Sliding Mode Control and Observation. The sliding mode keep an eye on technique has confirmed powerful in facing advanced dynamical platforms tormented by disturbances, uncertainties and unmodeled dynamics. Powerful keep an eye on know-how in accordance with this technique has been utilized to many real-world difficulties, particularly within. Sliding Mode Control and Observation provides the necessary tools for graduate students, researchers and engineers to robustly control complex and uncertain nonlinear dynamical systems. Exercises provided at the end of each chapter make this an ideal text for an advanced course taught in control theory. Sliding mode control implies that control actions are discontinuous state. If it would be enforced in the control system. First, in sliding mode the input s of the element implementing. Frencis, London. [The conventional theory is presented along with new methods of control and observation and new application areas]. Filippov, A., (1988. About this book. Sliding Mode Control and Observation represents the first textbook that starts with classical sliding mode control techniques and progresses toward newly developed higher-order sliding mode control and observation algorithms and their applications.
Download Book Sliding Mode Control And Observation Control Engineering in PDF format. You can Read Online Sliding Mode Control And Observation Control Engineering here in PDF, EPUB, Mobi or Docx formats.Sliding Mode Control And Observation
Author :Yuri ShtesselISBN :9780817648930
Genre :Science
File Size : 54.49 MB
Format :PDF, Mobi
Download :498
Read :1298
The sliding mode control methodology has proven effective in dealing with complex dynamical systems affected by disturbances, uncertainties and unmodeled dynamics. Robust control technology based on this methodology has been applied to many real-world problems, especially in the areas of aerospace control, electric power systems, electromechanical systems, and robotics. Sliding Mode Control and Observation represents the first textbook that starts with classical sliding mode control techniques and progresses toward newly developed higher-order sliding mode control and observation algorithms and their applications. The present volume addresses a range of sliding mode control issues, including: *Conventional sliding mode controller and observer design *Second-order sliding mode controllers and differentiators *Frequency domain analysis of conventional and second-order sliding mode controllers *Higher-order sliding mode controllers and differentiators *Higher-order sliding mode observers *Sliding mode disturbance observer based control *Numerous applications, including reusable launch vehicle and satellite formation control, blood glucose regulation, and car steering control are used as case studies Sliding Mode Control and Observation is aimed at graduate students with a basic knowledge of classical control theory and some knowledge of state-space methods and nonlinear systems, while being of interest to a wider audience of graduate students in electrical/mechanical/aerospace engineering and applied mathematics, as well as researchers in electrical, computer, chemical, civil, mechanical, aeronautical, and industrial engineering, applied mathematicians, control engineers, and physicists. Sliding Mode Control and Observation provides the necessary tools for graduate students, researchers and engineers to robustly control complex and uncertain nonlinear dynamical systems. Exercises provided at the end of each chapter make this an ideal text for an advanced course taught in control theory.
Sliding Mode Control
Author :Hebertt Sira-RamírezISBN :9783319172576
Genre :Science
File Size : 61.61 MB
Format :PDF, ePub, Mobi
Download :816
Read :407
This monograph presents a novel method of sliding mode control for switch-regulated nonlinear systems. The Delta Sigma modulation approach allows one to implement a continuous control scheme using one or multiple, independent switches, thus effectively merging the available linear and nonlinear controller design techniques with sliding mode control. Sliding Mode Control: The Delta-Sigma Modulation Approach, combines rigorous mathematical derivation of the unique features of Sliding Mode Control and Delta-Sigma modulation with numerous illustrative examples from diverse areas of engineering. In addition, engineering case studies demonstrate the applicability of the technique and the ease with which one can implement the exposed results. This book will appeal to researchers in control engineering and can be used as graduate-level textbook for a first course on sliding mode control.
