Windup in Control: Its Effects and Their Prevention (Advances in Industrial Control)

Windup in Control: Its Effects and Their Prevention Advances in Industrial Control aims to report and encourage the transfer of technology in control.
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The result is to match the car's speed to the reference speed maintain the desired system output. Now, when the car goes uphill, the difference between the input the sensed speed and the reference continuously determines the throttle position. As the sensed speed drops below the reference, the difference increases, the throttle opens, and engine power increases, speeding up the vehicle.

In this way, the controller dynamically counteracts changes to the car's speed. The central idea of these control systems is the feedback loop , the controller affects the system output, which in turn is measured and fed back to the controller. To overcome the limitations of the open-loop controller , control theory introduces feedback.

A closed-loop controller uses feedback to control states or outputs of a dynamical system. Its name comes from the information path in the system: Closed-loop controllers have the following advantages over open-loop controllers:. In some systems, closed-loop and open-loop control are used simultaneously.

A common framework for anti-windup, bumpless transfer and reliable designs

In such systems, the open-loop control is termed feedforward and serves to further improve reference tracking performance. A common closed-loop controller architecture is the PID controller. The output of the system y t is fed back through a sensor measurement F to a comparison with the reference value r t. The controller C then takes the error e difference between the reference and the output to change the inputs u to the system under control P.

This is shown in the figure. This kind of controller is a closed-loop controller or feedback controller. In such cases variables are represented through vectors instead of simple scalar values. For some distributed parameter systems the vectors may be infinite- dimensional typically functions.

If we assume the controller C , the plant P , and the sensor F are linear and time-invariant i. This gives the following relations:. The numerator is the forward open-loop gain from r to y , and the denominator is one plus the gain in going around the feedback loop, the so-called loop gain. A proportional—integral—derivative controller PID controller is a control loop feedback mechanism control technique widely used in control systems.

PID is an initialism for Proportional-Integral-Derivative , referring to the three terms operating on the error signal to produce a control signal. The theoretical understanding and application dates from the s, and they are implemented in nearly all analogue control systems; originally in mechanical controllers, and then using discrete electronics and latterly in industrial process computers. The PID controller is probably the most-used feedback control design. Stability can often be ensured using only the proportional term.

The integral term permits the rejection of a step disturbance often a striking specification in process control. The derivative term is used to provide damping or shaping of the response. PID controllers are the most well-established class of control systems: The plant output is fed back through. With this tuning in this example, the system output follows the reference input exactly. However, in practice, a pure differentiator is neither physically realizable nor desirable [14] due to amplification of noise and resonant modes in the system. Therefore, a phase-lead compensator type approach or a differentiator with low-pass roll-off are used instead.

Mathematical techniques for analyzing and designing control systems fall into two different categories:. In contrast to the frequency domain analysis of the classical control theory, modern control theory utilizes the time-domain state space representation, a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations. To abstract from the number of inputs, outputs, and states, the variables are expressed as vectors and the differential and algebraic equations are written in matrix form the latter only being possible when the dynamical system is linear.

The state space representation also known as the "time-domain approach" provides a convenient and compact way to model and analyze systems with multiple inputs and outputs. With inputs and outputs, we would otherwise have to write down Laplace transforms to encode all the information about a system. Unlike the frequency domain approach, the use of the state-space representation is not limited to systems with linear components and zero initial conditions.

The state of the system can be represented as a point within that space. Control systems can be divided into different categories depending on the number of inputs and outputs. The stability of a general dynamical system with no input can be described with Lyapunov stability criteria.

For simplicity, the following descriptions focus on continuous-time and discrete-time linear systems. Mathematically, this means that for a causal linear system to be stable all of the poles of its transfer function must have negative-real values, i. Practically speaking, stability requires that the transfer function complex poles reside. The difference between the two cases is simply due to the traditional method of plotting continuous time versus discrete time transfer functions. When the appropriate conditions above are satisfied a system is said to be asymptotically stable ; the variables of an asymptotically stable control system always decrease from their initial value and do not show permanent oscillations.


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Permanent oscillations occur when a pole has a real part exactly equal to zero in the continuous time case or a modulus equal to one in the discrete time case. If a simply stable system response neither decays nor grows over time, and has no oscillations, it is marginally stable ; in this case the system transfer function has non-repeated poles at the complex plane origin i.

Oscillations are present when poles with real part equal to zero have an imaginary part not equal to zero. If a system in question has an impulse response of. This system is BIBO asymptotically stable since the pole is inside the unit circle. Numerous tools exist for the analysis of the poles of a system.

1. Introduction

These include graphical systems like the root locus , Bode plots or the Nyquist plots. Mechanical changes can make equipment and control systems more stable. Sailors add ballast to improve the stability of ships. Cruise ships use antiroll fins that extend transversely from the side of the ship for perhaps 30 feet 10 m and are continuously rotated about their axes to develop forces that oppose the roll. Controllability and observability are main issues in the analysis of a system before deciding the best control strategy to be applied, or whether it is even possible to control or stabilize the system.

