Such data recovery task can be realized in the processing/control nodes by ... at the center of successful implementation of networked control systems (NCS).
Predictive Control Strategy in Distributed Networked Control Systems for Turbine Engine Under Faulty Communication Network Saleh Zein-Sabatto1, Tayo Adedokun2, Mohammad Bodruzzaman3 Tennessee State University, Nashville, TN 37209 and James Ramsey4 The Boeing Company, St Louis, MO
Alireza Behbahani5 Air Force Research Laboratory Wright-Patterson AFB, OH, 45433, USA
Future turbine engines will require more efficient consumption of energy and greater reliability. A reduction in weight of turbine engine control systems and increased robustness will be critical in achieving said requirements. This paper presents the development of an advanced control strategy to replace the Full Authority Digital Electronic Control (FADEC) system (commonly used by turbine engines) with a lighter weight, Distributed Networked Control System (DNCS) that uses smart nodes (SN) architecture to enhance robustness. The concept of Distributed Networked Control Systems (DNCS) is rooted in the idea that the sum of the parts can be designed to weigh less than the whole, thereby allowing a single control system to be replaced by a set of sub-controller components that interact effectively through a network with improved functionality. The addition of artificial intelligent techniques employed to overcome the challenges inherent in DNCS operating under faulty communication networks are included. Specifically, an Artificial Neural Fuzzy Inference System (ANFIS) is employed to function as a state estimator within the distributed control nodes. The full implementation of the developed DNCS consists of distributed controllers, state estimators (ANFIS), and a simulated network interface. The focus of this paper is to report the development and test results related to the implementation of the described advanced distributed control methodology and its influence in recovering the engine operation in the presence of faults occurring within the communication network. The complete DNCS was tested on the MAPSS turbine engine simulation model. The test results showed that the developed DNCS with ANFIS state estimators improved turbine engine performance even under severe network delay conditions. As a result, the developed control system proved to be a viable alternative to the current engine control system. The research demonstrates that DNCS technology yields a reduction in engine weight leading to a reduction in energy consumption and a corresponding increase in engine efficiency and performance.
I. Introduction To achieve efficient operation and desired flight objectives, turbine engines must be equipped with robust control systems. The expectation is to provide smooth, stable, and stall free operation of the engine. Historically this has been accomplished via a single input single output (SISO) control scheme. A single command to the engine is determined by the Power Lever Angle (PLA), generating a single burner fuel flow rate, which ultimately produced engine thrust, the force to be governed. Essentially, fuel flow was the only controllable variable1. As time progressed actuators were added to engines, and these voltage controlled mechanisms needed additional control signals. Although, these advancements in turbine engine control systems led to improved engine safety, they also produced additional complexity, weight and reduced efficiency. 1
Faculty, College of Engineering, 3500 John Merritt Blvd, Nashville, TN. Graduate Student, College of Engineering, 3500 John Merritt Blvd, Nashville, TN. 3 Faculty, College of Engineering, 3500 John Merritt Blvd, Nashville, TN. 4 Senior Researcher, The Boeing Company, St Louis, MO. 5 Sr. Aerospace Engineer, Wright-Patterson AFB Bldg. 18D, 1950 Fifth Street, 2
Hence, there is a clear need for reduced and more efficient consumption of energy within the turbine engine system. This need can be addressed by considering the contribution of the turbine engine control system to the overall of the energy consumption of turbine engines. Particular factors in consideration are the contribution of the control system to the engine weight and its effect on the engine weight distribution. These two factors undoubtedly hinder the efficient use of energy by the turbine engine. Analysis of these factors, as affected by the control system, leads to an avenue for addressing the need for reduced and efficient energy consumption by turbine engines. In both commercial and military aircraft systems, the Full Authority Digital Electronic Control (FADEC) system is the industry choice for achieving turbine engine controls. The system was introduced in the 1980s during the advent of electronic control systems2. A FADEC system controls all the functions required of the engine and introduces a number of improvements, such as: (1) The possibility of implementing sophisticated techniques from the modern control theory, (2) A reduction in weight owing to the limited use of hydro mechanics, and (3) The possibility of implementing built-in support for maintenance which lowers the cost of and improves the efficiency of the engines. FADEC