Sliding Mode Control In Engineering
Author :Wilfrid PerruquettiISBN :0203910850
Genre :Technology & Engineering
File Size : 65.91 MB
Format :PDF, ePub
Download :230
Read :405
Provides comprehensive coverage of the most recent developments in the theory of non-Archimedean pseudo-differential equations and its application to stochastics and mathematical physics--offering current methods of construction for stochastic processes in the field of p-adic numbers and related structures. Develops a new theory for parabolic equat
Recent Trends In Sliding Mode Control
Author :Leonid FridmanISBN :9781785610769
Genre :Technology & Engineering
File Size : 30.45 MB
Format :PDF
![And And](/uploads/1/3/3/8/133866047/407907134.gif)
Download :252
Read :382
In control theory, sliding mode control, or SMC, is a nonlinear control method that alters the dynamics of a nonlinear system by application of a discontinuous control signal that forces the system to 'slide' along a cross-section of the system's normal behaviour. This book describes recent advances in the theory, properties, methods and applications of SMC. The book is organised into four parts. The first part is devoted to the design of higher-order sliding-mode controllers, with specific designs presented in the context of disturbance rejection by means of observation and identification. The second part offers a set of tools for establishing different dynamic properties of systems with discontinuous right-hand sides. Time discretization is addressed in the third part. First-order sliding modes are discretized using an implicit scheme - higher-order sliding-mode differentiators, typically used in output-feedback schemes, are discretized in such a way that the optimal accuracy of their continuous-time counterparts is restored. The last part is dedicated to applications. In the context of energy conversion, sliding-mode control is applied to variable-speed wind turbines, fuel cell coupled to a power converter, rugged DC series motors and rectifiers with unity power factor, and electropneumatic actuator. Finally, an event-triggered sliding-mode scheme is proposed for networked control systems subject to packet loss, jitter and delayed transmissions.
Advances And Applications In Sliding Mode Control Systems
Author :Ahmad Taher AzarISBN :9783319111735
Genre :Computers
File Size : 55.50 MB
Format :PDF, ePub, Docs
Download :261
Read :391
This book describes the advances and applications in Sliding mode control (SMC) which is widely used as a powerful method to tackle uncertain nonlinear systems. The book is organized into 21 chapters which have been organised by the editors to reflect the various themes of sliding mode control. The book provides the reader with a broad range of material from first principles up to the current state of the art in the area of SMC and observation presented in a clear, matter-of-fact style. As such it is appropriate for graduate students with a basic knowledge of classical control theory and some knowledge of state-space methods and nonlinear systems. The resulting design procedures are emphasized using Matlab/Simulink software.
Advanced And Optimization Based Sliding Mode Control Theory And Applications
Author :Antonella FerraraISBN :9781611975840
Genre :Mathematics
File Size : 63.99 MB
Format :PDF, ePub, Mobi
Download :758
Read :1100
A compendium of the authors’ recently published results, this book discusses sliding mode control of uncertain nonlinear systems, with a particular emphasis on advanced and optimization based algorithms. The authors survey classical sliding mode control theory and introduce four new methods of advanced sliding mode control. They analyze classical theory and advanced algorithms, with numerical results complementing the theoretical treatment. Case studies examine applications of the algorithms to complex robotics and power grid problems. Advanced and Optimization Based Sliding Mode Control: Theory and Applications is the first book to systematize the theory of optimization based higher order sliding mode control and illustrate advanced algorithms and their applications to real problems. It presents systematic treatment of event-triggered and model based event-triggered sliding mode control schemes, including schemes in combination with model predictive control, and presents adaptive algorithms as well as algorithms capable of dealing with state and input constraints. Additionally, the book includes simulations and experimental results obtained by applying the presented control strategies to real complex systems. This book is suitable for students and researchers interested in control theory. It will also be attractive to practitioners interested in implementing the illustrated strategies. It is accessible to anyone with a basic knowledge of control engineering, process physics, and applied mathematics.
Applied Computer Sciences In Engineering
Author :Juan Carlos Figueroa-García![Control Control](/uploads/1/3/3/8/133866047/183636161.png)
Genre :Computers
File Size : 37.99 MB
Format :PDF, Kindle
Download :419
Read :991
This two-volume set (CCIS 915 and CCIS 916) constitutes the refereed proceedings of the 5th Workshop on Engineering Applications, WEA 2018, held in Medellín, Colombia, in October 2018. The 41 revised full papers presented in this volume were carefully reviewed and selected from 101 submissions. The papers are organized in topical sections such as green logistics and optimization, Internet of Things (IoT), digital signal processing (DSP), network applications, miscellaneous applications.