Controllability is related to the possibility of forcing the system into a particular state by using an appropriate control signal. If a state is not controllable, then no signal will ever be able to control the state. If a state is not controllable, but its dynamics are stable, then the state is termed stabilizable. Observability instead is related to the possibility of observing , through output measurements, the state of a system.

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If a state is not observable, the controller will never be able to determine the behavior of an unobservable state and hence cannot use it to stabilize the system. However, similar to the stabilizability condition above, if a state cannot be observed it might still be detectable. From a geometrical point of view, looking at the states of each variable of the system to be controlled, every "bad" state of these variables must be controllable and observable to ensure a good behavior in the closed-loop system.

That is, if one of the eigenvalues of the system is not both controllable and observable, this part of the dynamics will remain untouched in the closed-loop system. If such an eigenvalue is not stable, the dynamics of this eigenvalue will be present in the closed-loop system which therefore will be unstable. Type 1 diabetes mellitus T1DM is a chronic disease that occurs when the pancreatic beta cells are destroyed, leaving the body unable to produce sufficient insulin to maintain glycemic homeostasis.

To manage this condition, people with T1DM need to self-administer exogenous insulin based on measurements of their blood glucose concentration BG and an estimation of carbohydrate CHO content in their meals. This procedure requires the person to measure their blood glucose concentration several times per day using a fingerstick method to access capillary blood.

Both hyper- and hypoglycemia lead to health complications, although the effects of hypoglycemia are more sudden and can quickly escalate to become life-threatening. While diabetes management can be an onerous task, technological advances have begun to reduce the difficulty of treatment and provide better health outcomes overall. The introduction of insulin pumps to provide continuous subcutaneous SC insulin infusion has allowed many people to achieve better glucose control than they could using multiple daily injections of insulin.

Another important technological advance was the development of the continuous glucose monitor CGM , a device that uses a subcutaneous electrode to measure the glucose concentration in the interstitial fluid. In combination, insulin pumps and sensors allow people with diabetes to exert much more influence over their health than what was previously possible. Even with the use of insulin pumps and glucose sensors, the treatment process is ultimately an open-loop one, with the patient manually observing the glucose concentration, calculating an insulin dose, and using the pump to command that dose.

While control engineering is a well-developed field, its use is relatively new in medical applications. The ability to close the loop between glucose sensor and insulin pump is an exciting development that will bring a new era to diabetes management. The artificial pancreas AP will advance the state-of-the-art technology of diabetes treatment by using a control algorithm to close the loop between the insulin pump and the CGM, providing automated insulin dosing. The system will use feedback and potentially feedforward control to maintain glucose concentrations near a desired set point or within a desired zone.

Many variations of the AP have already been tested in clinical studies, with some even taking place in an outpatient environment. In this work, we present a design process for a controller that will work with implantable insulin pumps and glucose sensors, greatly reducing the delays and resulting in overall better glycemic control. The objective of the artificial pancreas is to provide safe and effective glycemic control for people with T1DM. In addition, the controller must prevent hypoglycemic episodes.

Since safety must remain the top priority in any medical device system, some AP designs introduce glucagon as a second manipulated variable. However, there are practical difficulties with using glucagon in a closed-loop system, and the effects of long-term glucagon use are unknown. An important constraint in this system is that insulin cannot be removed once it has been delivered, so the AP must be tuned accordingly to avoid a potentially dangerous situation. There are several disturbance challenges that the AP must face to successfully control BG.

The most difficult disturbances to control occur following the ingestion of a meal, when the BG concentration increases rapidly. Other challenges include periods of exercise, which can result in unpredictable BG changes, and overnight periods, during which the AP user is asleep and therefore dependent on the AP to maintain the BG within a safe range.

To effectively reject glycemic disturbances, the AP controller must have access to rapid sensing and actuation. The majority of AP designs tested thus far rely on commercially available insulin pumps and glucose sensors that operate in the subcutaneous space. Unfortunately, diffusion lags between the interstitial fluid and the blood introduce severe delays in both glucose sensing and insulin action, making fully automated closed-loop control much more difficult.

While the addition of the meal announcement improves the resulting BG profile following a meal, it also poses a safety risk by requiring the user to accurately and reliably perform an action. The reduction of delays may be accomplished with the use of alternate insulin delivery and glucose sensing methods. The intraperitoneal IP space was first introduced as an alternative insulin delivery route in the s.

The improvements gained by faster actuation through IP insulin delivery will be limited without the implementation of fast glucose sensing. In initial clinical studies, an AP using intraperitoneal insulin delivery did not perform as well as expected because the sensor introduced a lag to the glucose measurement.

