332 research outputs found

    Design of generalized minimum variance controllers for nonlinear multivariable systems

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    The design and implementation of Generalized Minimum Variance control laws for nonlinear multivariable systems that can include severe nonlinearities is considered. The quadratic cost index minimised involves dynamically weighted error and nonlinear control signal costing terms. The aim here is to show the controller obtained is simple to design and implement. The features of the control law are explored. The controller obtained includes an internal model of the process and in one form is a nonlinear version of the Smith Predictor

    State dependent NGMV control of delayed piecewise affine systems

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    A Nonlinear Generalized Minimum Variance (NGMV) control algorithm is introduced for the control of delayed piecewise affine (PWA) systems which are an important subclass of hybrid systems. Under some conditions, discrete-time PWA systems can be transferred into their equivalent state dependent nonlinear systems form. The equivalent state dependent systems that include reference and disturbances models are very general. The process is assumed to include common delays in input or output channels of magnitude k. Then the NGMV control strategy [16] can be applied. The NGMV controller is related to a well-known and accepted solution for time delay systems but has the advantage that it can stabilize open-loop unstable processes [17]

    NGMV control of delayed piecewise affine systems

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    A Nonlinear Generalized Minimum Variance (NGMV) control algorithm is introduced for the control of piecewise affine (PWA) systems. Under some conditions, discrete-time PWA systems can be transferred into an equivalent state-dependent nonlinear system form. The equivalent state-dependent systems maintain the hybrid nature of the original PWA systems and include both the discrete and continuous signals in one general description. In a more general way, the process is assumed to include common delays in input or output channels of magnitude k. Then the NGMV control strategy [1] can be applied. The NGMV controller is related to a well-known and accepted solution for time delay systems (Smith Predictor) but has the advantage that it may stabilize open-loop unstable processes [2]

    Polynomial approach to nonlinear predictive generalized minimum variance control

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    A relatively simple approach to non-linear predictive generalised minimum variance (NPGMV) control is introduced for non-linear discrete-time multivariable systems. The system is represented by a combination of a stable non-linear subsystem where no structure is assumed and a linear subsystem that may be unstable and modelled in polynomial matrix form. The multi-step predictive control cost index to be minimised involves both weighted error and control signal costing terms. The NPGMV control law involves an assumption on the choice of cost-function weights to ensure the existence of a stable non-linear closed-loop operator. A valuable feature of the control law is that in the asymptotic case, where the plant is linear, the controller reduces to a polynomial matrix version of the well known generalised predictive control (GPC) controller. In the limiting case when the plant is non-linear and the cost-function is single step the controller becomes equal to the polynomial matrix version of the so-called non-linear generalised minimum variance controller. The controller can be implemented in a form related to a non-linear version of the Smith predictor but unlike this compensator a stabilising control law can be obtained for open-loop unstable processes

    Advances in Urban Traffic Network Equilibrium Models and Algorithms

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    Nonlinear predictive restricted structure control