systems are currently in operation in a number of aircraft: the F18E/F, Euro-fighter, Airbus 320, 321 and the Boeing 777 aircraft3. Two common architectures are found in the design of FADEC control systems--centralized and decentralized architectures4. The most reliable and well understood is the centralized architecture. In the centralized case, the sensor and actuator electronics are located within the FADEC unit. Cables run to and from the actual sensors and actuators. An alternative, usable architecture for the control system design is the decentralized FADEC. In this implementation, sensor and actuator electronics are located outside the FADEC unit. The decentralized architecture maintains an advantage of flexibility over the centralized architecture, however there remains a trade-off in complexity. Although well developed, the single Full Authority Digital Electronic Control system poses a problem of system efficiency regardless of which architecture is employed. Hence, distributed network control system architectures have been proposed and developed in the literature for turbine engines, including the authors of this paper 5. In this paper, the limitation imposed by communication network failures in the distributed network control systems of turbine engines is addressed. A predictive control strategy is used in the development of smart processing nodes. Then, the developed smart processing nodes are used to construct a distributed networked control system for turbine engines. In Section II we present a brief review of the challenges faced in the implementation of distributed control systems. Then, a detailed development of communication network for the distributed control system is reported along with the development steps of the different state estimators and the associated predictive strategies are all presented in Section III. Finally, testing and performance evaluation of the distributed networked control system with predictive control strategy is conducted and the results are reported in Section IV, followed by conclusions and recommendations in Section V.
II. Distributed Network Control System Challenges A. Challenge of the Communication Networks in DNCS Networked Control Systems (NCS) is an area of controls that expands the common control feedback structure to include distributed components implemented on physically separate hardware 6. With the consideration of these networked interfaces as part of the control strategy, NCS become an integration of three areas of study: control systems, communication networks, and information theory7. Many challenges arise with this expansion of the control theory, and networked control systems are designed with these challenges in mind--some being more application--sensitive than others. Of current consideration is the inclusion of distributed control theory. Contrary to decentralized control strategies where all control efforts are processed on a single global processor, a distributed control system utilizes independently acting local control modules8. Local control units are specialized so that the feedback control strategy can be simplified to whatever grade the designer wishes by dividing the control efforts among many locally executed smart processing nodes. For full control system distribution, both the computational efforts and the control efforts will be distributed among these processing nodes. Distribution of the system control involves the reduction of control effort to only a subset of the I/O relations, rather than the complete combination of relations used in classical feedback control strategy. The system will retain the full-state feature, but loose the full control matrix structure. It is precisely this distributive property that transforms a network control system into a Distributed Networked Control System (DNCS). The DNCS general system architecture is presented in Figure 1. In designing DNCS, two primary challenges arise that must be addressed in order to have an operationally stable control system. First, the design of a Full State Distributed Feedback Controller is necessary, given that only a subset of I/O feedback gain relations is typically realizable. In this regard, adequate consideration must be offered towards choosing a
suitable I/O subset and then finding the best corresponding gains to achieve a desired system response. Second, compensation for Network Induced Delay(s) (NID) is a design requirement because NID occur when sensors, actuators, and controllers exchange information across shared networks. These induced delays can be constant, time varying, or even random7. System latencies can degrade the performance of the actual control system if ignored during the design process and can even destabilize the system by introducing excessive phase lag. The focus of the paper will be mainly on addressing the challenge of maintaining stability and robustness of the distributed networked control system in the presence of a faulty communication network, i.e., network delay(s) and packets drop out. The idea is to locally estimate the needed information at each control node in a distributed control system and use the information to achieve the designated control objectives.
