US 20090012773 A1
A control system representing a non-linear system may be modeled in block diagram form in a graphical environment. A linear model based on the block diagram may be generated. The linear model may then be used to design and tune the control system.
1. A computer-readable medium configured to store instructions executable by at least one processor to cause the at least one processor to:
provide a graphical user interface (GUI) associated with a control system, the GUI including a signal configuration input, an operating points input and a design tool input;
provide a first screen in response to selection of the signal configuration input received via the GUI, the first screen configured to allow a user to view signals associated with at least one control device in the control system and to configure settings for selected ones of the signals;
provide a second screen in response to selection of the operating points input received via the GUI, the second screen configured to allow the user to provide an operating point for the at least one control device;
provide a third screen in response to selection of the design tool input by the user, the third screen being configured to allow the user to specify performance constraints and design specifications to be used by a design tool for designing the control system; and
provide an interface configured to:
execute a linearization of a model of the control system relative to the at least one control device and the operating point for the at least one control device, and
import the linearization into the design tool.
2. The computer-readable medium of
3. The computer-readable medium of
4. The computer-readable medium of
map at least some performance constraints and design specifications into the design tool.
5. The computer-readable medium of
provide a fourth screen in response to selection of the closed loop response input by the user, the fourth screen being configured to allow the user to view a response of the control system based on the settings of the signals.
6. The computer-readable medium of
update a block diagram model of the control system in response to selection of the update model input.
7. The computer-readable medium of
8. The computer-readable medium of
9. The computer-readable medium of
allow a user to identify parts of the model of the control system that are to be linearized.
10. The computer-readable medium of
linearize at least portions of the model based on the identified parts.
11. A computer-implemented method, comprising:
displaying a block diagram model of a control system;
receiving input, from a user, identifying a portion of the control system;
receiving input, from the user, selecting closed loop signals associated with the identified portion of the control system;
receiving input, from the user, identifying performance constraints and design specifications for the control system;
generating a linearized model of the identified portion of the control system based on the block diagram model and the closed loop signals;
importing the linearized model into a design tool;
mapping, by the design tool, a response of the control system using the linearized model; and
providing a graphical view of the mapped response of the control system.
12. The computer-implemented method of
determining a performance level of the control system based on the mapped response and the design specifications.
13. The computer-implemented method of
updating the block diagram model based on the performance level.
14. The computer-implemented method of
receiving, from the user, information specifying an equilibrium condition for the control system.
15. The computer-implemented method of
performing a trim analysis to generate a set of operating points for the control system that satisfy the equilibrium condition.
16. The computer-implemented method of
providing, a graphical user interface (GUI) to the user, the GUI including at least one screen configured to allow the user to modify the performance constraints and design specifications for the control system and to tune the control system.
17. The computer-implemented method of
18. A system, comprising:
means for displaying a block diagram representing a control system;
means for allowing a user to identify at least a portion of the control system;
means for allowing the user to identify closed loop signals and set operating points for at least one element of the control system;
means for allowing the user to specify at least one of a performance constraint or a design specification for the at least one element of the control system;
means for generating a linearized model of the identified portion of the control system;
means for importing the linearized model into a design tool;
means for mapping, by the design tool, the at least one of the performance constraint or the design specification to at least one design criterion associated with the control system; and
means for tuning the control system based on the mapping.
19. The system of
means for determining a performance level of the control system based on the mapping.
20. The system of
21. The system of
This application is a continuation of U.S. patent application Ser. No. 10/991,899 filed Nov. 17, 2004, the disclosure of which is hereby incorporated by reference herein.
This application is related to “Tool For Design Of Multiple Single-Input-Single-Output Control Loops”, Attorney Docket No. MWS-094, filed on Jun. 15, 2004, the contents of which are hereby incorporated by reference.
The present invention relates to a method for analysis of control systems in a block diagram environment. Specifically, a linear model can be extracted to enable the use of design methodologies to design and tune control systems.
