Correlation-Based Tuning of a Restricted-Complexity Controller for an Active Suspension System

A correlation-based controller tuning method is proposed for the ``Design and optimization of restricted-complexity controllers'' benchmark problem. The approach originally proposed for model following is extended to solve the disturbance rejection problem. The idea is to tune the controller parameters such that the closed-loop output be uncorrelated with the disturbance signal. Since perfect decorrelation between the closed-loop output and the disturbance signal is not attainable in the restricted-complexity controller design, the cross correlation between these two signals is minimized iteratively using the stochastic approximation method. Since control specifications can normally be expressed in terms of constraints on the sensitivity functions, a frequency-domain analysis of the criterion is performed. Straightforward implementation of the proposed approach on the active suspension system of the Automatic Control Laboratory of Grenoble (LAG) provides a 2nd-order controller that meets the control specifications very well

Correlation-Based Tuning of a Restricted-Complexity Controller for an Active Suspension System

A correlation-based controller tuning method is proposed for the \Design and optimization of restricted-complexity controllers" benchmark problem. The approach originally proposed for model following is applied to solve the disturbance rejection problem. The idea is to tune the controller parameters such that the closed-loop output be uncorrelated with the measured disturbance. Since perfect decorrelation between the closed-loop output and the disturbance is not attainable with a restricted-complexity controller, the cross-correlation of these two signals is minimized. This is done iteratively using stochastic approximation. A frequency analysis of the tuning criterion allows dealing with control speci cations expressed in terms of constraints on the sensitivity functions. Application to the active suspension system of the Automatic Laboratory of Grenoble (LAG) provides a 2nd-order controller that meets the control speci cations to a large extent

Data-driven controller tuning using the correlation approach

The essential ingredients of control design procedures include the acquisition of process knowledge and its efficient integration into the controller. In many practical control applications, a reliable mathematical description of the plant is difficult or impossible to obtain, and the controller has to be designed on the basis of measurements. This thesis proposes a new datadriven method labeled Correlation-based Tuning (CbT). The underlying idea is inspired by the well-known correlation approach in system identification. The controller parameters are tuned iteratively either to decorrelate the closed-loop output error between designed and achieved closed-loop systems with the external reference signal (decorrelation procedure) or to reduce this correlation (correlation reduction). Ideally, the resulting closedloop output error contains only the contribution of the noise and perfect model-following can be achieved. By the very nature of the control design criterion, the controller parameters are asymptotically insensitive to noise. Both theoretical and implementation aspects of CbT are treated. For the decorrelation procedure, a correlation equation is solved using the stochastic approximation method. The iterative procedure converges to the solution of the correlation equation even in the case when an approximate gradient of the closed-loop output error with respect to controller The asymptotic distribution of the resulting controller parameter estimates is analyzed. When perfect decorrelation is not possible, the correlation reduction method can be used. That is, instead of solving the correlation equation, the norm of a cross-correlation function is minimized. A frequency domain analysis of the criterion shows that the algorithm minimizes the two-norm of the difference between the achieved and designed closed-loop systems.With the correlation reduction method, an unbiased estimate of the gradient of the closed-loop output error is necessary to guarantee convergence of the algorithm to a local minimum of the criterion. Furthermore, this criterion can be generalized to allow handling the mixed sensitivity specifications. An extension of this method for the tuning of linear time-invariant multivariable controllers is proposed for both procedures. CbT allows tuning some of the elements of the controller transfer function matrix to satisfy the desired closed-loop performance, while the other elements are tuned to mutually decouple the closed-loop outputs. The tuning of all decouplers and controllers can be made by performing only one experiment per iteration regardless of the number of inputs and outputs since all reference signals can be excited simultaneously. However, due to the fact that decoupling is imposed as a design criterion, simultaneous excitation of all references brings a negative impact on the variance of the estimated controller parameters. In fact, one must choose between low experimental cost (simultaneous excitation) and better accuracy of the estimated parameters (sequential excitation). The CbT algorithm has been tested on numerous simulation examples and implemented experimentally on a magnetic suspension system and the active suspension system benchmark problem proposed for a special issue of European Journal of Control on the design and optimization of restricted-complexity controllers

Control of an Active Suspension System as a Benchmark for Design and Optimization of Restricted Complexity Controllers

A benchmark problem for restricted complexity controller design is introduced. The objective is to design the lowest-order controller which meets the control specifications for an active suspension system. The input-output data of the plant are provided on the benchmark site and the final controllers are evaluated using the closed-loop data. Thirteen solutions proposed to solve the benchmark problem are briefly presented and classified in terms of methodology and compared with respect to their complexity and performance

A pneumatic semi-active control methodology for vibration control of air spring based suspension systems