Figure 1. Distributed Networked Control System Architecture The type of communication network used within the distributed control systems is as vital to the success of the DNCS as the other components of the control system. For example, a network protocol, i.e., the User Datagram Protocol (UDP) or the Transmission Control Protocol (TCP) offers different quality of service (QoS) and hence has direct impact on the stability of the control system as explained in the next paragraph. Regardless, of the chosen network type, certain requirements must be met. The communication network in DNCS must achieve the following: (1) minimize data loss probability within the network, (2) allow for end-to-end connection of sensor-to-controller, controller-to-actuator through a shared network medium, and (3) maximize the integrity of information sent from transmitters to receivers. Three major attributes must be considered in selecting the type of communication network in DNCS; the network topology, the network transmission protocol, and the network distribution configuration9, 10. All communication networks have these attributes inherent to its operation, and modification to these attributes may affect the network performance. The network topology deals with the physical and logical arrangement of the nodes within the network. Physical topology dictates the geometrical arrangement of the various network nodes, while logical arrangement deals with media access control methods in the network. Some network topologies affect both the physical and logical arrangement of the network. For turbine engine controls, topology is highly application dependent, and relies greatly on the actual engine for implementation. The second attribute is the network transmission protocol. Data sent through the network is transmitted according to a set order of communication actions between two nodes. The communication actions (protocols) are similar to the actions in making calls with proper phone etiquette. Just as various cultures have unique phone etiquette, there exist multiple network transmission protocols. The third attribute is the network configuration, which determine the hardware used within the network and the connection type. To meet the network requirements of the distributed control systems, consideration must be given to the choices according to these attributes. The network topology is application dependent, and isn’t expected to have significant influence on the network performance so its effects on the distributed controller will not be considered in this work. Among the others, two alternatives are considered for network protocol; the User Datagram Protocol (UDP), and the Transmission Control Protocol (TCP). Each of these protocols offers different quality of service measures11. In this work, the Transmission Control Protocol is used for the network implementation within the DNCS. In the implementation, the TCP protocol is designed to minimize probability of packet loss by the use of packet re-transmit feature. Additionally the TCP uses system acknowledgments to check for data arrival and accuracy. These two features qualified the TCP to meeting the network requirements of the DNCS. For network configuration selection, two network configuration are possible; the Personal Area Network (PAN/WPAN), and the Local Area Network (LAN/WLAN). Also known as Wi-Fi, the Wireless Local Area Network (Wireless LAN) is a set of
low tier technologies for data communication. The IEEE standards for this configuration operate under the 2.4 GHz and 5 GHz ISM bands12. There are many variations of this configuration standard within the 802.11 bracket; such as 802.11a, 802.11b, 802.11g, and 802.11n. The most commonly used variant is the 802.11b. This is the used standard of the configuration alternative. Personal Area Networks and Wireless Personal Area Networks are utilized under various aliases. The most common WPAN networks are Bluetooth, and Zig-Bee. The set of WPAN systems operate under the IEEE 802.15 standards, having a wide array of applications and service measures. Bluetooth operates in the same 2.4 GHz range as some Wi-Fi (WLAN) networks, and Zig-Bee has operation in; 868 MHz, 915 MHz, and 2.4 GHz ISMs12. Based on analysis conducted on the turbine engine simulation model for determining minimum network requirements, the Local Area Network was selected as the most appropriate network configuration for this work. No significant distinctions exist between the selected network configurations when considering performance of the DNCS, as all the configurations proved to meet the network requirements of DNCS. Finally, communication within the DNCS is proposed to occur through a Local Area Network, Peer to Peer configuration. The system operates under IEEE 802.11b standards; meaning a transmission frequency of approximately 2.4 GHz, and a transmission propagation speed ranging from 1-11 Mbps. The system will utilize the Transmission Control Protocol in transmitting and receiving data packets transmitted through the network. This selected communication network serves to meet all the three network requirements; by minimizing the data loss probability, allowing end-to-end connectivity, and maximizing the data integrity. B.
