2.15

Model-Free Adaptive (MFA) Control G. S. CHENG

(2005)

Model-free adaptive (MFA) control, as its name suggests, is an adaptive control method that does not require process models. An MFA control system is defined to have the following properties: 1. No precise quantitative knowledge of the process is available. 2. No process identification mechanism or identifier is included in the system. 3. No controller design for a specific process is needed. 4. No manual tuning of controller parameters is required. 5. Closed-loop system stability analysis and criteria are 1–3 available to guarantee the system stability. Derivations of the core MFA control technology address 4–14 specific control problems as described here: • • • • • • • • •

SISO MFA to replace PID so that manual controller tuning is eliminated Nonlinear MFA to control nonlinear processes MFA pH controller to control pH processes Feedforward MFA controller to deal with measurable disturbances Antidelay MFA to control processes with large time delays Robust MFA to protect the process variable from running outside a bound Time-varying MFA controller to control time varying processes Antidelay MFA pH controller for pH processes with varying time delays MIMO MFA to control multivariable processes

MFA controllers can be readily embedded into various control equipment and are becoming available on more and more platforms offered by multi-vendors including building controllers, single-loop controllers, programmable logic controllers (PLC), hybrid controllers, process automation controllers (PAC), control software, and distributed control systems (DCS).

SISO MFA controller, and a feedback loop. The control objective is for the controller 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, disturbance, and process dynamics. In other words, the task of the MFA controller is to minimize the error e(t) in an online fashion, where e(t) is the difference between the setpoint r(t) and the process variable y(t). The minimization of error 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 the dynamic changes, disturbances, and other uncertainties of the control system. MFA Controller Architecture Figure 2.15b illustrates the core architecture of a single-input single-output MFA controller. A multilayer perceptron (MLP) artificial neural network (ANN) is used in the design of the controller. The ANN has 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 dynamic block. The algorithm for updating the weighting factors is based on the goal of minimizing the error between the setpoint and process variable. 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. From another point of view, the artificial 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 controller remembers only the current and previous two samples. In this regard, PID has

d(t) r(t) + –

e(t)

MFA controller

u(t)

SINGLE-LOOP MFA CONTROL SYSTEM Figure 2.15a illustrates a single-loop MFA control system that includes a single-input single-output (SISO) process, a 224 © 2006 by Béla Lipták

FIG. 2.15a Single-loop MFA control system.

SISO process

x(t) + +

y(t)

2.15 Model-Free Adaptive (MFA) Control

wij

E0 = 1 e(t)

225

N(.) E1

Σ

p1

q1

ϕ(.)

hi

Z–1 E2

Σ

p2

q2

ϕ(.)

Z–1 E3

Σ

p3

q3

ϕ(.)

q0 = 1 o(t) Σ

ϕ(.)

ψ(.)

Kc

+

v(t)

+

..... ..... qN

Z–1 EN

Σ

pN

ϕ(.)

FIG. 2.15b Architecture of a SISO MFA controller.

almost no memory, and MFA possesses the memory that is essential to a “smart” controller. SISO MFA Control Algorithm

The weighting factors can be updated online at every sample interval using the following formulas: N

The core MFA control algorithm comprises the following difference equations:

∑ h (n) ,

∆wij (n) = η Kce(n)q j (n)(1 − q j (n)) Ei (n)

2.15(5) ∆h j (n) = η Kc e(n)q j (n).

N

p j (n) =

∑

wij (n) Ei (n) + 1,

2.15(1)

i =1

N

∑ j =1

2.15(2)  h j (n)q j (n) + 1  ,   

N

=

∑ h ( n ) q ( n ) + 1, j

MFA and PID

2.15(3)

j

j =1

v(t ) = Kc [o(t ) + e(t )],

2.15(4)

where n denotes the nth iteration, o(t) is the continuous function of o(n), v(t) is the output of the MFA controller, Kc > 0 and is the MFA controller gain, and wij and hj are weighting factors.

