Jürgen Ackermann

Analysis and Design

By assuming controller structures in Chapter 2 we have generated several examples of closed-loop characteristic polynomials p(s, q,k), where the vector k contains the free design parameters in the fixed controller structure and q contains the uncertain plant parameters in a given operating domain Q, i.e. q ∈Q.

Parameter space design of robust control systems

Find a state or output feedback with fixed gains such that nice stability (defined by a region in the eigenvalue plane) is robust with respect to large plant parameter variations, sensor failures, and quantization effects in the controller. Keep the required magnitude of control inputs small in this design. A tool for tackling such problems by design in the controller parameter space K is introduced. Pole placement is formulated as an affine map from the space P of characteristic polynomial coefficients to the K space. This allows determining the regions in the K space, which place all eigenvalues in the desired region in the eigenvalue plane. Then tradeoffs among a variety of different design specifications can be made in K space. The use of this tool is illustrated by the design of a crane control system. Several open research problems result from this approach: graphical computer-aided design of robust systems, algebraic robustness conditions, and algorithms for iterative design of robust control systems.

Linear and nonlinear controller design for robust automatic steering

For an automatic steering problem of a city bus the reference maneuvers and specifications are introduced. The robustness problem arises from large variations in velocity, mass, and road-tire contact. Two controller structures, both with feedback of the lateral displacement and the yaw rate, are introduced: a linear controller and a nonlinear controller. The controller parameters are first hand-tuned and then refined by performance vector optimization. Both controllers meet all specifications. Their relative merits are analyzed in simulations for four typical driving maneuvers. >

Robust control prevents car skidding

The author discusses a system of robust unilateral decoupling of car steering dynamics. Its effect is that the driver has to concern himself much less with disturbance attenuation. The important quick reaction to disturbance torques is done by the automatic feedback system. The yaw dynamics no longer interfere with the path-following task of the driver. The safety advantages have been demonstrated in experiments with a test vehicle. By empirical improvements, we have modified the controller such that it preserves the robust decoupling advantages for the first 0.5 seconds after a disturbance and then returns the steering authority gradually back to the driver.

Robust yaw damping of cars with front and rear wheel steering

For a linear model of active car steering, a robust decoupling control law by feedback of the yaw rate to front wheel steering has previously been derived. This control law is extended by feedback of the yaw rate to rear wheel steering. A controller structure with one free damping parameter k/sub D/ is derived with the following properties: damping and natural frequency of the yaw mode are independent of speed; k/sub D/ can be adjusted to the desired damping level; and a variation of k/sub D/ has no influence on the natural frequency of the yaw mode and no influence on the steering transfer function by which the driver keeps the car-considered as a mass point at the front axle-on a planned path. Simulations with a nonlinear car steering model show significant safety advantages of the new control concept in situations when the driver of the conventional car has to stabilize unexpected yaw motions. >

Robust automatic steering control for look-down reference systems with front and rear sensors

This paper describes a robust control design for automatic steering of passenger cars. Previous studies showed that reliable automatic driving at highway speed may not be achieved under practical conditions with look-down reference systems which use only one sensor at the front bumper to measure the lateral displacement of the vehicle from the lane reference. An additional lateral displacement sensor is added here at the tail bumper to solve the automatic steering control problem. The control design is performed stepwise: an initial controller is determined using the parameter space approach in an invariance plane; and this controller is then refined to accommodate practical constraints and finally optimized using the multiobjective optimization program. The performance and robustness of the final controller was verified experimentally at California PATH in a series of test runs.

Robust decoupling, ideal steering dynamics and yaw stabilization of 4WS cars

Abstract Four-wheel car steering is modeled by a single-track model with nonlinear tire characteristics. A generic control law for robust decoupling of lateral and yaw motion by yaw-rate feedback to front-wheel steering is derived. Ideal steering dynamics are achieved by velocity-scheduled lateral acceleration feedback to front-wheel steering. For robust yaw stabilization a velocity-scheduled yaw-rate feedback to rear-wheel steering is given, by which the linearized system gets velocity-independent yaw eigenvalues.

Yaw disturbance attenuation by robust decoupling of car steering

Abstract Robust decoupling of the lateral and yaw motions of a car has been achieved by feedback of the integrated yaw rate into front wheel steering. In the present paper the yaw disturbance attenuation is analyzed for a generic single-track vehicle model. The frequency limit, up to which yaw disturbances are attenuated, is calculated. For specific vehicle data, it is shown that this control law significantly reduces the influence of yaw disturbances on yaw rate and side-slip angle for low frequencies. This safety advantage is experimentally verified for μ-split braking.

Robust car steering by yaw rate control

It is shown that feedback control can improve the robustness of the driver-car system with respect to uncertain operating conditions. Robustness is achieved by controlling the yaw rate instead of the steering angle. Integrating unit feedback of the yaw rate error makes the yaw mode unobservable from the front axle lateral acceleration and thereby take uncertainty out of the steering transfer function. Rear-wheel steering allows pole placement for the yaw mode. A main result of this study is a robust compensator/actuator design for all cars and all operating conditions. A further result applies to cars with additional rear-wheel steering. This second input can be used to place yaw-mode eigenvalues in desired locations. By the decoupling property, shifting of these eigenvalues has no influence on the transfer function from the steering wheel to the lateral acceleration of the front axle.<<ETX>>

Robust gamma-stability analysis in a plant parameter space

Abstract Given a characteristic polynomial whose coefficients depend polynomially on l uncertain parameters, the following robustness problem arises: Determine whether all the roots of the polynomial are located in a prescribed region Г in the complex plane for all admissible parameter values. To this end, the boundary ∂Г of Г is mapped into the parameter space. A necessary and sufficient condition for Г-stability of an operating domain in parameter space is that it contains at least one Г-stable point and is not intersected by the image of ∂Г. This condition may be tested graphically by gridding l − 2 parameters and projecting all boundaries into a two-dimensional subspace of the parameter space. Finally the method is applied to a track-guided bus with uncertain mass and velocity.