Predictive Control for Information Recovery of Faulty Communication Networks in DNCS
The stability and robust operation of turbine engine distributed networked controllers are highly dependent on the integrity of the feedback information provided by the communication network to the distributed control nodes. In case of network failures, the integrity of such feedback information is lost and its responsibility falls back on the processing/control nodes. A smart processing/control node must be capable of locally generating trustworthy necessary information to act on it. This leads to the concept of using predictive control strategy embedded in each processing and control node while implementing the distributed control laws. Such data recovery task can be realized in the processing/control nodes by states estimation algorithm. Hence, the state estimator will play a key role in the performance of the predictive control strategy to overcome adverse network effects. The state estimator must: (1) Successfully estimate the states of the closed loop system under imperfect transmission conditions, (2) Help the control system maintain stability at a static transmission delay greater than half the closed loop Minimum Allowable Transmission Interval (MATI), (3) Minimize the steady-state value error between the implemented networked control system and a base-line controller without communication network and, (4) The state estimator shall maintain accurate state recovery of the feedback signals required by individual processing and control nodes. In all of the above situations the communication network condition and parameters will be assumed to be known and utilized by the state estimator in propagating state estimates. Finally, the state estimator must function to keep transmission intervals well within the MATI time established for the engine distributed network controller. In the following, we considered three different approaches for design and implementation of state estimators for the smart processing and control nodes, i.e., a predictive model that is parametric and regressive. It is assumed that the estimation algorithm cannot rely solely on current input from the network in order to produce dependable state estimations. Rather, the algorithm shall utilize a combination of control signal and state feedback history to determine accurate future states. The aim is to locally predict the engine states prior to the signal entering the network communication. Various parametric and regressive system modeling alternatives exist of which; three are analyzed in the scope of this work. B.1. Kalman Filter Predictor The Kalman filter has been subjected to extensive research and application, particularly in the areas of prediction and estimation. It is a set of mathematical equations that provide an efficient computational (recursive) means to estimate the state of a process, in a way that minimize the mean of the squared error 13. It supports estimation of past, present, and even future states. It can do so without precise knowledge of the system dynamics at hand. The design of a discrete Kalman filter is introduced in13. Two processing steps implemented by the Kalman filter; time update, and measurement update steps. The time update step is responsible for state prediction with use of a measurement corrected state and error co-variance value. The measurement update step corrects previous state prediction and co-variance values using the current state measurement. B.2. Parametric Auto-Regressive Predictor For any continuous time system, the input to output relationship can be considered a parametric equation whose variables are the historical I/O data. In system identification, it is desirable to find the governing coefficients that produce the
next step output based on previous input and output information. The auto-regressive with exogenous input model captures the current output as a function of some order of parameters; depending on the input and output order. B.3. Artificial Neuro-Fuzzy Inference System The Adaptive-Neuro Fuzzy Inference System (ANFIS) combines two intelligent techniques; the artificial neural network and the fuzzy inference developed by Takagi and Sugeno14,15. The ANFIS model is an adaptation of the fuzzy logic model to include neural network based learning function. In the model, the premise parameters determine the membership function type in the input layer. The model can ideally have any number of inputs and any number of membership functions for each input but must have only one output. Conventionally, ANFIS is designed to take an aggregation of inputs and make a single output decision. As a state estimator, ANFIS will take the state history as input and produce a single state estimation as output. Also, ANFIS offers high accuracy state prediction since it combines two artificial intelligence techniques. All the above discussed approaches to state estimation are; parametric and regressive by nature, serve to model linear and nonlinear systems, and offer tuning parameters to increase their estimation performance. However, ANFIS has been proven to perform well in state estimation and signal prediction without much dependence on accurate real-time information. This feature proves beneficial in order to compensate for the DNCS network delay effects. The three estimation approaches are implemented and tested in this work, and the results validate the use of the ANFIS for state estimation. As a result, the proposed predictive control strategy is implemented utilizing ANFIS as a local state estimator in the distributed controller nodes. Detail development and implementation information is presented in the next section.