A dynamic system (either natural or man-made) is a system whose response at any given time is a function of its input stimuli, its current state, and the current time. Such systems range from simple to highly complex systems. Physical dynamic systems include a falling body, the rotation of the earth, bio-mechanical systems (muscles, joints, etc.), bio-chemical systems (gene expression, protein pathways), weather and climate pattern systems, etc. Examples of man-made or engineered dynamic systems include: a bouncing ball, a spring with a mass tied on an end, automobiles, airplanes, control systems in major appliances, communication networks, audio signal processing, nuclear reactors, a stock market, etc.
Professionals from diverse areas such as engineering, science, education, and economics build mathematical models of dynamic systems in order to better understand system behavior as it changes with the progression of time. The mathematical models aid in building “better” systems, where “better” may be defined in terms of a variety of performance measures such as quality, time-to-market, cost, speed, size, power consumption, robustness, etc. The mathematical models also aid in analyzing, debugging and repairing existing systems (be it the human body or the anti-lock braking system in a car). The models may also serve an educational purpose of educating others on the basic principles governing physical systems. The models and results are often used as a scientific communication medium between humans. The term “model-based design” is used to refer to the use of graphical models in the development, analysis, and validation of dynamic systems.
Dynamic systems are typically modeled in simulation environments as sets of differential, difference, and/or algebraic equations. At any given instant of time, these equations may be viewed as relationships between the system's output response (“outputs”), the system's input stimuli (“inputs”) at that time, the current state of the system, the system parameters, and time. The state of the system may be thought of as a numerical representation of the dynamically changing configuration of the system. For instance, in a physical system modeling a simple pendulum, the state may be viewed as the current position and velocity of the pendulum. Similarly, a signal-processing system that filters a signal would maintain a set of previous inputs as the state. The system parameters are the numerical representation of the static (unchanging) configuration of the system and may be viewed as constant coefficients in the system's equations. For the pendulum example, a parameter is the length of pendulum and for the filter example; a parameter is the values of the filter taps.
In practice, except for the most basic systems, mathematical models for dynamic systems involve a complex set of mathematical transformations applied in some prescribed manner with the outputs of some transformations forming the inputs of others. Each elemental transformation may be viewed in isolation as a simple dynamic system falling into one of the categories listed above. Therefore, a complex dynamic system may be modeled as an interconnection of various simple dynamic systems.
A schematic representation of such an interconnection that has evolved over the years is the graphical model. Such graphical models have now become a standard means in textbooks, design papers, journal articles, and specifications to communicate the details of a dynamic system's behavior. Various classes of graphical models describe computations that can be performed on computational hardware, such as a computer, microcontroller, FPGA, and custom hardware. Classes of such graphical models include time-based block diagrams, such as those found within SIMULINK from The MathWorks, Inc. of Natick, Mass., state-based and flow diagrams, such as those found within STATEFLOW from The MathWorks, Inc. of Natick, Mass., data-flow diagrams, circuit diagrams, and software diagrams, such as those found in the Unified Modeling Language. A common characteristic among these various forms of graphical models is that they define semantics on how to execute the model.
Generally, graphical analysis and simulation methods, such as the block diagram method, are used in modeling for design, analysis, and synthesis of engineered systems. The visual representation allows for a convenient interpretation of model components and structure and provides a quick intuitive notion of system behavior. Block diagrams are a set of graphical connections between blocks to model a system. The individual blocks in a block diagram represent mathematical operations and output a result.
Conventional simulation models become more complex as models are developed that model more complex systems. Hundreds of thousands of blocks that represent primitive and aggregate mathematical operations may be present. To manage the complexity of such models, principles of partitioning, abstraction, and hierarchy are applied.
In addition to graphical based modeling or simulation, other applications can be utilized to model a system, such as a control system or dynamic system. For example, MATLAB provided by The MathWorks, Inc. of Natick, Mass., is an interactive programming and interpretive application that can implement a variety of computing tasks in engineering and science, while also having the ability to execute other executable programs. Some of the tasks that MATLAB can perform range from data acquisition and analysis to application development. The MATLAB environment integrates mathematical computing, visualization, and technical programming language. MATLAB includes built-in interfaces that provide access and import data from instruments, files, and external databases and programs.