© 2006 by Béla Lipták

2.15(6)

A more detailed MFA control algorithm and discussions can be found in references 1 and 2.

q j (n) = ϕ ( p j (n)),   o(n) = ψ ϕ    

k

k =1

Most industrial processes are still being controlled by PID (proportional–integral-derivative) controllers. PID is a simple general-purpose automatic controller that is useful for controlling simple processes. However, PID has major problems in controlling complex systems and also requires frequent manual tuning of its parameters when the process dynamics change. The performance of MFA (top) and PID (bottom) controllers is compared in Figure 2.15c to show how MFA adapts when process dynamics change. Starting from the same oscillating control condition, the system will continue to oscillate under PID control, while the MFA system will quickly adapt to an excellent control

226

Control Theory

FIG. 2.15c Comparison of MFA and PID.

condition. If both controllers start from a sluggish situation, MFA will control the process faster and better. MFA Control System Requirements As a feedback control system, MFA requires the process to have the following behavior: 1. The process is controllable. 2. The process is open-loop stable. 3. The process is either direct or reverse acting (process does not change its sign). 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 1 its operating range, special MFA controllers are required. SISO MFA Configuration A SISO MFA controller has only a few parameters to configure: 1. Sample interval—the interval between two samples or calculations in seconds. A high-speed MFA controller can run at a 1 millisecond rate.

© 2006 by Béla Lipták

2. Controller gain—use of a default value is recommended. 3. Time constant—a rough estimate of the process time constant in seconds. 4. Acting type—direct or reverse action of the process. If the process input increases and then its output increases, it is direct acting, and vice versa. However, M FA controllers embedded in various platforms always use the vendor’s definition. Sometimes, controller acting type is used, which is different than the process acting type. According to the principles in the information theory, it is required that sample interval be less than or equal to one third of the time constant. That is, Ts ≤

1 T, 3 c

2.15(7)

where Ts is the sample interval, and Tc is the time constant. Once the configuration is done, MFA can be launched at any time and will control the process immediately. MFA does not require process identification and is not a dynamic modelingbased controller; there is no need to first collect data to train the model. MFA controllers can be switched between automatic and manual at any time. No specific bumpless transfer procedure is required.

2.15 Model-Free Adaptive (MFA) Control

227

NONLINEAR MFA CONTROLLER Nonlinear control is one of the most challenging topics in modern control theory. Although linear control system theory has been well developed, it is the nonlinear control problems that present the most headaches. The main reason that a nonlinear process is difficult to control is because there could be so many variations in process nonlinear behavior. Therefore, it is difficult to develop a single controller to deal with the various nonlinear processes. Traditionally, a nonlinear process has to be linearized first before an automatic controller can be effectively applied. This is typically achieved by adding a reverse nonlinear function to compensate for the nonlinear behavior so that the overall process input–output relationship becomes somewhat linear. It is usually a tedious job to match the nonlinear curve, and process uncertainties can easily ruin the effort. The nonlinear MFA controller is a general-purpose controller that provides a more uniform solution to nonlinear control problems. The nonlinear MFA controller is well suited for nonlinear processes or processes with nonlinear sensors, actuators, and other elements. A flow or high-pressure loop is a typical nonlinear process that can cause the actuator to lose its authority in different operating conditions. Inevitable wear and tear on a valve typically makes a linear valve nonlinear. The dissolved oxygen in a bio-tech micro reactor to cultivate cells is another nonlinear process example. As cells grow, they suddenly start to consume much more oxygen. Since the number of bio-tech experiments is huge and the types of cells to grow can vary significantly, it is difficult and costly to deal with nonlinear characterization problems. The general-purpose nonlinear MFA controller is well suited for this application. Nonlinear MFA Configuration In addition to the parameters used in SISO MFA including sample interval, time constant, controller gain, and acting type, the nonlinear MFA has an extra parameter to enter: the process nonlinearity factor. As shown in Figure 2.15d, the graph on the menu shows how severe the nonlinear behavior is between the process input and process output. The process linearity factor is a number between 0 and 10. A 10 represents an extremely nonlinear process while a 0 represents a linear process. Notice that the graph shows a nonlinear curve marked with 10 on both upper and lower positions. This means that a nonlinear M FA controller does not care what the nonlinear characteristics are for this process. For instance, the valve can be either “fast open” or “fast close,” as represented by these two convex and concave curves. When using nonlinear MFA, there is no need to worry about how the nonlinear curve is laid out. The curve can be concave, convex, or S-shaped. Simply advise the controller whether the process is extremely nonlinear (enter a 9 or 10), quite nonlinear (enter a 5 or 6), or somewhat nonlinear (enter

© 2006 by Béla Lipták

FIG. 2.15d Configuration menu of nonlinear MFA.

a 1 or 2). The nonlinear MFA controller will be smart enough to handle the rest. Simulations and real applications show that the nonlinear MFA controller can easily deal with a nonlinear process even if its gain changes hundreds of times. In a nonlinear MFA, there is no linearization calculation or process model. The MFA controller gain Kc is simply set at its nominal point and not retuned.