Sliding Mode Control For Synchronous Electric Drives
Author :Sergey E. RyvkinISBN :9780203181386
Genre :Technology & Engineering
File Size : 67.57 MB
Format :PDF, Mobi
Download :515
Read :808
This volume presents the theory of control systems with sliding mode applied to electrical motors and power converters. It demonstrates the methodology of control design and the original algorithms of control and observation. Practically all semiconductor devices are used in power converters, that feed electrical motors, as power switches. A switching mode offers myriad attractive, inherent properties from a control viewpoint, especially a sliding mode. Sliding mode control supplies high dynamics to systems, invariability of systems to changes of their parameters and of exterior loads in combination with simplicity of design. Unlike linear control, switching sliding mode control does not replace the control system, but uses the natural properties of the control plant system effectively to ensure high control quality. This is the first text that thoroughly describes the application of the highly theoretical control design approach to synchronous drives in practice. It examines in detail the different features of various types of synchronous motors and converters with regard to sliding mode control design. It further presents a detailed analysis of control issues and mechanical coordinate observation design for various types of synchronous motors, of power converters, and various drive control structures. It also discusses the digital implementation of control, observation and identification algorithms. The potential of sliding mode control and observation are moreover demonstrated in numerical and experimental results from real control plants. This work is intended for professionals and advanced students who work in the field of electric drive control. It is also recommended to experts in control theory application, who work with sliding modes for the control of electrical motors and power converters.
Deterministic Control Of Uncertain Systems
Author :Alan S. I. ZinoberISBN :0863411703
Genre :Technology & Engineering
File Size : 40.65 MB
Format :PDF, Docs
Download :338
Read :841
Includes sections on: Sliding mode control with switching command devices. Hyperplane design and CAD of variable structure control systems. Variable structure controllers for robots. The hyperstability approach to VSCS design. Nonlinear continuous feedback for robust tracking. Control of uncertain systems with neglected dynamics. Control of infinite dimensional plants.
Modern Sliding Mode Control Theory
Author :Giorgio BartoliniISBN :9783540790150
Genre :Technology & Engineering
File Size : 78.21 MB
Format :PDF, ePub
Download :136
Read :970
This concise book covers modern sliding mode control theory. The authors identify key contributions defining the theoretical and applicative state-of-the-art of the sliding mode control theory and the most promising trends of the ongoing research activities.
Top Download:
In control theory, a state observer is a system that provides an estimate of the internal state of a given real system, from measurements of the input and output of the real system. It is typically computer-implemented, and provides the basis of many practical applications.
Knowing the system state is necessary to solve many control theory problems; for example, stabilizing a system using state feedback. In most practical cases, the physical state of the system cannot be determined by direct observation. Instead, indirect effects of the internal state are observed by way of the system outputs. A simple example is that of vehicles in a tunnel: the rates and velocities at which vehicles enter and leave the tunnel can be observed directly, but the exact state inside the tunnel can only be estimated. If a system is observable, it is possible to fully reconstruct the system state from its output measurements using the state observer.
- 1Typical observer model
- 2State observers for nonlinear systems
Typical observer model[edit]
Discrete-time case[edit]
The state of a linear, time-invariant physical discrete-time system is assumed to satisfy
where, at time , is the plant's state; is its inputs; and is its outputs. These equations simply say that the plant's current outputs and its future state are both determined solely by its current states and the current inputs. (Although these equations are expressed in terms of discrete time steps, very similar equations hold for continuous systems). If this system is observable then the output of the plant, , can be used to steer the state of the state observer.
The observer model of the physical system is then typically derived from the above equations. Additional terms may be included in order to ensure that, on receiving successive measured values of the plant's inputs and outputs, the model's state converges to that of the plant. In particular, the output of the observer may be subtracted from the output of the plant and then multiplied by a matrix ; this is then added to the equations for the state of the observer to produce a so-called Luenberger observer, defined by the equations below. Note that the variables of a state observer are commonly denoted by a 'hat': and to distinguish them from the variables of the equations satisfied by the physical system.