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    This thesis defines new developments in predictive restricted structure control for industrial applications. It begins by describing the augmented system for both state-space and polynomial model descriptions. These descriptions can contain the plant model, the disturbance model, and any additional essential model subsystems. It then describes the predictive restricted structure control solution for both linear and nonlinear systems in state-space form. The solution utilizes the recent development in nonlinear predictive generalized minimum variance by adding a general operator subsystem that defines nonlinear system along with the linear or the linear parameter varying output subsystem. The next contribution is the polynomial predictive restricted structure control algorithm for polynomial linear parameter varying model that may result from nonlinear equations or experimental data-driven model identification. This algorithm utilizes the generalised predictive control method to approximate and control nonlinear systems in the linear parameter varying system inputoutput transfer operator matrices. The solution is simple in unconstrained and constrained optimization solutions and required a small computing capacity. Four examples have been chosen to test the algorithms for different nonlinear characteristics. In the first three examples, state-space versions of the algorithm for the linear, the quasi-linear parameter varying and the state-dependent were employed to control the quadruple tank process, electronic throttle body, and the continuous stirred tank reactors. In the last example, the polynomial linear parameter varying restricted structure controller is used to control automotive variable camshaft timing system.This thesis defines new developments in predictive restricted structure control for industrial applications. It begins by describing the augmented system for both state-space and polynomial model descriptions. These descriptions can contain the plant model, the disturbance model, and any additional essential model subsystems. It then describes the predictive restricted structure control solution for both linear and nonlinear systems in state-space form. The solution utilizes the recent development in nonlinear predictive generalized minimum variance by adding a general operator subsystem that defines nonlinear system along with the linear or the linear parameter varying output subsystem. The next contribution is the polynomial predictive restricted structure control algorithm for polynomial linear parameter varying model that may result from nonlinear equations or experimental data-driven model identification. This algorithm utilizes the generalised predictive control method to approximate and control nonlinear systems in the linear parameter varying system inputoutput transfer operator matrices. The solution is simple in unconstrained and constrained optimization solutions and required a small computing capacity. Four examples have been chosen to test the algorithms for different nonlinear characteristics. In the first three examples, state-space versions of the algorithm for the linear, the quasi-linear parameter varying and the state-dependent were employed to control the quadruple tank process, electronic throttle body, and the continuous stirred tank reactors. In the last example, the polynomial linear parameter varying restricted structure controller is used to control automotive variable camshaft timing system

    Restricted structure non-linear generalized minimum variance control

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    This research presents the Restricted Structure Non-linear Generalized Minimum Variance (RS-NGMV) algorithm for Linear Parameter-Varying (LPV) systems. The LPV systems are defined as linear plant subsystems within the control diagram and may include Non-linear (NL) input subsystems. The RS-NGMV control solution for the latter will be slightly different than the first one and have the capability of dealing with NL characteristics such as saturation, discontinuities and black-box terms. The controller is built in a low-order Restricted Structure (RS) in the form of a general z-transfer function. This brings forward two major advantages. First, it offers a high-order advanced control solution inside low-order control structures which are known for their natural robustness. Secondly, it is easier to operate and re-tune for the classically trained staff in the industry as it can be given the structures they are rather familiar with such as the PID. Another advantage of the RS-NGMV is its model-based design that enables a faster adaptation to implement different systems. Features of the RS-NGMV are investigated throughout the thesis with case studies from trends in engineering like robotics, autonomous and electric vehicles. The results show that the RS-NGMV is highly capable of adapting to set-point changes, parameter variations with its ability to update the control gains rapidly by using optimizations. Some extensions of algorithms have also been studied following recent directions in optimal/predictive control resulting in a new preview control approach and Scheduled RS-NGMV control.This research presents the Restricted Structure Non-linear Generalized Minimum Variance (RS-NGMV) algorithm for Linear Parameter-Varying (LPV) systems. The LPV systems are defined as linear plant subsystems within the control diagram and may include Non-linear (NL) input subsystems. The RS-NGMV control solution for the latter will be slightly different than the first one and have the capability of dealing with NL characteristics such as saturation, discontinuities and black-box terms. The controller is built in a low-order Restricted Structure (RS) in the form of a general z-transfer function. This brings forward two major advantages. First, it offers a high-order advanced control solution inside low-order control structures which are known for their natural robustness. Secondly, it is easier to operate and re-tune for the classically trained staff in the industry as it can be given the structures they are rather familiar with such as the PID. Another advantage of the RS-NGMV is its model-based design that enables a faster adaptation to implement different systems. Features of the RS-NGMV are investigated throughout the thesis with case studies from trends in engineering like robotics, autonomous and electric vehicles. The results show that the RS-NGMV is highly capable of adapting to set-point changes, parameter variations with its ability to update the control gains rapidly by using optimizations. Some extensions of algorithms have also been studied following recent directions in optimal/predictive control resulting in a new preview control approach and Scheduled RS-NGMV control

