term "model predictive control" (MPC) is used to define the class of control techniques which include: MPHC (model predictive heuristic control) (Richalet et al., 1978); DMC (dynamic matrix control) (Cutler and Ramaker, 1980); MAC (model algorithmic control) (Rouhani and Mehra, 1982); IMC (internal model control) (Garcia and Morari, 1982); and MOCCA (multivariable, optimal, constrained control algorithm) (Sripada and Fisher, 1985). Each of these control schemes differs in detail but includes the following key features as illustrated in Figure 1: 1. The future outputs Y i ( k ) = ( y i ( k + i l k ) , i -0, 1, . . . , P } are predicted using a set of discrete step or impulse response coefficients rather than a typical state space or transfer function model. 2. A "correction term" for each element of the predicted output is usually calculated to account for the difference between the estimated value and the measured plant output. This correction can be calculated using known disturbance response data, by identifying parameters on-line to permit forecasting of future values or by estimation techniques such as a Kalman filter. The model based value, Y ; ( k ) , and the correction term, R ( k ) , are combined to produce the estimated trajectory p ( k ) = { j ( k + i l k ) , i = 1,. . . , P}. 3. A predictive control strategy is used to calculate the control action (Ahu(k + i). i = 0, 1, . . . , M -1; M s P ) which minimizes a user-specified performance index, e.g., which minimizes the square of the difference between the desired trajectory Y,,(k) and predicted trajectory p ( k ) that would result if no further control action were taken. S. Li is on leave from4. The control calculation is usually formulated as an optimization problem: linear or nonlinear; weighted or unweighted; constrained or unconstrained. Depending on the characteristics of the optimization problem, the solution may require anything from simple off-line calculations to on-line, constrained, nonlinear optimization.MPC is popular in industry and academia because it: Uses step response data which is relatively easy to obtain Is multivariable Handles tim...
The adaptive Generalized Predictive Controller (Clarke et al., 1987a, b) is capable of controlling plants with variable dead‐time, unknown model orders and unstable poles and zeros. This paper shows how the GPC control law can be written in an equivalent general linear transfer function form which simplifies closed‐loop (eg. root locus) analysis. Three recommended strategies for selecting the design parameters during the commissioning stage allow the user to adjust the closed‐loop speed of response on‐line using only a single active tuning parameter. Experimental runs confirm the ability of adaptive GPC to provide a consistent closed‐loop response in spite of large process changes.
Most published "interaction measures" can produce misleading results and often do not measure the true closed-loop interaction. Therefore, closed-loop transmittances are defined mathematically as direct, parallel, disturbance, and interaction transfer functions and it is shown that the direct Nyquist array design method includes an excellent basis for interaction analysis. SCOPEMultivariable processes are typically much more difficult to design and operate than single-input /singleoutput processes, due to the interactions that occur between the input /output variables. For example, changing one input variable, ri, on a process system may cause changes in several output variables, yj, and hence make it difficult to maintain product quality. Similarly, the performance of one feedback control loop can be strongly affected by the controller parameters used in other loops on the same multivariable system. Therefore, in the past few years a significant amount of research has been done on the analysis of process interactions.Interaction analysis is strongly affected by the amount of information that is available, i.e., applications and is a topic in many textbooks. Unfortunately, it is easy to show by example that the RGA frequently fails to indicate when a system has significant interaction problems and may even give misleading information about steady state interactions. Also, there is rarely any indication that the RGA has failed until the closed-loop process is simulated or operated. Difficulties such as these led to the development of alternative interaction measures by Rijnsdorp (1965), Bristol (1968, Suchanti and Fournier (1973), Witcher and McAvoy (1977), Tung and Edgar (1977, McAvoy (1979McAvoy ( , 1981McAvoy ( , 1983a, Gagnepain and Seborg (1979), Jaaksoo (1979), and others. This paper includes a critical review of these interaction measures and shows that the various authors have not used a consistent definition of interaction and that the proposed dynamic interaction measures usually do not estimate the actual interaction in the closed-loop system. This paper therefore develops a formal definition of interaction and divides the transmittances between the input/output variables of a process into direct, parallel, and interaction components. Also, since most of the published interaction measures have significant shortcomings, it is recommended that when a dynamic model of the open-loop system is available (point 2 above), the various transmittances and interactions in the closed-loop system be evaluated by examining the process transfer function matrix and l o r the corresponding direct Nyquist array (DNA) plots.Vol. 32, No. 6 959
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