III. System Development and Implementation A. Development of the Communication Network Network implementation issues are at the center of successful implementation of networked control systems (NCS). Therefore, NCS have introduced considerable changes to the way control systems are implemented. Analysis of both the networked and network-free closed loop systems stability must be conducted in the design of NCS. The designer must find the minimum rate at which feedback information must be processed and used to close the control loop and maintain the controlled system stability16. This inherent minimum data rate of networked control systems is characterized by the Minimum Allowable Transmission Interval (MATI) of these systems17. For this class of networked control systems it is critical for the controller be designed with knowledge of the system’s MATI. Hence, in the following we cover the process of analyzing a discrete control system to find its MATI at which stability holds. The controller communication network must ensure signal transmission at a rate upholding this minimum interval. Consider the following closed-loop discrete LTI system. x(t +Δ t) = (A + B K) x(t) + B r(t) y(t) = (C + D K) x(t) + D r(t)
(1)
Where, Δt is the sampling interval of the discrete system. For such a system, with a sampling interval exceeding the MATI of the system, the controller pushes the system towards instability. The sampling boundary can be determined by trial and error using network simulator integrated with the controller. To perform such analysis we have used a distributed control system developed and implemented on the MAPSS turbine engine simulation model and it was reported in our previous work5. The following is a summary of the development of the distributed control system with presentation of its basic performance under network constraints. For a LTI system described by its state space model in the continuous time domain as in equation (2), a distributed controller is designed to force the dynamics of the controlled system to exhibit a desired behavior specified by the eigenvalues of the closed-loop system matrix “Acld” and meet the following constraints: (1) The controller parameters must be decentralized, and (2) The controller will be implemented in the form of distributed network control system. ̇ (2) Using the feedback control law control system is derived.
and inserting it into the state space equation (2), a new closed loop
̇ (3)
The system with input and output is the “open-loop" system, and the system with input and output is the “closed-loop" system. To satisfy the constraint imposed on the control system, the controller matrix “K” must satisfy the following two conditions; the matrix K has full row rank, and must satisfy the equation for some real matrix 6. Understanding that , a controller matrix can be computed by. (4) Where, is controller matrix, and is the desired closed-loop system matrix. Matrix in equation (3) is important in ensuring a one-to-one relationship of input to output for the controlled system. Forcing the matrix K to be fully distributed and choosing, by use of Grammian interaction measure18, a single nonzero value from each vector in the column space of the K matrix yields the following system of equations. { }}
{
(5)
, and { } . Solving the above system of equations does not lead to a unique solution. For controller parameters optimization, first, the desired closed loop system behavior is specified, then selecting the elements of the closed loop characteristic matrix as search parameters, an optimization algorithm is used to find the elements of the matrix K (with elements Ki K ) that closest serve to meet the desired system behavior. The optimization algorithm is developed and implemented using MATLAB optimization Toolbox to minimize the following cost function. {
} {
(6.a)
}
(6.b)
∫ |
[|
|
|]
(6.c)
where: y1(t): desired system response y2(t): intermediate system response w1, w2 weight coefficients e1(t): overshoot error e2(t): steady state response error. The above procedure for designing a distributed controller is applied to a linearized model of turbine engine. Also, network implementation of the distributed controller is conducted to test the controller performance under communication network constraints. The following matrices A, B, C, and D are used in the design of the controller. They represent a linearized model of turbine engine at a specific operating point and extracted from the Modular Aero-Propulsion System Simulation (MAPSS) software19. The three state of the engine considered are: the low pressure spool speed (Xnl), the high pressure spool speed (Xnh), and the average hot section temperature (T mpc). A= [
];
B= [
]; C= I(3), D={0}
Choosing the structure of the distributed controller (K) as shown below, the controller gains are computed using optimization algorithm for the desired characteristics parameters of the closed-loop system as, . K=: [
];
K=[
]
The above developed distributed controller for the turbine engine is implemented with communication network connecting the different elements of the controller with the engine sensors and actuators. The distributed networked control system is tested using the TrueTime network simulation software written under MATLAB/Simulink 20. Two network conditions are
tested. Run-1 represents moderate constrained network condition and, Run-2 represents network under extreme constrained conditions (network packet loss). The network and its simulation parameters are summarized in Table 1. Table 1. Network Implementation Parameters Network Parameters Controller Sampling Rate Network Type Network Transmission Rate Probability of Network Packet Loss
Run-1 Moderate Constrained Network 20 (msec) CSMA/CD (Ethernet) 10 (Mbps) 50%
Run-2 Severely Constrained Network 20(msec) CSMA/CD (Ethernet) 10 (Mbps) 85%
Figure 2 shows the system responses under the network implementation without predictive control strategy (without state estimation). The dashed lines indicate the responses without network effects, and the solid "blue" lines indicate the system response with network effects through packed loss constrain.