The observer is called asymptotically stable if the observer error converges to zero when . For a Luenberger observer, the observer error satisfies . The Luenberger observer for this discrete-time system is therefore asymptotically stable when the matrix has all the eigenvalues inside the unit circle.
For control purposes the output of the observer system is fed back to the input of both the observer and the plant through the gains matrix .
The observer equations then become:
or, more simply,
Due to the separation principle we know that we can choose and independently without harm to the overall stability of the systems. As a rule of thumb, the poles of the observer are usually chosen to converge 10 times faster than the poles of the system .
Continuous-time case[edit]
The previous example was for an observer implemented in a discrete-time LTI system. However, the process is similar for the continuous-time case; the observer gains are chosen to make the continuous-time error dynamics converge to zero asymptotically (i.e., when is a Hurwitz matrix).
For a continuous-time linear system
where , the observer looks similar to discrete-time case described above:
- .
The observer error satisfies the equation
- .
The eigenvalues of the matrix can be made arbitrarily by appropriate choice of the observer gain when the pair is observable, i.e. observability condition holds. In particular, it can be made Hurwitz, so the observer error when .
Peaking and other observer methods[edit]
When the observer gain is high, the linear Luenberger observer converges to the system states very quickly. However, high observer gain leads to a peaking phenomenon in which initial estimator error can be prohibitively large (i.e., impractical or unsafe to use).[1] Idm 6.18 full crack raritan. As a consequence, nonlinear high gain observer methods are available that converge quickly without the peaking phenomenon. For example, sliding mode control can be used to design an observer that brings one estimated state's error to zero in finite time even in the presence of measurement error; the other states have error that behaves similarly to the error in a Luenberger observer after peaking has subsided. Sliding mode observers also have attractive noise resilience properties that are similar to a Kalman filter.[2][3]Another approach is to apply multi observer, that significantly improves transients and reduces observer overshoot. Multi observer can be adapted to every system where High Gain Observer is applicable.[4]
State observers for nonlinear systems[edit]
Sliding mode observers can be designed for the non-linear systems as well. For simplicity, first consider the no-input non-linear system:
where . Also assume that there is a measurable output given by
There are several non-approximate approaches for designing an observer. The two observers given below also apply to the case when the system has an input. That is,
- .
Linearizable error dynamics[edit]
One suggestion by Krener and Isidori[5] and Krener and Respondek[6] can be applied in a situation when there exists a linearizing transformation (i.e., a diffeomorphism, like the one used in feedback linearization) such that in new variables the system equations read
The Luenberger observer is then designed as
- .
The observer error for the transformed variable satisfies the same equation as in classical linear case.
- .
As shown by Gauthier, Hammouri, and Othman[7]and Hammouri and Kinnaert,[8] if there exists transformation such that the system can be transformed into the form
then the observer is designed as
- ,
where is a time-varying observer gain.
Ciccarella, Dalla Mora, and Germani [9] obtained more advanced and general results, removing the need for a nonlinear transform and proving global asymptotic convergence of the estimated state to the true state using only simple assumptions on regularity.
Sliding mode observer[edit]
As discussed for the linear case above, the peaking phenomenon present in Luenberger observers justifies the use of a sliding mode observer. The sliding mode observer uses non-linear high-gain feedback to drive estimated states to a hypersurface where there is no difference between the estimated output and the measured output. The non-linear gain used in the observer is typically implemented with a scaled switching function, like the signum (i.e., sgn) of the estimated – measured output error. Hence, due to this high-gain feedback, the vector field of the observer has a crease in it so that observer trajectories slide along a curve where the estimated output matches the measured output exactly. So, if the system is observable from its output, the observer states will all be driven to the actual system states. Additionally, by using the sign of the error to drive the sliding mode observer, the observer trajectories become insensitive to many forms of noise. Hence, some sliding mode observers have attractive properties similar to the Kalman filter but with simpler implementation.[2][3]
As suggested by Drakunov,[10] a sliding mode observer can also be designed for a class of non-linear systems. Such an observer can be written in terms of original variable estimate and has the form
where:
- The vector extends the scalar signum function to dimensions. That is,
- for the vector .
