Lurie Systems Stability Approach for Attraction Domain Estimation in the Wheeled Robot Control Problem

Fixed-Order H∞ Control Design via a Partially Augmented Lagrangian Method

<div class="htmlview paragraph">The Purdue Univ. soil-vehicle laboratory located in the Agricultural Engineering Building was used to study the effect of dual, single, and tandem drives on artificial soils. The dual versus single tire comparisons were made with 4.00 × 8 tires. Two tandem drive combinations were used. The first combination utilized 4.00 × 8 tires for both the front and rear wheels, and the second combination used a 4.00 × 8 tire for the front wheel and a 6.00 × 12 tire for the rear wheel.</div> <div class="htmlview paragraph">Dual tires performed better than single wheels of the same weight when tested on loose soils. The full advantage of dual tires was not obtained without lowering the inflation pressure below that of a single tire of the same weight.</div> <div class="htmlview paragraph">A weight distribution of 60% of the total weight on the front wheel produced better performance for the tandem drive using equal size tires than did the weight distribution of 50% or 40% on the front wheel. The performance at a tire pressure of 6 psi was superior to that at 9 and 12 psi.</div> <div class="htmlview paragraph">The performance of the tandem drive using the smaller front wheel was nearly equal for all weight distributions at higher tire pressures. However, at a tire pressure of 6 psi the weight distribution with 25% of the weight on the front wheel proved to have a higher tractive coefficient than either of the other two weight distributions of 35 or 45% on the front wheels.</div>

Linear matrix inequality (LMI) methods, novel techniques in solving optimisation problems, were introduced as a unified approach for vehicle's active suspension system controller design. LMI methods were used to provide improved and computationally efficient controller design techniques. The active suspension problem was formulated as a standard convex optimisation problem involving LMI constraints that can be solved efficiently using recently developed interior point optimisation methods. An LMI based controller for a vehicle system was developed. The controller design process involved setting up an optimisation problem with matrix inequality constraints. These LMI constraints were derived for a vehicle suspension system. The resulting LMI controller was then tested on a quarter-car model using computer simulations. The LMI controller results were compared with an optimal PID controller design solution. The LMI controller was further tested by incorporating a nonlinear term in the vehicle's suspension model; the LMI's controller degraded response was enhanced by using gain-scheduling techniques. The LMI controller with gain-scheduling gave good results in spite of the unmodelled dynamics in the suspension system, which was triggered by large deflections due to off-road driving.

An analysis of methods for calculating the distribution of normal reactions of the road between the axles of the tractor unit was carried out. It is shown that they are based on the misconception that traction forces and rolling resistance forces are applied in the spots of contact of the wheels with the road. The research shows that installing a towing link on a tractor self-propelled chassis through the rear suspension system at a level below the axis of the rear wheels (the diameter of which is larger in relation to the diameter of the front wheels) allows reducing the additional unloading of the front wheels. A more correct scheme of the tractor unit with the application of the traction force and the rolling resistance force on the wheel axles is calculated, which determines the increase in the total normal reaction on the front wheels of the tractor self-propelled chassis when working with the towing link. It is shown that an increase in the difference in the dynamic radii of the front and rear wheels, a decrease in the vertical coordinate of the center of mass of the tractor unit leads to an increase in the normal reaction of the road on the front wheels. Since the controllability of wheeled machines increases with the growth of the normal reaction on the front wheels, the presence of towing links with the attachment point located below the axis of the rear driving wheel increases the controllability of the tractor unit based on the self-propelled chassis. The problem of determining the total normal reaction of the road on the front wheels of a tractor self-propelled chassis with a trailing link in the case of application of the traction force and the force of movement resistance on the wheel axles has been solved. To increase the accuracy of finding the total normal reaction of the road on the front wheels of the tractor self-propelled chassis, which will allow to clarify the assessment of the controllability of the latter when moving with a towed link. Increasing the difference in the dynamic radii of the wheels and reducing the base of the tractor self-propelled chassis allows you to increase the value of the total normal reaction of the road on the wheels in relation to the horizontal reaction in the hinge of the axle of the trailer link. It was determined that the operation of the tractor self-propelled chassis with trailing links is characterized by a higher efficiency factor of its chassis compared to a universal tractor of class 0.6 and higher efforts under the condition that its front platform is loaded.

This paper investigates the effects of dissipativity on the performance of semiactive systems with smart dampers via linear matrix inequality (LMI) methods. First, a linear quadratic regulator (LQR) problem is defined in terms of a linear objective function and several LMI constraints. Second, two dissipativity indices are proposed to quantify the dissipative nature of a force. One of the dissipativity indices is appended as an LMI constraint in its weak form to the LMI-LQR problem to exploit the dissipative nature of a smart damper. The dissipativity indices and the proposed controller are employed for a two-degree-of-freedom structure with a clipped optimal control problem. It is observed that the proposed method is able to improve the dissipative nature of the controller, improving the semiactive performance.

How the Four Wheels should Share Forces in an Optimum Cooperative Chassis Control

Semidefinite programs derived from the Kalman-Yakubovich-Popov (KYP) lemma are quite common in control and signal processing applications. The programs are often of high dimension which makes them hard or impossible to solve with general-purpose solvers. Here we present a customized preprocessor, KYPD, that utilizes the inherent structure of this particular optimization problem. The key to an efficient implementation is to transform the optimization problem into an equivalent semidefinite program. This equivalent problem has much fewer variables and the matrices in the linear matrix inequality constraints are of low rank. KYPD can use any primal-dual solver for semidefinite programs as an underlying solver.