MFA pH CONTROLLER Most process plants generate a wastewater effluent that must be neutralized prior to discharge or reuse. Consequently, pH control is needed in just about every process plant, yet a large percentage of pH loops perform poorly. The results are inferior product quality, environmental pollution, and material waste. With ever-increasing pressure to improve plant efficiency and tighter regulations in environmental protection, effective continuous pH control is highly desirable. A strong-acid-strong-base pH process is highly nonlinear. The pH value vs. the reagent flow has a logarithmic relationship. Away from its neutrality, the process gain is relatively small. Near the neutrality where pH = 7, its process gain can be a few thousand times higher. There is no way for a fixed controller such as PID to effectively control this process. In practice, most pH loops are in a “bang-bang” type of control, with pumps turning on and off, resulting in large oscillations. Since acid and caustic neutralize each other, over-dosing acid and caustic is like continuously burning money. Statistics show that a poorly controlled pH process can cost tens of thousands of dollars in chemical usage each month, not counting the penalties imposed by violating Environmental Protection Agency (EPA) or local government discharge codes. The MFA pH controller is able to control a wide range of pH loops because its adaptive capability allows it to compensate

228

Control Theory

d(t)

Feedforward MFA

uf (t)

Process Gp2 r(t) + –

e(t)

+ uc(t) MFA controller +

u(t)

Process Gp1

y1(t)

+ y2(t)

y(t)

+

FIG. 2.15f Feedback and feedforward MFA control system.

FIG. 2.15e Configuration menu of MFA pH controller.

for the large nonlinear gain changes. In addition, it can control the full pH range with high precision and enables automatic control of acid or alkaline concentration, both of which are critical quality variables for the chemical process industry.

general-purpose feedforward controller. It does not attempt a perfect cancellation of the disturbances, which is very difficult to implement in industrial applications due to changing process dynamics and operating conditions. A feedback/feedforward MFA control system diagram is illustrated in Figure 2.15f, where Gp1 is the main process and Gp2 is the process with disturbance input and the process variable as output.

MFA pH Controller Configuration

Feedforward MFA Controller Configuration

As shown in Figure 2.15e, one can easily enter Break Points A and B to define the estimated shape of the titration curve of the pH process. Then the MFA controller gain Kc for the flat portion and steep slope can be entered. For a strong-acidstrong-base pH process, if the controller gain for the flat portion is one, then the gain for the steep slope can be estimated as 0.001, which is 1000 times smaller. Due to the adaptive capability of the MFA controller, the titration curve does not have to be accurate and, in fact, its shape can vary in real applications. In addition, the flow rate and the pH value of the inflows may vary significantly. The MFA pH controller can effectively deal with these large disturbances. The MFA pH controller has helped many users effectively control their tough pH loops. Return-on-investment in weeks or even days has been reported with savings on chemical reagents, no violation of discharge code, and smoother production operation.

Since the feedback MFA controller has strong adaptive capabilities, the feedforward MFA can be designed in a simple form. There are two parameters to configure, the feedforward controller gain and time constant. The controller gain can be estimated based on the following formula:

FEEDFORWARD MFA CONTROLLER

The feedforward MFA time constant can be an estimate of the time constant of Gp2. This is related to how fast the disturbance will affect the process variable (PV).

Feedforward is a control scheme to take advantage of disturbance signals. If a process has a significant measurable disturbance, a feedforward controller can be used to reduce its effect before the feedback loop takes corrective action. A good feedforward controller can improve the control system performance economically. Feedforward compensation can be as simple as a ratio between two signals. It could also involve complicated energy or material balance calculations. The feedforward MFA is a

© 2006 by Béla Lipták

K fc = −

K p2 K p1

,

2.15(8)

where Kp1 and Kp2 are the estimated static gain for processes Gp1 and Gp2, respectively. The rules for selecting the sign in order to ensure that the feedforward action rejects the disturbance can be summarized as follows: • •

If processes Gp1 and Gp2 have the same sign, the feedforward gain should be negative. If processes Gp1 and Gp2 have different signs, the feedforward gain should be positive.