This research investigates a pneumatic suspension system containing an air spring, air flow valve, and an accumulator, where the spring and damping functions are combined into one package. The spring and accumulator provide the spring characteristics, and the computer controlled adjustable valve provides the damping characteristics by automatically adjusting the air flow between the air spring and the accumulator. An extensive analysis and investigation of the plant dynamics is performed. A dynamic plant model is developed and tuned to experimental data. The plant model is then used in the design of a semi-active control system. A detailed description of the model tuning procedure is provided. Based upon the insights gained through analysis and system identification, a semi-active control methodology is developed, which exploits certain unique features of the system. Three potential controllers are developed and compared, where each controller uses different measurement feedback signals. However, all three controllers measure direct force generation through a pressure feedback signal. Both experimental and simulation data for the controllers is provided. The first controller uses an LQI (Linear Quadratic Impulse) optimal solution, based on Covariance Control Theory, to generate an optimal active damping control force, along with a Set-Point plus PI tracking controller to adjust the valve opening to cause the system to track this desired force during a switching event or control window of opportunity. The second controller uses a Modified Skyhook solution to generate the ideal tracking signal, along with a Set-Point plus PI tracking controller. The LQI controller is used in simulation (offline) to aid in setting the skyhook gain on the Modified Skyhook controller. The third controller uses a Relative Displacement solution to generate the ideal tracking signal, along with a Set-Point plus PI tracking controller. The LQI controller is used (offline) to aid in setting the gain on the Relative Displacement controller. This controller is probably the most useful for vehicular applications, since only relative coordinates and a pressure are required for feedback. It was found that all three controllers could track an optimally generated active signal during the switching event, provided the proper gains were chosen

Advance control strategies for Maglev suspension systems

The Birmingham Maglev developed over fifteen years ago has successfully demonstrated the inherent advantages of low speed maglev over comparable wheeled systems. It remains the only commercially operational Maglev in the world today. To develop the next generation of Maglev vehicles which will overcome some of the limitations of the Birmingham system, such as chassis length and cost, the following issues are addressed in this thesis. 1) The possibility of interaction between the chassis resonant frequencies and the suspension control system causing poor ride quality and at worst instability, are formally analysed. In the Birmingham vehicle a stiff chassis (fundamental bending mode 40Hz) is used avoiding significant interaction with the suspension controller. Using advanced control strategies the low frequency chassis resonances can be controlled allowing a vehicle structure to be used with a fundamental bending mode of about 12Hz. 2) A modem control strategy is developed which delivers an improved ride quality compared with the present classical control system despite having to operate with a 'soft' chassis. Kalman filters are digitally implemented and conclusions drawn about their performance. The classical control strategy is also successfully demonstrated on a 3 m long 'flexible beam' rig. 3) An associated Maglev suspension problem for the response to ramp inputs such as the transition onto gradients which causes either a large steady state tracking error or a worsening ride quality is addressed by modern control theory using integral feedback techniques and classical theory using third order filters. These controllers are globally optimised by a multi-objective parameter optimisation system which formally considers the conflicts inherent in a suspension system between response to stochastic inputs and deterministic inputs

An investigation of multibody system modelling and control analysis techniques for the development of advanced suspension systems in passenger cars

The subject of this thesis is the investigation of multibody system modelling and control analysis techniques for the development of advanced suspension systems in passenger cars. A review of the application of automatic control to all areas of automotive vehicles illustrated the important factors in such developments, including motivating influences, constraints and methodologies used. A further review of specific applications for advanced suspension systems highlighted a major discrepancy between the significant claims of theoretical performance benefits and the scarcity of successful practical implementations. This discrepancy was the result of idealistic analytical studies producing unrealistic solutions with little regard for practical constraints. The predominant application of prototype testing methods in implementation studies also resulted in reduced potential performance improvements. This work addressed this gap by the application of realistic modelling and control design techniques to practical realistic suspension systems. Multibody system modelling techniques were used to develop vehicle models incorporating realistic representations of the suspension system itself, with the ability to include models of the controllers, and facilitate control analysis tasks. These models were first used to address ride control for fully active suspension systems. Both state space techniques, including linear quadratic regulator and pole placement and frequency domain design methods were applied. For the multivariable frequency domain study, dyadic expansion techniques were used to decouple the system into single input single output systems representing each of the sprung mass modes. Both discretely and continuously variable damping systems were then addressed with a range of control strategies, including analytical solutions based on the active results and heuristic rule-based approaches. The controllers based on active solutions were reduced to satisfy realistic practical limitations of the achievable damping force. The heuristic techniques included standard rule-based controllers using Boolean logic for the discretely variable case, and fuzzy logic controllers for the continuously variable case