- The vector has components that are the output function and its repeated Lie derivatives. In particular,
- where is the ithLie derivative of output function along the vector field (i.e., along trajectories of the non-linear system). In the special case where the system has no input or has a relative degree of n, is a collection of the output and its derivatives. Because the inverse of the Jacobian linearization of must exist for this observer to be well defined, the transformation is guaranteed to be a local diffeomorphism.
- The diagonal matrix of gains is such that
- where, for each , element and suitably large to ensure reachability of the sliding mode.
- The observer vector is such that
- where here is the normal signum function defined for scalars, and denotes an 'equivalent value operator' of a discontinuous function in sliding mode.
The idea can be briefly explained as follows. According to the theory of sliding modes, in order to describe the system behavior, once sliding mode starts, the function should be replaced by equivalent values (see equivalent control in the theory of sliding modes). In practice, it switches (chatters) with high frequency with slow component being equal to the equivalent value. Applying appropriate lowpass filter to get rid of the high frequency component on can obtain the value of the equivalent control, which contains more information about the state of the estimated system. The observer described above uses this method several times to obtain the state of the nonlinear system ideally in finite time.
The modified observation error can be written in the transformed states . In particular,
and so
So:
- As long as , the first row of the error dynamics, , will meet sufficient conditions to enter the sliding mode in finite time.
- Along the surface, the corresponding equivalent control will be equal to , and so . Hence, so long as , the second row of the error dynamics, , will enter the sliding mode in finite time.
- Along the surface, the corresponding equivalent control will be equal to . Hence, so long as , the th row of the error dynamics, , will enter the sliding mode in finite time.
So, for sufficiently large gains, all observer estimated states reach the actual states in finite time. In fact, increasing allows for convergence in any desired finite time so long as each function can be bounded with certainty. Hence, the requirement that the map is a diffeomorphism (i.e., that its Jacobian linearization is invertible) asserts that convergence of the estimated output implies convergence of the estimated state. That is, the requirement is an observability condition.
In the case of the sliding mode observer for the system with the input, additional conditions are needed for the observation error to be independent of the input. For example, that
does not depend on time. The observer is then
Multi Observer[edit]
Multi observer extends High Gain Observer structure from single to multi observer, with many models working simultaneously. This has two layers: the first consists of multiple High Gain Observers with different estimation states, and the second determines the importance weights of the first layer observers. The algorithm is simple to implement and does not contain any risky operations like differentiation.[4] The idea of multiple models was previously applied to obtain information in adaptive control.[11]
- Multi Observer Schema
Assume that the number of High Gain Observers equals n+1
where is the observer index. The first layer observers consists of the same gain but they differ with the initial state . In the second layer all from observers are combined into one to obtain single state vector estimation
where are weight factors. These factors are changed to provide the estimation in the second layer and to improve the observation process.
Let assume that
and
where is some vector that depends on observer error .
Greatest hits tv show. Some transformation yields to linear regression problem
This formula gives possibility to estimate . To construct mainfold we need mapping between and ensurance that is calculable relying on measurable signals. First thing is to eliminate paeking phenomenon for from observer error
.
Free download dragon ball z game for windows 7. Calculate times derivative on to find mapping m lead to defined as
where is some time constant. Note that relays on both and its integrals hence it is easily available in the control system. Further is specified by estimation law; and thus it proves that mainfold is measurable. In the second layer for is introduced as estimates of coefficients. The mapping error is specified as
where . If coefficients are equal to , then mapping error Now it is possible to calculate from above equation and hence the peaking phenomenon is reduced thanks to properties of mainfold. The created mapping gives a lot of flexibility in the estimation process. Even it is possible to estimate the value of in the second layer and to calculate the state .[4]
Bounding observers[edit]
The Bounding [12] or Interval observers [13] constitute a class of observers that provide two estimationsof the state simultaneously: one of the estimations provides an upper bound on the real value of the state,whereas the second one provides a lower bound. The real value of the state is then known to be always within these twoestimations.
