A comparison of two robust control techniques for throttle valve control subject to nonlinear friction

Throttle valves for internal combustion engines suffer from considerable nonlinear friction in their mechanisms that is difficult to model and subject to significant variations due to changes in temperature and wear over the lifetime. The stick slip friction component is particularly troublesome. This presents a challenge to control system designers when it is important to obtain a prescribed dynamic response to reference input position changes. The contributions of this paper are a) the comparison of two different robust control techniques (sliding mode control and observer based robust control) aimed at overcoming this difficulty and b) a new simple but accurate nonlinear friction model for simulation. The control system performances using these techniques are compared with one another and with the performance attainable with a conventional PI controller

Forced dynamic control: a model based control technique illustrated by a road vehicle control application

Forced dynamic control (FDC) is a generally applicable model based control technique in the time domain originated by the author (Dodds, 2005), extending to nonlinear multivariable plants, which takes advantage of modern digital processor implementation. The closed-loop system is forced to obey a specified dynamics, which may be linear or nonlinear. The plant model and the FDC can be formulated in the continuous or discrete time domain and a general theory is presented, with the aid of a newly defined differential/difference operator. The control method is exemplified by its application for adaptive cruise control (ACC) in which an additional throttle input to the driver’s input is the control variable which modifies the road traffic dynamics to damp the well known wave motion that can build up in trails of vehicles on a motorway, thereby preventing traffic congestion. The Golzis- Herman-Rothery (GHR) vehicle following model is used. The simulations demonstrate very effective control

Hyper Sliding Mode Control: A Novel Approach Achieving Robustness With Model Order Uncertainty

A novel approach to the control of plants with model order uncertainty as well as parametric errors and external disturbances is presented, which yields a specified closed loop dynamic response. Its foundations lie in sliding mode control, but the set of output derivatives fed back extend to a maximum order of rmax −1, where rmax is the maximum likely rank of the plant. In conventional sliding mode control, the number of output derivatives fed back is a set of state variables equal in number to r −1, where r is the rank of the plant and derivatives of higher order than r −1, which are not state variables, are not fed back, meaning that the plant order must be known in advance. In hyper sliding mode control, originated by the author, although the output derivatives of higher order than r are not plant state variables, they become state variables of the closed-loop system and take part in the sliding mode. Thus, in cases where the maximum order of the output derivative exceeds r −1, the order of the closed-loop system is greater than that of the plant, which is a small price to pay for retaining the extreme robustness properties of sliding mode control. The method is illustrated by means of simulations of a motion control system employing a permanent magnet synchronous motor. An initial evaluation of the method is made by considering three plants with different orders and ranks, the first being the unloaded drive, the second being the drive controlling the motor rotor angle with a mass-spring load attached and the third being the drive controlling the load mass angle of the same attached mass-spring load. The simulations indicate that the control system does indeed yield robustness including plant order uncertainty

Settling time formulae for the design of control systems with linear closed loop dynamics

Two settling time formulae are numerically derived with the 5% and 2% criteria for the step responses of control systems having linear closed loop dynamics that may be designed by the method of pole assignment to have multiple closed loop poles. The formula is shown to be accurate for closed loop systems of up to tenth order. To clarify the use of the formulae, model based and robust control system designs are carried out for a high precision vacuum air bearing application and experimental results presented

Observer based robust control

This paper presents an original contribution to the field of robust control. Plant order uncertainty as well as parametric uncertainty is catered for while guaranteeing not only closed loop stability but also a precisely prescribed closed loop dynamic response to the reference inputs. The method extends to nonlinear multivariable plants. Its ability to control plants having different orders without adjustment and yielding the same closed-loop dynamics is demonstrated by simulation of its application to speed control and position control of a permanent magnet synchronous motor drive. The model of the plant used in the observer can simply be a chain of integrators driven by each control variable, at least equal in number to the rank of the plant with respect to the associated controlled output. The controller is simple, requires no adjustment and requires little more computational power than a typical classical PID controller

Sliding mode vector control of PMSM drives with flexible couplings in motion control

A new control system for permanent magnet synchronous motor electric drives with a significant torsion vibration mode in the mechanical coupling is presented based entirely on sliding mode principles to achieve robustness against external load torques and parametric modelling uncertainties. The user is only required to provide the demanded position and specify the settling time, no controller tuning being necessary. The vector control condition of keeping the direct axis current component approximately zero is satisfied as well as controlling either the rotor or load position to follow the demanded position with prescribed closed loop dynamics. To avoid control chatter, a boundary layer is introduced by replacing the relay control switching transfer characteristic (signum function) by a high gain having the same control saturation limits. Any steady state errors with a constant demanded rotor angle due to the finite value of the aforementioned gain are eliminated by means of an outer integral control loop. The simulations predict that the desired robustness will be achieved