Xnl
Xnl
Xnh Xnh
Tmpc Tmpc
(a)
(b)
Figure 2. System Responses with Network Simulator (a) Moderate Constrained Network, (b) Severely Constrained Network In the above implementation of the distributed controller, the system’s sampling period is increased from an acceptable small value until system instability occurred. To determine the point of system instability, the system response is analyzed using Fourier transform. Typically, Fourier transform is used to extract the dominance of the frequency within a signal and is given by the following equation for a discrete signal f(n). F
∑
(7)
where N is the total number of samples over finite time. By squaring the Fourier Transform values F(k), the Power Spectrum is computed as given in equation (8). Considering the engine model response, at stability the step response will tend towards a steady state value. At instability, the system will either tend towards an infinite pole, or oscillate between infinite asymptotes. Under stable conditions, the power spectrum of the system response indicates a dominant frequency matching the reference input frequency, with all other frequencies having very minimal to no power. When unstable, the input reference frequency loses its dominance in the system response and a different frequency becomes dominant.
≠
∑
(8)
To find the MATI for stable system operation, the power of the dominance frequency of the reference input signal is determined as a percentage of total power within the system response P(kR) using equation (8), where kR is determined by the input reference frequency ωR. For multiple sample rate test, the point at which the input reference frequency is no longer dominant, within the system response, is the point of system instability. The corresponding sampling rate at that point is the Minimum Allowable Transmission Interval (MATI) for the linear system in the control loop. B.
Development of State Estimators
Due to the intermittent nature of networked control systems, quality of the state feedback information may be compromised. To compensate for the occasional delay or loss of information that may occur between communication nodes, a state estimator can be used at the receiving node of the network. The estimator’s purpose is to recover or reconstruct the lost or over-delayed state feedback information to preserve continuity of the control efforts. In the following, a method of the model predictive control theory is highlighted from which the predictive control motivation arises. The proposed design makes use of state estimation with offline modeling technique. The three modeling options presented in the previous section are implemented and tested to validate the performance of the state estimation algorithm. Theoretical precepts and methodology for developing each estimator model are provided next. Kalman Filter State Estimator: - A stochastic discrete control system can be described by its difference equation (9) and measurement output equation (10) as shown below. xk = A xk−1 + B uk−1 + wk−1
(9)
zk = H xk + vk
(10)
The variables wk and vk represent the process and measurement noise, respectively. In the case of a NCS, the uncertainty of data due to intermittency within network transmission can be represented by both the process and measurement noise. Three assumptions are made concerning the noise variables within the Kalman filter design: (1) They are independent, (2) They are random (white noise) with normal probability distribution, and (3) They are constant with each time step. Defining ̂ as a priori state estimate (without knowledge of current process measurement zk), and ̂ as the posteriori state estimate (with knowledge of the current process measurement), two estimation errors can be defined as: ̂ Where
̂
(11)
represent the true state of the system. The corresponding error covariance is found by the following equation. ) = E(ek
(12)
Where, E[x] is the expected value of x against a normal distribution. During each sampling cycle of the discrete system Kalman filter performs a time update and a measurement update. Further details can be found in13, but for brevity the equations for those updates are given below. The time update of the discrete Kalman filter is given by the following equation. ̂
̂ (13)
And the measurement update of the discrete Kalman filter is computed by the following equation Kk = HT (H HT + R)−1 ̂ ̂ Kk (zk − H ̂ . Pk = (I − Kk H) Where I ϵ R
nxn
th
is the n order identity matrix.