In addition, MATLAB can integrate external routines written in C, C++, Fortran, and Java with MATLAB applications. As such, MATLAB provides an example of interactive programming and interpretive environments that can work in conjunction with C routines provided external to MATLAB including those provided by third party providers.
Control systems, specifically feedback control systems, can be designed and modeled based on conventional graphical model methodology. For example,
However, in real world applications a model of a plant and corresponding controller(s) is far more complex. Most control systems are MIMO (multi-input multi-output) in nature.
There is a need for an ability to analyze the behavior a controller within a control system to enable the controller to be designed or tuned. There is a further need for a graphical environment for interactively tuning design parameters and receiving feedback on how the tuning process affects a larger control system or dynamic system model. The present invention is directed toward further solutions to address these needs.
In accordance with one aspect, a computer-readable medium configured to store instructions executable by at least one processor is provided. The instructions cause the at least one processor to provide a graphical user interface (GUI) associated with a control system, the GUI including a signal configuration input, an operating points input and a design tool input. The instructions cause the at least one processor to provide a first screen in response to selection of the signal configuration input received via the GUI, the first screen configured to allow a user to view signals associated with at least one control device in the control system and to configure settings for selected ones of the signals. The instructions also cause the at least one processor to provide a second screen in response to selection of the operating points input received via the GUI, the second screen configured to allow the user to provide an operating point for the at least one control device. The instructions further cause the processor to provide a third screen in response to selection of the design tool input by the user, the third screen being configured to allow the user to specify performance constraints and design specifications to be used by a design tool for designing the control system. The instructions also cause the at least one processor to provide an interface configured to execute a linearization of a model of the control system relative to the at least one control device and the operating point for the at least one control device, and import the linearization into the design tool.
In accordance with another aspect, a computer-implemented method includes displaying a block diagram model of a control system, receiving input, from a user, identifying a portion of the control system, receiving input, from the user, selecting closed loop signals associated with the identified portion of the control system, and receiving input, from the user, identifying performance constraints and design specifications for the control system. The method also includes generating a linearized model of the identified portion of the control system based on the block diagram model and the closed loop signals and importing the linearized model into a design tool. The method further includes mapping, by the design tool, a response of the control system using the linearized model, and providing a graphical view of the mapped response of the control system.
In accordance with still another aspect, a system includes means for displaying a block diagram representing a control system, means for allowing a user to identify at least a portion of the control system, and means for allowing the user to identify closed loop signals and set operating points for at least one element of the control system. The system also includes means for allowing the user to specify at least one of a performance constraint or a design specification for the at least one element of the control system, means for generating a linearized model of the identified portion of the control system, and means for importing the linearized model into a design tool. The system further includes means for mapping, by the design tool, the at least one of the performance constraint or the design specification to at least one design criterion associated with the control system and means for tuning the control system based on the mapping.
The present invention will become better understood with reference to the following description and accompanying drawings, wherein:
The design of control systems using full non-linear/hybrid models can be mathematically intractable given the complexity of many industrial high fidelity models. A common approach to the analysis of these complex models is to develop an approximation to the non-linear behavior through a process known as linearization. The illustrative embodiment of the present invention provides a framework to let users systematically analyze, and design controllers for, complex non-linear dynamic systems modeled in a simulation based block diagram environment. The elements controllers refer to gains or dynamic systems whose structure and parameterizations are the subject of the design of the control system. In graphical block diagram languages, controllers refer to individual elements or elements grouped in individual subsystems or sub-models. By systematically extracting linearized models from non-linear plant models (block diagrams), users can leverage the vast array of control design and tuning methodologies available for linear systems.
The present invention can provide a link between non-linear modeling in graphical environments and the development of controllers for linearizations of these models around user-specified operating points. The invention automatically imports linearizations into an existing GUI that has highly developed analysis and design procedures. The present invention also allows for users to mark relevant signals for specifying and assessing the performance of the control system. These signals include reference, disturbance, feedback, and measured outputs. The marking of the signals allows for complex side effects, such as cross-coupling and exogenous disturbances, to be viewable and can be handled in real-time during a design. In addition to marking signals, users also may specify constraints on the dynamics of the system.