ANTIDELAY MFA CONTROLLER Many processes have large time delays due to the delay in the transformation of heat, materials, and signals. No matter what control action is taken, its effect is not measurable during a period of time delay. This is equivalent to disabling

2.15 Model-Free Adaptive (MFA) Control

d(t) r(t)

e(t)

+ –

yc(t)

MFA controller

u(t)

Process x(t) + with large + time delays

y(t)

Delay predictor

FIG. 2.15g Antidelay MFA control system.

the feedback for a period of time, where feedback information is essential to automatic control. If a PID is used to control a process with significant time delays, the controller output will keep growing during the delay time and cause a large overshoot in system responses or even make the system unstable. Typically, a PID has to be detuned significantly in order to stay in automatic but will sacrifice control performance. Generally speaking, a PID controller usually works for the process if its τ-T ratio (delay time/time constant) is smaller than one, unless it is detuned. When a controller is detuned, it loses the sharpness of its control capability, so the process cannot be tightly controlled. The Smith predictor is a useful control scheme to deal with processes with large time delays. However, a precise process model is usually required to construct a Smith predictor. Otherwise, its performance may not be satisfactory. Figure 2.15g shows a block diagram for a SISO antidelay MFA control system with an antidelay MFA controller and a process with large time delays. A special delay predictor is designed to produce a dynamic signal yc(t) to replace the process variable y(t) as the feedback signal. The idea here is to produce an e(t) signal for the controller and let it “feel” its control action without much delay so that it will keep producing proper control signals. In other words, the artificial dynamic signal yc(t) is able to keep the feedback loop working even when there is a large time delay. Since the MFA controller in the system has adaptive capability, the delay predictor can be designed in a simple form without 1,2 knowing the quantitative information of the process. Compared to the traditional Smith predictor, the antidelay MFA controller does not need a precise process model. It only needs an estimated delay time as the basic information for its delay predictor. If the delay time used in the MFA delay predictor has a mismatch with the actual process delay time, the controller is robust enough to deal with the difference. Typically, it can deal with the situation where the delay time is two to five times larger or smaller than the actual delay time with satisfactory control performance. In addition, there is no real limitation on how large the τ-T ratio is, as long as an estimated delay time is provided. The antidelay MFA controller is especially useful in controlling process quality variables since a quality variable is typically measured after the product or process material travels

© 2006 by Béla Lipták

229

to a certain point, cools off, forms its shape, etc. Antidelay MFA makes it possible for process industries to achieve six sigma or zero defects quality control objectives. In a semicontinuous production environment, the process line speed may change as many as 100 times or more, which will cause the delay time to change on a similar scale. Since the line speed is measurable, the delay time can be easily calculated and provided to the antidelay MFA controller in real time. In this way, the control performance will not sacrifice much even during large line speed changes. On the other hand, if the delay time of a process changes on a scale of more than five times, and the delay time information cannot be provided to the controller, the time-varying MFA controller will be more suitable for this application. ROBUST MFA CONTROLLER In complex control applications, the following challenges may occur: 1. A large change in the system dynamics occurs, so that a prompt control action is required to meet the control performance criteria. 2. The dominant disturbance to the system cannot be economically measured, and therefore feedforward compensation cannot be easily implemented. 3. A controller purposely detuned to minimize the variations in its manipulated variable may lose control when a large disturbance or significant dynamic behavior change occurs. 4. The system dynamic behavior or load change does not provide triggering information to allow the control system to switch operating modes. For instance, controlling the reaction temperature for a batch reactor is always a challenge due to the complex nature of the process, large potential disturbances, interactions between key variables, and multiple operating conditions. A large percentage of batch reactors running today cannot keep the reactor temperature in automatic control throughout the entire operating period, thus resulting in lower efficiency, wasted manpower and materials, and inconsistent product quality. An exothermal batch reactor process typically has four operating stages: 1. Startup stage: ramps up the reactor temperature by use of steam to a predefined reaction temperature. 2. Reaction and holding stage: holds the temperature by use of cooling water while chemical reaction is taking place and heat is being generated. 3. No-reaction and holding stage: holds the temperature by use of steam after the main chemical reaction is complete and heat is not being generated. 4. Ending stage: ramps down the reactor temperature for discharging the products.

