自动化专业英语(王树青)3.4

3.4.1 Introduction

Model (Based) Predictive Control (MBPC or MPC), is not a specific control strategy but more of a very ample range of control methods developed around certain common ideas. These design methods lead to linear controllers which have practically the same structure and present adequate degrees of freedom. The ideas appearing in greater or lesser degree in all the predictive control family are basically：

.Explicit use of a model to predict the process output at future time instants (horizon).

.Calculation of a control sequence minimizing a certain objective function.

.Receding strategy, so that at each instant the horizon is displaced towards the future, which involves the application of the first control signal of the sequence at each step.

The various MPC algorithms (also called long-range Predictive Control or LRPC) only differ amongst themselves in the model used to represent the process and the noises and the cost function to be minimized. This type of control is of an open nature within which many works have been developed, being widely received by the academic world and by industry. There are many applications of predictive control successfully in use at the present time, not only in the process industry but also applications to the control of a diversity of processes ranging from robot manipulators to clinical anesthesia. Applications in the cement industry, drying towers and in robot arms, are described, whilst developments for distillation columns, PVC plants, steam generators or servos are presented. The good performance of these applications shows the capacity of the MPC to achieve highly efficient control systems able to operate during long periods of time with hardly any intervention。

MPC presents a series of advantages over other methods, amongst which stand out:

·it is particularly attractive to staff with only a limited knowledge of control ,because the concepts are very intuitive and at the same time the tuning is relatively easy

.it can be used to control a great variety of processes, from those with relatively simple dynamics to other more complex ones, including systems with long delay times or of non-minimum phase or unstable ones.

.the multivariable case can easily be dealt with.

.it intrinsically has compensation for dead times.

.it introduces feed forward control in a natural way to compensate for measurable disturbances.

.the resulting controller is an easy to implement linear control law.

.its extension to the treatment of constraints is conceptually simple and these can be included systematically during the design process.

.it is very useful when future references (robotics or batch processes) are known.

.it is a totally open methodology based on certain basic principles which allow for future extensions.

As is logical, however, it also has its drawbacks. One of these is that although the resulting control law is easy to implement and requires little computation, its derivation is more complex than that of the classical PID controllers. If the process dynamic does not change, the derivation of the controller can be done beforehand, but in the adaptive control case all the computation has to be carried out at every sampling time. Although this, with the computing power available today, is not an essential problem one should bear in mind that many industrial process control computers are not at their best as regards their computing power and, above all that most of the

available time at the process computer normally has to be used for purposes other than the control algorithm itself (communications, dialogues with the operators, alarms, recording, etc). Even so the greatest drawback is need for an appropriate model of the process to be available. The design algorithm is based on a prior knowledge of the model and it is independent of it, But it is obvious that the benefits obtained will depend on the discrepancies existing between the real process and the model used.

In practice, MPC has proved to be a reasonable strategy for industrial control, in spite of the original lack of theoretical results at some crucial points such as stability or robustness.

3.4.2 MPC Strategy

The methodology of all the controllers belonging to the MPC family is characterized by the following strategy, represented in Figure 3.4.1.

(1)The future outputs for a determined horizon N1 called the prediction horizon, are predicted at each instant t using the process model. These predicted outputs y(t + k|t) for k=0,…，N-1,N. depend on the known values up to instant t (past inputs and outputs) and on the future control signals u(t + k|t), k=0,…,N-1,Which are those to be sent to the system and to be calculated.

(2) The set of future control signals is calculated by optimizing a determined criterion in order to keep the process as close as possible to the reference trajectory w(t+k) (which can be the set-point itself or a close approximation of it). This criterion usually takes the form of quadratic function of the errors between the predicted output signal and the predicted reference trajectory. The control effort is included in the objective function in most cases. An explicit solution can be obtained if the criterion is quadratic, the model is linear and there are no constraints otherwise an iterative optimization method has to be used. Some assumptions about the structure of the future control law are also made in some cases, such as that it will be constant from a given instant.

(3) The control signal u (t|t) is sent to the process whilst the next control signals calculated are rejected, because at the next sampling instant y(t+1) is already known and step (1) is repeated with this new value and all the sequences are brought up date. Thus the u(t +1|t+1) is calculated (which in principle will be different to the u(t+1|t) because of the new information available) using the receding horizon concept.

In order to implement this strategy, the basic structure shown in Figure 3.4.2 is used. A

model is used to predict the future plant outputs, based on past and current values and on the

proposed optimal future control actions. These actions are calculated by the optimizer taking into account the cost function (where the future tracking error is considered) as well as the constraints.

The process model plays, in consequence, a decisive role in the controller. The chosen model must be capable of capturing the process dynamics so as to precisely predict the future outputs as well as being simple to implement and to understand. As MPC is not a unique technique but a set of different methodologies, there are many勺 pes of models used in various formulations. One of the most popular in industry is the Truncated Impulse Response Model, which is very simple to obtain as it only needs the measurement of the output when the process is excited with an impulse input. It is widely accepted in industrial practice because it is very intuitive and can also be used for multivariable processes, although its main drawbacks are the large number of parameters needed and that only open-loop stable processes can be described this way. Closely related to this kind of model is the Step Response Model, obtained when the input is a step.

The Transfer Function Model is, perhaps, most widespread in the academic community and is used in most control design methods, as it is a representation that requires only a few parameters and is valid for all kind of processes. The State-Space Model is also used in some formulations, as it can easily describe multivariable processes.

The optimizer is another fundamental part of the strategy as it provides the control actions. If the cost function is quadratic, its minimum can be obtained as an explicit function (linear) of past inputs and outputs and the future reference trajectory. In the presence of inequality constraints the solution has to be obtained by more computationally taxing numerical algorithms. The size of the optimization problems depends on the number of variables and on the prediction horizons used and usually turn out to be relatively modest optimization problems which do not require sophisticated computer codes to be solved. However the amount of time needed for the constrained and robust cases can be various orders of magnitude higher than that needed for the unconstrained case and the bandwidth of the process to which constrained MPC can be applied is considerably reduce.

Selected from "Model Predictive Control in the process industry, Camacho, E.F. and C. Bordons, Spring Verlag, 1995"