This generalized model structure can be used for batch simulation, gain scheduling, and Monte Carlo techniques. Also, the user can move back and forth seamlessly between the linear and non-linear models. The ability to switch between linear and non-linear models allows for the rapid prototyping of linear controllers for non-linear systems. Further, mapping a MIMO non-linear physical model to the generalized LFT representation allows users to model non-linear controllers, Smith and model-predictive controllers, and other specialized control design techniques.
An embodiment of the invention can be used with MIMO systems. The invention can provide the ability to design MIMO control systems by designing each element and viewing the response of the closed loop system automatically. Input/Output (I/O) channels and closed-loop responses that are used by designers to verify that they have met the performance constraints on the signals and the design specifications of the control system individually. In one implementation, visual results can be immediately viewable in a graphical environment.
Accordingly, the present invention may be useful in the use of design tools that lend to the design of any type of linear time-invariant (LTI) model, including but not limited to continuous, discrete, hybrid, and multi-rate models, models with time delays, and models specified by measured frequency response data. Embodiments of the present invention can provide insight into time responses (time-domain behavior) of control systems, as well as frequency-domain characteristics, and poles and zero dynamics. A number of different linear analysis techniques can be employed within this framework.
In addition to analytical design techniques such as root locus and Bode or Nichols loop shaping, the framework of the present invention supports the deployment of systematic, automated tuning techniques, such as direct search, genetic algorithms, gradient-based optimization. These techniques can optimize a variety of time and frequency-domain criteria.
An example of the ability to isolate individual elements in a plant system may be seen in
According to an embodiment of the invention, a method 800 is illustrated in
With the selection of the signals, step 820, the method 800 can use linearization tools available in SIMULINK and other simulation environments to extract, step 840, a linear model of the model relative to the signals. The linearization tool uses exact small signal linearization or large signal linearization tools such as black box models and describing functions to automatically extract a linear model at specified operating points. These linear models relate the effect of reference and disturbance input changes on the response of the control system. The linearization tool is known to those of ordinary skill in the art, and can have many different forms.
The process of exact small scale linearization is the approximation of complex physical models that yields a sufficiently simple model for engineering analysis tools. Exact small scale linearization is a well-known commonly used analysis tool that has been documented in many control textbooks. A fundamental principle of exact small scale linearization analysis is that the approximation of a complex physical model is accurate for regions near a baseline or operating point.
A large class of physical systems is typically modeled using sets of non-linear differential equations of motion. The differential equations are written in the form:
Exact small scale linearization approximates a set of non-linear differential equations: The approximation is about an operating point where the states are at a nominal value x(t)=x0 and the model inputs are at a nominal value u(t)=u0. Exact small scale linearization uses a first order Taylor series approximation of (3) to give
Defining variables about the operating point:
or more commonly described as
where the matrices
are known as the Jacobian matrices. It is the task of a block diagram programming language tools to find the matrices A, B, C, and D.
In many block diagram programming tools, physical models can be described by both continuous differential equations and discrete equations of motion. These systems are known as multi-rate systems. This more general description of a multi-rate system is described by
The typical approach for this type of problem is to approximate this multi-rate system by a single rate discrete system:
It is the task of a block diagram programming language tools to find the matrices A, B, C, and D. This is a well known and understood problem and has been implemented in many block diagram programming languages.
In addition to exact small scale linearization another methodology for extracting linear models is to use large scale linearization analysis known as describing function analysis. The describing function problem (see figure below) involves the selection of a linear filter, denoted as w(t), that approximates a non-linear operator n[u(t)] for a particular wave form u(t) that minimizes the integral square error over a time interval, T
The class of input wave forms applicable to the describing function approximation includes sinusoidal, random noise, and exponential inputs along with various input combinations.
The benefit of the describing function approach is that the approximation is a function of both the input signal and its amplitude. This method is used in many applications including aerospace applications to capture the effects of non-linearities on a feedback system.
