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Model-Free Adaptive (MFA) Control

Concept and Significance of Model-Free Adaptive Control

A Model-Free Adaptive control system has the following properties or features:

• No precise quantitative knowledge of the process is available;
• No process identification mechanism or identifier is included in the system;
• No controller design for a specific process is needed;
• No complicated manual tuning of controller parameters is required; and
• Stability analysis criteria are available to guarantee the closed-loop system stability.

The essence of MFA control is described with discussions relating to combustion process control on the following five issues:

Process Knowledge Issue

Most advanced control methods are based on a good understanding of the process and its environment. Laplace transfer functions or differential equations are used to represent the process dynamics. In many process control applications, however, the dynamics may be too complex or the physical process is not well understood. Quantitative knowledge of the process is then not available. This is called a “black box” problem.

In many cases, we may have some knowledge of the process but are not sure if the knowledge is accurate or not. In process control including combustion control applications, we often deal with raw materials, wild inflows, changing fuel type and heating values, unpredictable downstream demand changes, and frequent switches of product size, recipe, batch, and loads. These all lead to a common problem: that is, we are not sure if the process knowledge is accurate or not. This is called a “gray box” problem.

If quantitative knowledge of the process is available, we have a “white box” to deal with. It is a relatively simple task to design a controller for the process in this case because we can use well-established control methods and tools.

Although Model-Free Adaptive control can actually deal with black, gray, and white box problems, it is more suitable to deal with the gray box problem. Most industrial processes are gray boxes.

Process Identification Issue

For traditional adaptive control methods, if the quantitative knowledge of the process is not available, an on-line or off-line identifier is required to obtain the process dynamics. This contributes to a number of fundamental problems:

• the headache of off-line training that might be required,
• the tradeoff between the persistent excitation of signals for correct identification and the steady system response for control performance,
• the model convergence and local minimum problems, and
• the system stability issues.

The main reason that identification-based control methods are not well suited to process control is that control and identification are always in conflict. Good control will lead to a steady state where setpoint (SP), controller output (OP), and process variable (PV) will show straight lines on a trend chart. Since any stable system can reach a steady state where process dynamic changes cannot be seen, good identification may require insertion of test signals. This requirement is not easily accepted by plant operators.

MFA control avoids the fundamental problems by not using any identification mechanism in the system. Once an MFA controller is launched, it will take over control immediately. The MFA algorithms used to update the weighting factors are based on a sole objective, which is to minimize the error between SP and PV. That means, when the process is in a steady state where error is close to zero, there is no need to update the MFA weighting factors.

Controller Design Issue

The main reason PID is still popular is that it is a general-purpose controller that does not require controller design procedures. Designing a controller for a specific application requires special expertise. Since most advanced controllers are model-based, they cannot be a general-purpose controller. Thus, they are not widely used in process control, although these methods have been developed for 30 to 40 years.

MFA controllers are general-purpose controllers. A number of MFA controllers have been developed to control a variety of problematic industrial loops. Examples include SISO MFA to replace PID and requires no manual tuning, Nonlinear MFA to control extremely nonlinear processes, Anti-delay MFA to control processes with large time delays; MIMO MFA to control multivariable processes; Feedforward MFA to deal with large measurable disturbances; and Robust MFA to force the process variable to stay within defined bounds.

For an MFA controller user, there are no controller design procedures required. One can simply select the appropriate controller as its name suggests, configure the controller with certain parameters and launch the MFA controller. This is one of the major differences between a Model-Free Adaptive controller and other model-based advanced controllers.

Controller Parameter Tuning Issue

An adaptive controller should not need to be manually tuned. This is also true for MFA controllers. MFA can adapt to new operating conditions due to changes in process dynamics, loads, or disturbances, and there is no manual tuning required. As a user-friendly feature, certain parameters are available to allow the user to quickly adjust the control performance.