A comparison of fixed final time optimal control computational methods with a view to closed loop implementation using artificial neural networks

The purpose of this paper is to lay the foundations of a new generation of closed loop optimal control laws based on the plant state space model and implemented using artificial neural networks. The basis is the long established open loop methods of Bellman and Pontryagin, which compute optimal controls off line and apply them subsequently in real time. They are therefore open loop methods and during the period leading up to the present century, they have been abandoned by the mainstream control researchers due to a) the fundamental drawback of susceptibility to plant modelling errors and external disturbances and b) the lack of success in deriving closed loop versions in all but the simplest and often unrealistic cases. The recent energy crisis, however, has promoted the authors to revisit the classical optimal control methods with a view to deriving new practicable closed loop optimal control laws that could save terawatts of electrical energy by replacement of classical controllers throughout industry. First Bellman’s and Pontryagin’s methods are compared regarding ease of computation. Then a new optimal state feedback controller is proposed based on the training of artificial neural networks with the computed optimal controls

Genetic algorithm based design optimisation for permanent magnet synchronous motors

This research work presents a new and efficient design methodology for the specification, development and manufacture of permanent magnet synchronous motors (PMSMs). In this paper a genetic algorithm based design optimisation technique for PMSMs is presented in which the multicriteria considered in the optimisation are the electromagnetic performance, the thermal performance and the material cost. Models have been developed for each criterion in order to calculate the objective vector. A software tool called PMSM Analyser was developed to assist the motor design methodology. The optimisation algorithms and the electromagnetic, thermal and cost models were integrated and interfaced using this software. The programme is demonstrated for the design of a 12 slot 10 pole PMSM. The design parameter vector contains stator bore diameter, stator tooth thickness and stator back iron thickness. For the base design the outer diameter of the stator is 180mm and the stack length of the motor is 90mm. The base design refers to the design before optimisation and the optimal design refers to the design with optimised dimensions. The optimisation programme predicts significant improvements over the baseline design and experimental results are presented which indicate good agreement with the predictions of the programme. The new approach has been used successfully in the development and design of a PMSM with a stall torque of 125Nm, rated torque of 75Nm at 1500r/min and output power of 12kW. The strengths of the design methodology are summarised with the genetic algorithm optimisation, innovative multi-objective handling and design models for the various disciplines of PMSM development

Forced dynamic control of non-minimum-phase plants via study of the classical inverted pendulum

The general problem of controlling a non-minimum-phase plant is tackled via study of the classical inverted pendulum (IP). A full nonlinear model of the IP is used for simulation and a linearised version is used for the controller design. The trolley position is controlled while keeping the pendulum inverted by use of an input/output feedback linearisation method called Forced Dynamic Control (FDC). This is generally more straightforward to apply than conventional techniques such as linear state feedback with pole assignment but in its basic form yields right half plane zero cancellation which creates an unstable closed loop mode. This is circumvented in this paper by creating an artificial controlled output that is a weighted sum of the state variables such that the right half plane zeros do not exist in the transfer function. Furthermore a non-oscillatory response with a specified settling time is achieved with the aid of the Dodds settling time formula (Dodds, 2008). The computational delay introduced to eliminate the algebraic loop in the nonlinear model is shown to have a negligible effect. Simulations are presented that demonstrate the correct operation of the control system and determine differences between the ideal and actual step responses due to the nonlinearities, parametric errors and external disturbances

Closed-loop control using a backpropagation algorithm: a practicable approach for energy loss minimisation in electrical drives.

In general, optimal controls are computed off line and subsequently applied in real time but this approach is impracticable due to lack of robustness with respect to the plant modelling errors and unknown external disturbances. Closed loop versions of these optimal controls could circumvent this problem but are only available in the analytical form for very simple cases, not including minimisation of frictional energy loss in motion control systems, which is the aim of the research programme. The approach suggested by Matieni and Dodds (2009), however, overcomes this obstacle by training an artificial neural network (ANN) to reproduce the optimal control values computed off-line from given states and reference inputs, thereby yielding a closed loop solution. The purpose of this paper is to present the results of an initial simulation experiment to assess the capability of a Multilayered Perceptron (MLP), in the backpropagation mode, to perform a direct state feedback function, which, to the authors‘ knowledge, is new. A known linear state feedback controller for a double integrator plant is used for this purpose. The control law is used to train the MLP. Then a simulation of the closed loop system formed using this MLP is compared with a simulation of the known linear state feedback control system. The results show that the closed loop step response with the MLP closely follows that of the conventional system