A final method for the linearization of a non-linear system is through the use of black box modeling methodologies. This is an approach that is taken when the exact small scale or large scale linearizations are not applicable to a problem. Typically, when a system is described by both event and time based dynamics, small and large scale linearization approaches are not applicable. Internal combustion engine control problems are applications that are usually described as both event (combustion events) and time (manifold filling dynamics) based dynamics. The fundamental idea behind these methodologies is to use simulation to generate a set of data that is used to fit a black box model. The details of the model fitting are specific to each approach that is taken. Black box modeling methodologies are well known as engineering tools and are implemented in add-on products to MATLAB such as the System Identification Toolbox or the spectral estimation tools in the Signal Processing Toolbox. Once linearization is complete, users can have a generalized linear fractional representation of their model that is automatically loaded into a design tool.
The operating points of a physical model define its total “state” at any given time. For example, for a model of a car engine, the operating points are typically described by variables such as engine speed, throttle angle, engine temperature, and the surrounding atmospheric condition. The behavior or what it typically known as the “dynamics” of the model are generally affected by the levels of the operating points. In block diagram programming languages, such as SIMULINK, the user can specify the operating points through settings in each block in the model. The operating points may be specified in the provided plant model (step 810) or as a specified design constraint (step 830) in the sequence of steps discussed in
In SIMULINK and all other block diagram simulation tools there are two commonly used approaches to specifying equilibrium conditions of a physical model. The first method is that the users employ their intuitive knowledge about the system to pick an equilibrium condition. This can be a very time consuming and difficult process due to the large number of operating points that must be specified in a complicated physical model. The second option is to employ an approach known as trim analysis. The approach is to use optimization to solve for a set of operating points that satisfy the equilibrium conditions.
Trim analysis works well for small models, but for large models, initial guesses of the values x(t), x1(k1), . . . , xi(ki) and u(t) must be chosen very close to an equilibrium operating point. This can be a problem since there are a large number of unknown variables that must be specified. Another approach is to utilize simulation to recover a set of equilibrium conditions. Simulation based operating points can be generated with SIMULINK CONTROL DESIGN using the time-based and trigger-based operating point snapshot feature. The time-based operating point snapshot creates a snapshot of the operating point when the simulation clock reaches the time specified by the user. The trigger-based operating point snapshot generates an operating point when triggered.
The user can select a design methodology to tune or design the control elements in the system. An important aspect of this framework is that many well-known methodologies can be leveraged to seamlessly assist in the design of the feedback controllers. For example since linear models can be extracted from the non-linear block diagram, classical methodologies such as Bode plots and root locus can be employed. Additionally, more advanced control techniques, including H-infinity, optimal control, etc., can be used. The tool can then automatically map user-defined performance constraints and design specifications on the control system to problem specific requirements on these advanced control techniques. For example, in the case of a second order performance constraint such as a step response, or overshoot is mapped to restricted pole locations on a root locus or closed magnitude response curves on a Nichols plot.
Once controllers are tuned and/or analyzed, the block diagram in which they belong, can be updated, step 860. For example, the controller can be uploaded to a SIMULINK model which can validate the controller against a full scale non-linear model. In addition to updating the controller elements in a model, the operating point can also be updated. For example, a user may specify a steady state operating point before the controller is updated. When the controller has been updated the user can be given tools to ensure that the equivalent steady state operating point is maintained.
According to embodiments of the invention, control design in SIMULINK can be an integrated environment. Tools and GUIs can interact to develop models, set operating points, linearize as needed, launch design tools, step 850, and export completed compensator designs back to SIMULINK. According to embodiments of the invention, using a graphical user interface, a user can systematically design and tune controllers in real time. The GUI will allow users to see the results of their tuning in real-time. Cross-coupling and other parasitic effects are immediately viewable. For MIMO systems, a user may simultaneously tune multiple controllers and immediately view responses.
A further example of a GUI according to an embodiment of the invention will be discussed in relation to
A GUI 1000 is illustrated having a block diagram model 1010 of an idle speed controller for a spark ignition engine. The block diagram model 1010 can be used to control the engine speed based on changes in the speed references and torque disturbances. Therefore, in the present example, three closed loop signals are selected to be designed: the reference speed step 1020, the torque disturbance 1040 and the vehicle dynamics 1060. The engine speed 1080 output can be displayed on a scope 1100.