230

Control Theory

During the transition period from Stage 2 to Stage 3, the reactor can change its nature rapidly from a heat-generation process to a heat-consumption process. This change happens without any triggering signal because the chemical reaction can end at any time depending on the types of chemicals, their concentration, the catalyst, and the reaction temperature. Within a very short period of time, the reactor temperature can drop significantly. The control system must react quickly to cut off the cooling water and send in a proper amount of steam to drive the reactor temperature back to normal. A regular feedback controller is not able to automatically control a batch reactor during this transition. In practice, batch reactors are usually switched to manual control and rely on well-trained operators during critical transitions. It is a tedious and nerve-wracking job that can result in low product quality and yield. The robust MFA controller is able to control the problematic processes described. Without the need to redesign a controller, using feedforward compensation, or retune the controller parameters, the robust MFA controller is able to keep the system in automatic control through normal and extreme operating conditions when there are significant disturbances or system dynamic changes.

output (OP), where a hard limit or constraint can be set. PV is a process variable that can only be controlled by manipulating the OP. Therefore, the upper and lower bounds for PV are very different from the OP constraints. 2. Gain ratio—The coefficient to increase or decrease the MFA control action. Typically, you want to enter gain ratio = 3, which implies that the MFA gain working in abnormal situations is three times higher than the regular MFA gain setting. It is important to understand that this is not a gain scheduling approach, although it appears to be this way. Gain scheduling will not be able to resolve the complex problems described.

TIME-VARYING MFA CONTROLLER

Robust MFA Controller Configuration

The time-varying M FA controller is used to control a process with large time constant and /or delay variations. For instance, a temperature control loop usually has a shorter time constant when it heats up and a much longer time constant when it cools down because adding heat to the process is much faster than taking it away. Also, a line speed or flow rate change will cause the process delay time to vary significantly.

As shown in Figure 2.15h, the robust MFA controller can be easily configured with these parameters:

Time-Varying MFA Controller Configuration

1. Upper and lower bound—the bounds for the process variable (PV) being controlled. They provide “intelligent” upper and lower boundaries for the PV. These bounds are typically the marginal values that the PV should not go beyond. PV is unlike the controller

As shown in Figure 2.15i, the time-varying MFA controller can be easily configured with an estimated minimum and maximum process time constant plus delay time. The controller is able to deal with the large time constant and/or delay time changes without having to retune any parameters.

FIG. 2.15h Robust MFA controller configuration menu.

FIG. 2.15i Time-varying MFA controller configuration menu.

© 2006 by Béla Lipták

2.15 Model-Free Adaptive (MFA) Control

231

ANTIDELAY MFA pH CONTROLLER When combining the time-varying MFA and MFA pH control functions, an antidelay MFA pH controller is generated that can control a pH process with large and varying time delays. When a pH process has large varying time delays as well as large inflow rates and pH changes, the difficulty for this control loop quadruples. The extremely large gain changes with varying time delays make an already bad situation worse, causing the process to become almost “uncontrollable.” Traditionally, a “bang-bang” type of control or batch-based pH neutralization would be the only solution. The antidelay MFA type pH controller has the combined power of being predictive, adaptive, and robust. It is adaptive to compensate for the large gain changes, predictive to deal with large time delays, and robust enough to handle inflow changes, titration curve moves, and other uncertainties.

MULTIVARIABLE MFA CONTROL SYSTEM Figure 2.15j illustrates a multivariable feedback control system with a model-free adaptive controller. The system includes a multi-input multi-output (MIMO) process, a set of controllers, and a set of signal adders, respectively, for each control loop. Similar to a SISO system, the MIMO system has controller setpoints r(t), error signals e(t), controller outputs u(t), process variables y(t), and disturbance signals d(t). Since it is a multivariable system, all the signals here are vectors represented in bold type.

TWO-INPUT TWO-OUTPUT MFA CONTROL SYSTEM Without losing generality, we will show how a multivariable model-free adaptive control system works with a two-input twooutput (2 × 2) system as illustrated in Figure 2.15k, which is the 2 × 2 arrangement of Figure 2.15j. In the 2 × 2 MFA control system, the MFA controller set consists of two controllers—C11 and C22 —and two compensators—C21 and C12. The process has four subprocesses—G11, G21, G12, and G22.