These bounds are very important in practical applications,[14][15] as they make possible to know at each time the precision of the estimation.
Mathematically, two Luenberger observers can be used, if is properly selected, using, for example, positive systems properties:[16] one for the upper bound (that ensures that converges to zero from above when , in the absence of noise and uncertainty), and a lower bound (that ensures that converges to zero from below). Tube increaser 2 1 cracked. That is, always
See also[edit]
References[edit]
- In-line references
- ^Khalil, H.K. (2002), Nonlinear Systems (3rd ed.), Upper Saddle River, NJ: Prentice Hall, ISBN978-0-13-067389-3
- ^ abUtkin, Vadim; Guldner, Jürgen; Shi, Jingxin (1999), Sliding Mode Control in Electromechanical Systems, Philadelphia, PA: Taylor & Francis, Inc., ISBN978-0-7484-0116-1
- ^ abDrakunov, S.V. (1983), 'An adaptive quasioptimal filter with discontinuous parameters', Automation and Remote Control, 44 (9): 1167–1175
- ^ abcBernat, J.; Stepien, S. (2015), 'Multi modelling as new estimation schema for High Gain Observers', International Journal of Control, 88 (6): 1209–1222, doi:10.1080/00207179.2014.1000380
- ^Krener, A.J.; Isidori, Alberto (1983), 'Linearization by output injection and nonlinear observers', System and Control Letters, 3: 47–52, doi:10.1016/0167-6911(83)90037-3
- ^Krener, A.J.; Respondek, W. (1985), 'Nonlinear observers with linearizable error dynamics', SIAM Journal on Control and Optimization, 23 (2): 197–216, doi:10.1137/0323016
- ^Gauthier, J.P.; Hammouri, H.; Othman, S. (1992), 'A simple observer for nonlinear systems applications to bioreactors', IEEE Transactions on Automatic Control, 37 (6): 875–880, doi:10.1109/9.256352
- ^Hammouri, H.; Kinnaert, M. (1996), 'A New Procedure for Time-Varying Linearization up to Output Injection', System and Control Letters, 28 (3): 151–157, doi:10.1016/0167-6911(96)00022-9
- ^Ciccarella, G.; Dalla Mora, M.; Germani, A. (1993), 'A Luenberger-like observer for nonlinear systems', International Journal of Control, 57 (3): 537–556, doi:10.1080/00207179308934406
- ^Drakunov, S.V. (1992), 'Sliding-Mode Observers Based on Equivalent Control Method', Proceedings of the 31st IEEE Conference on Decision and Control (CDC) (Tucson, Arizona, December 16–18): 2368–2370, doi:10.1109/CDC.1992.371368, ISBN978-0-7803-0872-5
- ^Narendra, K.S.; Han, Z. (August 2012). 'A new approach to adaptive control using multiple models'. International Journal of Adaptive Control and Signal Processing. 26 (8): 778–799. doi:10.1002/acs.2269. ISSN1099-1115.
- ^http://www.nt.ntnu.no/users/skoge/prost/proceedings/ecc03/pdfs/437.pdf
- ^http://www.nt.ntnu.no/users/skoge/prost/proceedings/cdc-2008/data/papers/1446.pdf
- ^http://www.iaeng.org/publication/WCE2010/WCE2010_pp656-661.pdf
- ^Hadj-Sadok, M.Z.; Gouzé, J.L. (2001). 'Estimation of uncertain models of activated sludge processes with interval observers'. Journal of Process Control. 11 (3): 299–310. doi:10.1016/S0959-1524(99)00074-8.
- ^Ait Rami, M., Tadeo, F., Helmke, U. (2011),'Positive observers for linear positive systems, and their implications',International Journal of Control 84
Sliding Mode Control And Observation Pdf Free
- General references
- Sontag, Eduardo (1998), Mathematical Control Theory: Deterministic Finite Dimensional Systems. Second Edition, Springer, ISBN978-0-387-98489-6
Sliding Mode Control Tutorial
Retrieved from 'https://en.wikipedia.org/w/index.php?title=State_observer&oldid=906459896'