Approximately linear phase FIR filters with reduced group delays are desirable in certain applications. Conventional design methods indirectly achieve the desired group delay by approximating the complex frequency response, resulting in large group delay error, especially at the vicinity of the band edge. A new design method based on semidefinite programming is proposed. An explicit expression for the group delay of an FIR filter is given. With some approximations, a linear matrix inequality constraint on group delay is formulated so that approximately linear phase FIR filters with reduced group delays can be designed using the powerful semidefinite programming approach. An illustrative design example is presented.

Several important problems in control theory can be reformulated as semidefinite programming problems, i.e., minimization of a linear objective subject to linear matrix inequality (LMI) constraints. From convex optimization duality theory, conditions for infeasibility of the LMIs, as well as dual optimization problems, can be formulated. These can in turn be reinterpreted in control or system theoretic terms, often yielding new results or new proofs for existing results from control theory. We explore such connections for a few problems associated with linear time-invariant systems.

Frequency-based multivariable control design with stability margin constraints: A linear matrix inequality approach

Considered is the control design problem for planar motion of a wheeled robot. The mathematical model of the robot accounts for kinematic relationships between the velocity of a given point of chassis referred to as the reference point, orientation of the chassis, and control. Among the kinematic relations is the requirement that each of the four wheels perform a slip-free motion. The rear wheels are assumed to be driving while the front wheels are responsible for the rotation of the chassis. The control objective is to place the reference point in the prespecified trajectory and to stabilize the motion of the reference point along the prespecified trajectory. The trajectory consists of line segments and circular arcs. In the mathematical model under consideration, the current curvature of the trajectory of the reference point is taken as control; it is related to the steering angle of the front wheels by a simple algebraic expression. The control is subject to two-sided constraints due to limitations on the steering angle of the front wheels. For the control law proposed, the attraction domain in the space "distance to the trajectory—orientation" is analyzed. For the initial conditions from this domain, the system is guaranteed to hit a trajectory with given index of exponential stability.

This paper proposes an algorithm to obtain better results in the integrated control by reflecting the characteristics of the individual control of the front wheel and the rear wheel of tram systems. In the case of the surface transportation, which has recently been introduced, severely curved driving performance is required for the downtown. It is possible to decrease the curve radius and to improve the performance of the straight driving with the individual torque control. Therefore, the individual torque control performance of the motor is the most important point of the surface transportation. The front and rear wheels have different torque characteristics, and the length of the bogie during curve travel also affects these results. This system is more controllable than the system with 1Controller 4Motor (1C4M) in the form of 2C4M with the front and rear wheels being individually controlled, allowing more precise control because of its higher degree of freedom. Because of this individually controlled characteristic, it is possible to control more precisely in the integrated control considering the characteristics of the front wheel and the characteristics of the rear wheel. The validity of the proposed control algorithm is verified by experimental results using a small-scale bogie system.

Traditional structural feedback control systems are centralized systems. The applications of these systems to large scale structures usually encounter a number of difficulties regarding system reliability, cost, and feedback latency. Decentralized control strategies offer promising alternatives that can address some of these difficulties. When making control decisions, decentralized controllers may only require data from sensors located in the neighborhood of a control device. Control decentralization lowers the demand on communication range in the sensing and control network, reduces feedback latency, and removes the risk associated with a centralized controller where single-point failure can paralyze the entire control system. This paper presents a time-delayed decentralized structural control strategy that aims to minimize the H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> norm of the closed-loop system. Feedback time delay is included in the formulation for the decentralized controller design, which employs a homotopy method through linear matrix inequalities (LMI). Corresponding to certain decentralized feedback patterns, the homotopy method gradually degenerates a centralized control design into a decentralized control scheme. At each homotopy step, LMI constraints are satisfied to guarantee the performance requirement for the closed-loop H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> norm. The proposed algorithm is validated through numerical simulations with an example structure.

This paper deals with the guaranteed cost control problem for a class of uncertain linear discrete-time switched systems with time-delay under arbitrary switching laws. The purpose is to design a state feedback control law such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties. A sufficient condition on the existence of guaranteed cost controllers is derived based on Lyapunov theory together with linear matrix inequality (LMI) approach. Furthermore, a convex optimization problem with LMIs constraints is formulated to select the suboptimal guaranteed cost controller. A numerical example demonstrates the validity of the proposed design approach.

The problem of guaranteed cost (GC) control using static-state feedback controllers for uncertain linear discrete time-delayed systems subjected to actuator saturation is studied in this paper. The stability analysis of closed-loop systems is carried out using a Lyapunov-Krasovskii functional. Conditions for the existence of state-feedback GC controllers are developed using a linear matrix inequality (LMI)-based criterion. The approach ensures a sufficient performance bound over all the acceptable parameter uncertainties. The scheme of the optimal GC controller problem is framed as a convex optimization problem with LMI constraints. The design of GC controllers for discrete-time systems subjected to actuator saturation without considering the effect of state-delay is also discussed. The effectiveness of the proposed approach is illustrated using suitable examples.