+

–

r1

d1 + u1

e1 2 × 2 MFA controller with decoupling compensators

r2 + –

e2

G11

G21

G12 u2

G22

x11

+

+

y1

+

y2

x21

x12

x22 +

d2

+

2 × 2 process

FIG. 2.15k Two-input two-output MFA control system.

The measured process variables y1 and y2 are used as the feedback signals of the main control loops. They are compared with the setpoints r1 and r2 to produce errors e1 and e2. The output of each controller associated with one of the inputs, e1 or e2, is combined with the output of the compensator associated with the other input to produce control signals u1 and u2. The output of each subprocess is cross-added to produce measured process variables y1 and y2. Notice that in real applications the outputs from the subprocesses are not measurable and only their combined signals y1 and y2 can be measured. Thus, by the nature of the 2 × 2 process, the inputs u1 and u2 to the process are interconnected with outputs y1 and y2. The change in one input will cause both outputs to change. The control objective for this 2 × 2 MFA control system is to produce control outputs u1(t) and u2(t) to force the process variables y1(t) and y2(t) to track their setpoints r1(t) and r2(t), respectively. The minimization of e1(t) and e2(t) is achieved by: 1. The regulatory control capability of the MFA controllers 2. The decoupling capability of the MFA compensators 3. The adjustment of the MFA weighting factors, which allow the controllers to deal with the dynamic changes, large disturbances, and other uncertainties

2 x 2 MFA Controller Configuration d(t) r(t)

e(t)

MIMO MFA

u(t)

controller

FIG. 2.15j Multivariable MFA control system.

© 2006 by Béla Lipták

MIMO processes

x(t)

y(t)

A 2 × 2 MFA controller can be considered to have two main controllers, C11 and C22. For each main controller, the parameters to configure are: 1. Sample interval—the interval between two samples or calculations in seconds. A high-speed MFA controller can run at a 1 millisecond rate. 2. Controller gain—use of a default value is recommended.

232

Control Theory

3. Time constant—a rough estimate of the process time constant in seconds. 4. Acting type—direct or reverse acting of the process. 5. Compensator gain—to deal with the interaction from the other loop.

MIMO MFA CONTROLLER APPLICATION GUIDE A MIMO system can be much more complex than a SISO system; precautious have to be taken when applying a MIMO MFA controller. When designing a multivariable control system, the first step is to decide which process variable is paired with a manipulated variable. A MIMO MFA control system should follow these pairing rules: 1. Each process of the main loops has to be controllable, open-loop stable, and either reverse or direct acting. 2. A process with a large static gain should be included in the main loop as the main process (G11, G22), and a process with a small static gain should be treated as a subprocess (G21, G12). 3. A faster process should be paired as the main process and a slower process, and processes with time delays should be treated as subprocesses. 4. If pairing rules 2 and 3 should result in a conflict, a tradeoff is the only option. In addition, an MFA control system should be designed based on the degree of interactions between the loops. Table 2.15l lists the control system design strategy based on the degree of interaction of a MIMO process. MFA CONTROL METHODOLOGY “All roads lead to Rome.” A problem usually has multiple possible solutions, and a process can usually be controlled using different controllers based on different control methods. Almost every control method has its merits and weakness. What is important is to use the right controller to fit the application at a minimum cost.

TABLE 2.15l MIMO System Design Strategy Interaction Measure

Control Strategy

Small to no interaction

Tighten both loops with SISO MFA

Moderate interaction

Tighten important loops with SISO MFA and detune less important loops or use MIMO MFA for better overall control

Severe interaction

Use MIMO MFA to control the process; may need to de-tune less important loops

© 2006 by Béla Lipták

In natural science, the combination of physics, mathematics, and philosophy plays an integral part in developing a theory that is practically useful. Physics is the foundation for the study of the physical process or environment, mathematics provides the tools to precisely describe the physical process or phenomenon, and equally important is the philosophy that provides directions. The development of model-free adaptive control technology started from a simple desire to develop a new controller that could easily and effectively solve various industrial control problems. The actual development process has evolved from a prolonged interest in the study of combined intelligence methodology. Since model-free adaptive control does not follow the traditional path of model-based adaptive control, the philosophy behind the combined intelligence has led the way up this long and rocky road.