    Cross Entropy-based Analysis of Spacecraft Control Systems

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    Space missions increasingly require sophisticated guidance, navigation and control algorithms, the development of which is reliant on verification and validation (V&V) techniques to ensure mission safety and success. A crucial element of V&V is the assessment of control system robust performance in the presence of uncertainty. In addition to estimating average performance under uncertainty, it is critical to determine the worst case performance. Industrial V&V approaches typically employ mu-analysis in the early control design stages, and Monte Carlo simulations on high-fidelity full engineering simulators at advanced stages of the design cycle. While highly capable, such techniques present a critical gap between pessimistic worst case estimates found using analytical methods, and the optimistic outlook often presented by Monte Carlo runs. Conservative worst case estimates are problematic because they can demand a controller redesign procedure, which is not justified if the poor performance is unlikely to occur. Gaining insight into the probability associated with the worst case performance is valuable in bridging this gap. It should be noted that due to the complexity of industrial-scale systems, V&V techniques are required to be capable of efficiently analysing non-linear models in the presence of significant uncertainty. As well, they must be computationally tractable. It is desirable that such techniques demand little engineering effort before each analysis, to be applied widely in industrial systems. Motivated by these factors, this thesis proposes and develops an efficient algorithm, based on the cross entropy simulation method. The proposed algorithm efficiently estimates the probabilities associated with various performance levels, from nominal performance up to degraded performance values, resulting in a curve of probabilities associated with various performance values. Such a curve is termed the probability profile of performance (PPoP), and is introduced as a tool that offers insight into a control system's performance, principally the probability associated with the worst case performance. The cross entropy-based robust performance analysis is implemented here on various industrial systems in European Space Agency-funded research projects. The implementation on autonomous rendezvous and docking models for the Mars Sample Return mission constitutes the core of the thesis. The proposed technique is implemented on high-fidelity models of the Vega launcher, as well as on a generic long coasting launcher upper stage. In summary, this thesis (a) develops an algorithm based on the cross entropy simulation method to estimate the probability associated with the worst case, (b) proposes the cross entropy-based PPoP tool to gain insight into system performance, (c) presents results of the robust performance analysis of three space industry systems using the proposed technique in conjunction with existing methods, and (d) proposes an integrated template for conducting robust performance analysis of linearised aerospace systems

    Model predictive control system design and implementation for spacecraft rendezvous

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    This paper presents the design and implementation of a model predictive control (MPC) system to guide and control a chasing spacecraft during rendezvous with a passive target spacecraft in an elliptical or circular orbit, from the point of target detection all the way to capture. To achieve an efficient system design, the rendezvous manoeuvre has been partitioned into three main phases based on the range of operation, plus a collision-avoidance manoeuvre to be used in event of a fault. Each has its own associated MPC controller. Linear time-varying models are used to enable trajectory predictions in elliptical orbits, whilst a variable prediction horizon is used to achieve finite-time completion of manoeuvres, and a 1-norm cost on velocity change minimises propellant consumption. Constraints are imposed to ensure that trajectories do not collide with the target. A key feature of the design is the implementation of non-convex constraints as switched convex constraints, enabling the use of convex linear and quadratic programming. The system is implemented using commercial-off-the-shelf tools with deployment using automatic code generation in mind, and validated by closed-loop simulation. A significant reduction in total propellant consumption in comparison with a baseline benchmark solution is observed

    Non-linear predictive generalised minimum variance state-dependent control

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    A non-linear predictive generalised minimum variance control algorithm is introduced for the control of nonlinear discrete-time state-dependent multivariable systems. The process model includes two different types of subsystems to provide a variety of means of modelling the system and inferential control of certain outputs is available. A state dependent output model is driven from an unstructured non-linear input subsystem which can include explicit transport delays. A multi-step predictive control cost function is to be minimised involving weighted error, and either absolute or incremental control signal costing terms. Different patterns of a reduced number of future controls can be used to limit the computational demands
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