(14)
Parametric Auto-Regressive State Estimator: - Parameter estimation is well-established theory with numerous methods exist to compute parameters of Auto-Regressive with eXternal input (ARX) models based on a finite array of continuous or discrete time data series. The least squares method is the most common method used for estimating the model parameters21. Consider the (modified) continuous-time ARX process (pn + a1 pn−1 + · · · + an) y(t) = (b1pm + b2 pm-1 · · · + bm) u(t) + e(t)
(15)
where p denotes the differentiation operation, y(t) is the output, u(t) is the input, and e(t) is estimation error represented by continuous-time white noise source21. With substitution of derivatives by numerical approximations (pn ~ Dn) a new realization of equation (15) is derived21. ω(t) = φT(t) θ + e(t) where
(16)
ω(t) = Dn y(t) φT(t)= [−Dn−1y(t) · · · −D0y(t) Dmu(t) Dm−1u(t) · · ·D0u(t)] θ= [a1 · · · a , b1 b2 · · · bm]
where e(t) is the estimation error. This model can be viewed as a discrete-time linear regression. It is of interest to find an estimate ̂ to the parameter vector θ. Using the least squares approach reported in21, the parameter estimate vector can be found by the following formula assuming that y(t) and its all derivatives Dn y(t) are uncorrelated with e(t). ̂ = [E{φ(t) φT(t)}]−1 [E{φ(t) ω(t)}]
(17)
Where E(·) denotes the covariance function. Inserting the estimate parameters ̂ into equation (16), the linear ARX model is developed for the system whose history data are used to compose the φT(t) matrix. Adaptive Neuro-Fuzzy Inference System State Estimator: - For most cases, and in this design, the Gaussian type membership function show below is used for the ANFIS model development. μA(x) =
|
|
(18)
In equation 18, values for a, b, and c are the premise parameters to be optimized for a given system during the training of the ANFIS estimation model. Similarly the ANFIS model consists of consequent parameters, which are found in the fourth layer of the node output function. Every node in this layer has node function defined as Oi = ̅ fi = ̅ (gi x + qi y + r) s.t. ̅ =∑
;
for i = 1 → R
= {(μ1(x1), μ2(x2), . . . , μj(xn)}
(19)
Where R is the number of rules within the fuzzy inference system, j is the number of membership functions, and n is the number of inputs. In most fuzzy inference systems, j is less than n, and does not exceed three (3) membership functions. These parameters are also optimized during the training of the ANFIS. Consequent parameters for this model are the values for g, q, and r. The single output decision of the ANFIS is found by summation of the output of the individual node functions. ̂
∑
(20)
In the final implementation, the distributed networked control system utilized a predictive control strategy by adding the state estimation to the control nodes as shown in Figure 3. The distributed feedback gains were designed, as explained in5, for the MAPSS turbine engine linear models using an optimization process to generate desired step responses. Linear state space models were extracted for various operating points of the turbine engine. These quiescent points were arbitrarily chosen on the flight envelop of an aircraft. Additionally, discrete analysis is performed on the engine linear models to determine the Minimum Allowable Transmission Interval (MATI) for each operating region, and as a result for the entire turbine engine as
a complete nonlinear system. The MATI time is used to determine network design parameters and to provide a threshold for the state estimation process during implementation and testing of the predictive control strategy. When the measured state transmission rate approaches the established MATI for the turbine engine, the state estimator is activated and the estimated state is utilized by the controller node instead of the transmitted state. For proof of concept simulation test results are presented in the next section.