The IP sensor time constants were lower and had a tighter distribution than the SC time constants. This evidence suggests that a glucose sensor implanted within the IP space will provide a more useful estimation of the blood glucose concentration by reducing the diffusion lag. Box plot showing the statistical properties of the fitted time constants for sensors placed in the IP space or the SC space of swine, demonstrating that the IP sensors had a lower mean time constant and a tighter distribution than the SC sensors data from experimental study presented in Burnett et al.

A fully implanted AP will make use of both intraperitoneal insulin delivery and glucose sensing. The pump, sensor, and controller will all be implanted, and the system will be operated using a hand-held remote. This approach will eliminate the need to remove and apply new sensors and insulin infusion sets, as must be done with subcutaneous devices. Externally worn devices can be cumbersome, so this approach may also increase patient compliance.

We hypothesize that the glycemic control provided by a fully implantable system will be superior to that which is possible with a subcutaneous system. Since the sensing time constant is up to two times faster, the controller can react promptly to impending hypo- and hyperglycemia. Several control strategies have been evaluated for AP applications, including proportional-integral-derivative control PID , model predictive control MPC , and fuzzy logic.

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Model predictive control has been proposed as a suitable strategy for AP designs using subcutaneous insulin delivery and sensing because of the large delays in these systems. In this case, we anticipate that the advanced control capability of MPC may no longer needed, and that a PID controller will provide satisfactory performance. Because the insulin will act quickly and glucose changes will be sensed rapidly, the system can operate well without the predictive power offered by MPC. The use of model based tuning is recommended for the AP because online tuning through trial and error is not acceptable for a medical application; however, we need to find a balance between a general and personalized model.

Completing time-consuming model identification procedures for individual subjects is not feasible, especially if the AP is to be adopted on a large scale. Still, individual subjects have widely varying insulin sensitivities. The model that was identified for intraperitoneal insulin action on blood glucose concentration is. Internal model control IMC is a comprehensive tuning method that allows PID parameters to be calculated directly from the process model.

This conversion can be done using several methods, but the zero-pole matching method was determined to best preserve the model characteristics. Therefore, the final tuning parameters are robust to the conversion method. Internal model control tuning rules require a second-order model to obtain a PID controller. An important feature of the velocity PID form is that it must include the use of integral action. If it is desired to exclude integral action, the position form should be used instead.

PID Control - A brief introduction

A derivative filter can be implemented with this controller. The derivative filter prevents excessive controller action in the presence of measurement noise. In this case, the derivative term becomes. The tuning parameters obtained using the procedure outlined above are shown in Table 2 , along with parameters determined for a PID controller using SC insulin in Laxminarayan et al. The safety and efficacy of an AP device need to be demonstrated in human clinical trials before it can be considered for widespread use.

Prior to these clinical studies, the controller must first show promise in simulation studies. In the case of the implantable AP, there is a further requirement to be evaluated in an animal model because the system involves novel pump and sensor devices that are not already approved for use by the United States Food and Drug Administration.

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In this study, the metabolic simulator was used to determine the optimal tuning parameters and evaluate the controller performance. This value was chosen based on the data presented in Burnett et al. A large meal of g of carbohydrates CHO was administered to evaluate the meal response and the set point undershoot. The change was simulated by multiplying the insulin delivered by 0. A 27 h clinical protocol was simulated to evaluate the controller performance for a typical real-life scenario. Closed-loop control was initiated at This meal was followed by an overnight period from A breakfast of 40 g-CHO occurred at Closed-loop control was ended at Scenarios 1—3 were previously tested in Laxminarayan et al.

The scenarios were repeated here to allow for direct comparison to show the improvement gained by using IP insulin and the design procedure implemented in this paper. The best controller design was selected using Scenarios 1—3. The final controller was tested in Scenario 4, including simulated sensor noise to demonstrate a true-to-life protocol with potential measurement errors. Scenario 4 was used in Lee et al. The bottom panel shows the buildup of the integral term that occurs during the large meal disturbance, leading to the set point undershoot.

Demonstration of set point undershoot encountered when using integral action after a g-CHO meal.

A common framework for anti-windup, bumpless transfer and reliable designs

The top panel shows the glucose deviation from the set point after the meal for subject 1 under PID control. The bottom panel shows the insulin trace for PID control dashed gray line with the integral component plotted separately dashed black line. Also on the bottom panel are the advisory mode calculations for PID with anti-reset windup protection solid lines with the gray line showing the total insulin and the black line showing the integral component. This undershoot is highly undesirable because it indicates insulin overdelivery and increases the risk of hypoglycemia.

Several approaches have been used to circumvent this effect. However, the use of PD control is not ideal because set point tracking is sacrificed. Without set point tracking, the controller will not be able to react to changes in insulin sensitivity. Other clinical studies have detuned the integral component to prevent insulin overdelivery. Prevention of Controller Windup. Prevention of Plant Windup in Stable Systems Further Methods for the Prevention of Windup. Prevention of Plant Windup in Stable and Unstable. Prevention of Windup in Multivariable Systems. Additional Rate Constraints A Design of Observerbased Controllers.

Undesired Effects of Input Saturation.