With reference to
A further example of implementing the invention with SIMULINK can be summarized in a four-step, model-based design process. The first step occurs in SIMULINK. A plant model is developed and a control structure is defined. Any block diagram based MathWorks tools for modeling may be used, including, for example, the SIGNAL PROCESSING BLOCKSET, STATEFLOW, and SIMULINK FIXED POINT.
Step two involves SIMULINK CONTROL DESIGN. In this step, a user can specify which parts of the block diagram model to be linearized. SIMULINK CONTROL DESIGN has algorithms that analyze the block diagram to determine which blocks must be involved to correctly linearize the subsystem you have selected. Therefore, the user specifies closed loop signals, sets SIMULINK model operating points and establishes control system design specifications and performance constraints for specific signals in the block diagram. These design specifications and performance constraints can include many standard engineering requirements for a control system. These include 2nd order system specifications such as rise and settle time, overshoot constraints, reference tracking performance constraints along with control system design specifications such as gain, phase, and delay margin of a feedback loop. Performance constraints on the norm properties of signals in the system. These include H∞, L2, and L∞ constraints. The model is then linearized, enabling the use of a design tool.
Step three occurs in one or more analysis and/or design tools. The details of the linear model are loaded into the design tool. The user designs the compensator, optionally utilizing rapid prototyping. In this step, many MathWorks design tools may be used. Examples of possible design techniques include classical and modern control approaches, stochastic control, Kalman filtering, and model predictive control. The rapid prototyping techniques refer to synthesis routines such as H∞, H2, μ-Synthesis, LQG, LQR, and LTR. When a linear model is loaded into a design tool the performance constraints that a user imposes on a signal or design specifications on a feedback loop will mapped to specific design criterion. An example of this would be the mapping of 2nd order performance constraints like overshoot and settle time to the closed loop pole location on a root locus. Additionally gain, phase, and delay margins can be mapped to required constraints on Bode, Nyquist, and Nichols plots. The performance constraints and design specifications additionally can also be applied to the synthesis routines that are mentioned above. For example, the trade off between performance and stability is a well understood application in synthesis methods using weights on the resulting optimization problem. In this case the constraints and specifications from step two are mapped to this trade off. During the design process the response of the linear closed loop system can always be viewed in any linear response type plot. These response plots include step, impulse, Bode, Nyquist, Nichols, singular value, and pole zero plots. Included in the plots will be the performance constraints and design specifications that the user has employed. The closed and open loop linear responses of the control system can be examined and the results of the design can be exported back to SIMULINK.
In step four, once a candidate compensator design is established, SIMULINK can be used to fully evaluate how well that design meets specifications. For example, a user can validate the design with the newly-designed compensator functioning in the block diagram model. The validation can be automated by comparing the user-defined design specifications to the resulting non-linear simulation. Simulations on the full non-linear physical model plus the compensator can be run. The Real Time Workshop can be used to speed up simulation or generate embeddable C-code.
The present invention can be implemented on an electronic device.
It should be noted that the electronic device 700 is merely representative of a structure for implementing the present invention. However, one of ordinary skill in the art will appreciate that the present invention is not limited to implementation on only the described device 700. Other implementations can be utilized, including an implementation based partially or entirely in embedded code, where no user inputs or display devices are necessary. In such an instance, a processor can communicate directly with another processor, or other device.
Examples of industries in which control systems are used include, but are not limited to, Aerospace, Automotive, Chemical, Biochemical/Pharmaceutical, Process (e.g., paper mills). Embodiments of the present invention may have broad applications to all these industries.
The present invention has been described by way of example, and modifications and variations of the described embodiments will suggest themselves to skilled artisans in this field without departing from the spirit of the invention. Aspects and characteristics of the above-described embodiments may be used in combination. The described embodiments are merely illustrative and should not be considered restrictive in any way. The scope of the invention is to be measured by the appended claims, rather than the preceding description, and all variations and equivalents that fall within the range of the claims are intended to be embraced therein.