System Stability Issue

Control system stability analysis is always an important issue because it determines if the controller will be useful in practice. When the system stability criterion is available, one can use the criterion to decide if the control system can be safely put in operation. As shown in Figure 1, a model-based self-tuning adaptive control system has 3 major components: controller, process, and model. Here, the model refers to a mathematical representation describing the relationship between the process input and output. The model is usually built by an identifier that has a learning algorithm to minimize the model error em(t) (the difference between PV and model output y2(t) ) using the process input and output data.


r(t) – Setpoint
u(t) – Controller Output
y(t) – Process Variable
x(t) – Process Output
d(t) – Disturbances
e(t) – Error
e(t) = r(t) - y(t).
y2(t) – Model Output
em(t) – Model Error
em(t) = y2(t) - y(t).
Figure 1. Model-Based Adaptive Control System

Then, the stability of the overall closed-loop control system is related to the process, the controller, and the model in the following way:

• stability of the process is assumed (i.e., the process is open-loop stable);
• stability of the control loop must be guaranteed by the convergence of the model; but
• convergence of the model is dependent on the stability and persistent excitation of signals originating from the control loop.

This is a circular argument that it is difficult to resolve. Thus, there is no general stability criterion available for a model-based adaptive control system. In other words, each time a model-based adaptive controller is used in a control system, its stability has to be analyzed. This is certainly a major technical barrier in applying model-based adaptive control methods.

In contrast, since MFA does not have an identifier, a general system stability criterion is developed. That is, if the process is passive (a process that does not generate energy or heat by itself), the closed-loop MFA control system stability is guaranteed, and the process can be linear/nonlinear, time invariant/time-varying, etc. A combustion process is a passive process since the heat it generates has to come from burning fuel from outside of the process.

Single-Loop MFA Control System Structure

The system structure of a single-input-single-output (SISO) MFA control system is shown in Figure 2. The structure is as simple as a traditional single-loop control system that includes a SISO process, a SISO MFA controller, and a feedback loop.


r(t) – Setpoint, SP
u(t) – Controller Output, OP
y(t) – Process Variable, PV
x(t) – Process Output
d(t) – Disturbances
e(t) – Error, e(t)=r(t)-y(t).
Figure 2. Single-Loop MFA Control System

Control Objective

The control objective for the controller is to produce an output u(t) to force the process variable y(t) to track the given trajectory of its setpoint r(t) under variations of setpoint, disturbances, and process dynamics. In other words, the task of the MFA controller is to minimize the error e(t) in an online fashion. The minimization of e(t) is achieved by (i) the regulatory control capability of the MFA controller, and (ii) the adjustment of the MFA controller weighting factors that allow the controller to deal with process dynamic changes, disturbances, and other uncertainties.

Compared to Figure 1, the MFA system does not have a process model or identifier. Thus, no model error em(t) needs to be minimized and only the error e(t) between the setpoint (r(t) or SP) and process variable (y(t) or PV) needs to be minimized.

MFA Controller Architecture

Figure 3 illustrates the core architec¬ture of a SISO MFA controller. Used as a key component, a multilayer perceptron neural network consists of one input layer, one hidden layer with N neurons, and one output layer with one neuron.

Within the neural network there is a group of weighting factors (wij and hi) that can be updated as needed to vary the behavior of the controller. The algorithm for updating the weighting factors is based on the goal of minimizing the error e(t). Since this effort is the same as the control objective, the adaptation of the weighting factors can assist the controller in minimizing the error while process dynamics are changing.

Figure 3. Architecture of a SISO MFA controller

Also, the neural network based MFA controller “remembers” a portion of the process data providing valuable information for the process dynamics. In comparison, a digital version of the PID remembers only the current and previous two samples. In this regard, PID has almost no memory, and MFA possesses the memory that is essential to a “smart” controller.

MFA Control System Requirements

As a feedback control system, MFA requires that the process be

• controllable,
• open-loop stable, and
• either direct or reverse acting (process does not change signs).

If the process is not controllable, improvement of the process structure or its variable pairing is required.

If the process is not open-loop stable, it is always a good practice to stabilize it first. However, for certain simple open-loop unstable processes such as a non self-regulating level loop, no special treatment is required when using MFA.

If a process changes its sign within its operating range, special MFA controllers are required. MFA controllers can be easily configured with only a few parameters.

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