SUMMARY To see how the MFA control method is developed based on the combined intelligence methodology, we will relate MFA to each of four key points. Simple Solution PID control is simple since it is a general-purpose controller and its algorithm is easy to understand. However, PID is almost too simple to control complex systems. In this regard, PID cannot be considered an effective solution to the more difficult control problems. On the other hand, model-based advanced control methods have proven themselves too complex to launch and maintain since they depend on either a first principle or an identification-based process model. A dream controller has to be powerful enough to control various complex processes yet simple enough to use, launch, and maintain. MFA is a solution that fits these requirements. Use All Information Available Model-free adaptive control, as its name suggests, is a control method that does not depend on either first principle or identification-based process models. However, we do try to use all the process information available. For this reason, it can be considered an information-based controller. For instance, process time constant defines how fast a dynamic system responds to its input. A slow process might have a 10-hour time constant and a fast process might have a 10-millisecond time constant. It would be unwise not to use this information for the controller. In addition, it is relatively easy to estimate the time constant by reading a trend chart. Other important yet easily obtained information about a process includes its acting type (either direct or reverse), static gain, and delay time if any. An MFA controller is designed to use the process parameters that can be easily estimated.

2.15 Model-Free Adaptive (MFA) Control

Information’s Accuracy A process can be classified as a white, gray, or black box. If its input–output relationship is clear, the process is a white box. We can easily use existing well-established control methods and tools to design a controller for this process. When we are not sure if the process input–output relationship is accurate, or if the process has potential disturbances, dynamic changes, and uncertainties, the process is a gray box. In this case, MFA’s adaptive capability is able to handle such changes and uncertainties. PID or model-based control methods will have a much tougher time or higher cost addressing these uncertainties.

References 1. 2. 3.

4. 5. 6. 7. 8.

Technique That Fits the Application MFA is neither model based nor rule based. We might say that it is an information-based control method. If the argument is made that the process information used is equivalent to a process model, that is perfectly acceptable. The key to this approach is that we focus on delivering a simple, adaptive, and effective solution. To extend this idea, a series of MFA controllers, many of which are described here, has been developed to address different difficult control problems. Users can simply select the appropriate MFA, configure its parameters, launch the controller, and reap the benefits.

© 2006 by Béla Lipták

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9. 10. 11. 12. 13. 14.

Cheng, G. S., MFA in Control with CyboCon, Rancho Cordova, CA: CyboSoft, General Cybernation Group, Inc., March 2002. VanDoren, V., Techniques of Adaptive Control, Burlington, MA: Butterworth-Heinemann, 2003. VanDoren, V., “Model Free Adaptive Control—This New Technique for Adaptive Control Addresses a Variety of Technical Challenges,” Control Engineering Europe, March 2001. Major, M., “Model-Free Adaptive Control on an Evaporator,” Control, September 1998. Cheng, G. S., He, M., and Li, D. L., “Model-Free Coking Furnace Adaptive Control,” Hydrocarbon Processing, December 1999. Seiver, D., and Marin, O., “Air Separation Advances with MFA Control,” Control, May 2001. Cheng, G. S., and Huo, L. Q., “Control System Optimizes EOR Steam Generator Output,” Oil & Gas Journal, September 2003. Cheng, G. S., and Huo, L. Q., “Leading Edge Plant Control System— Model-Free Adaptive Control Puts Ling-Yuan Iron and Steel in League of Its Own,” InTech, October 2003. Cheng, G. S., CyboCon CE User Manual, Rancho Cordova, CA: CyboSoft, General Cybernation Group, Inc., 2001. Cheng, G. S., “Tomato Process Improvements Using Model-Free Adaptive Controllers,” Tomato News, April 2004. Harris, S., “Model-Free Adaptive Control Improves Productivity and Efficiency,” Control, June 2004. Cheng, G. S., “Model-Free Adaptive (MFA) Control,” IEE Computing and Control Engineering, June/July 2004. Cheng, G. S., and Zhang, Z. W., “Model-Free Adaptive Control in Water Treatment,” Control Engineering Europe, September 2004. Cheng, G. S., and Zhang, W. D., “Model-Free Adaptive Technology Improves Distillation Column Chain Control,” Hydrocarbon Processing, October 2004.