Figure 3. Distributed Networked Control System with State Estimators
IV. Test and Performance Evaluation Linear models were developed for military grade turbine engine nonlinear model using the Modular AeroPropulsion System Simulation (MAPSS) provided by NASA5. The MAPSS, developed in the MATLAB/Simulink environment, is a non-real time, multi-rate simulation of a modern high-pressure ratio, dual-spool, low bypass, variable cycle, military-type engine, with a digital controller. The model has three operating conditions: Power Lever Angle (PLA), Flight Altitude (Alt), and Plane Mach number (Mac); three inputs: fuel flow, nozzle exit area, and bypass exit area; and three outputs: low and high pressure spool speeds, and the ambient core metal temperature. The third output is a function of multiple measurements from various temperature sensors within the engine. The three engine states are the low pressure spool speed (xnl), high pressure spool speed (xnh), and the system core metal temperature (Tmpc). The final implementation architecture of the above developed distributed networked control system (DNCS) is shown in Figure 4. The main simulation results using Matlab environment are shown in Figure 5. Testing on the linearized model of the MAPSS turbine engine is performed to verify the performance of the DNCS with predictive control implementation in the form of state estimator and the communication network in place. The results of this test are shown in Figure 5 for each individual predictive/estimation method. Four plots are shown on each graph; performance of the base-control system with no networked interface, the control system with networked interface but without state estimator, the control system with an estimator but without network interface, and the final and complete system implementation with networked interface and state estimator. Also, each predictive method is tested for three types of network delay; sample delay, static time delay, and variable (random) time delay. The aim is to consider the breadth of effect of the network health on the performance of the distributed controller. On each plot the red line indicates the DNCS design performance, while the blue line indicates the ideal performance objectives. Figure 5 depicts the ANFIS state estimator performance in minimizing the network effects on the control system using only one side of the communication network, i.e., sensor to controller. The other communication sides of the control nodes are implemented with ideal transmission. The ANFIS performed very well at tracking the base-control system output; offering a precise state estimate. Concerning system recovery, this estimation model also succeeded as did the other two sate estimation algorithms. Their performance is omitted here for brevity. Because of the satisfactory results obtained from implementing the ANFIS state estimation model on one side of the communication network, a complete network implementation is conducted for the same system setup. The results are shown in Figure 6. In this test, the network transmission occurs on both ends of the distributed controller. With the full network implementation, the networked system with ANFIS state estimator performance still holds better than the networked system without a state estimator under all network delayed conditions.
Xnl (rpm)
Xnl (rpm)
Figure 4. DNCS Full Implementation Architecture
Time (Sec)
Xnl (rpm)
Xnl (rpm)
Time (Sec)
Time (Sec)
Time (Sec)
Figure 5. Performance of the DNCS with ANFIS and One Side Communication Network and One State Estimation (Xnl) a) No delay, b) Sample hold delay, c) Static time delay, and d) Random time delay.
Figure 6. Performance of the DNCS with ANFIS Estimator, Full Network Implementation and One State Estimation (Xnl) a) No delay, b) Sample hold delay, c) Static time delay, and d) Random time delay.
V. Conclusion In this paper, a Distributed Networked Control System utilizing a predictive control strategy was developed and implemented on turbine engine simulation model. As result, the turbine engine distributed control system was implemented in the form of individual smart processing nodes. These smart nodes (local controllers) consisted of individual communication modules and processing units that allow for local control actions. Signals between the engine’s sensors and actuators are transmitted across a dedicated communication network. A predictive control strategy was also developed and implemented utilizing local state estimators providing the needed information for the individual feedback controllers. Detail development and implementation information of completed control strategy was presented in the paper. Test results obtained from the half (one side) and the full (two sides) implementation of the communication network of the distributed networked control system showed performance robustness against network effects and failures. The distributed network control system
was able to maintain acceptable engine performance with failures in the communication network in the form of statics and random transmission delay time. Such robustness of the engine performance under moderate and sever network failures was attributed to the success of the state estimator in estimating the needed engine states feedback information for the local distributed controller.
Acknowledgment This work was funded in part by the Boeing Company and the US Air Force (AFRL). The authors would like to acknowledge both Boeing and AFRL for funding of this work. Also the authors would like to acknowledge NASA for provide the MAPSS turbine engine simulation software.
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