This article formulates the control problem of underactuated mobile robot as servo constraint-following, and develops a novel constraint-following servo control approach for underactuated mobile robot under both servo soft and hard constraints. Servo soft constraints are expressed as equalities, which may be holonomic or non-holonomic. Servo hard constraints are expressed as inequalities. It is required that the underactuated mobile robot motion eventually converges to servo soft constraints, and satisfies servo hard constraints at all times. Diffeomorphism is employed to incorporate hard constraints into soft constraints, yielding new soft constraints to relax hard constraints. By this, we design a constraint-following servo control based on the new servo soft constraints, which drives the system to strictly follow the original servo soft and hard constraints. The effectiveness of the proposed approach is proved by rigorous proof and simulations.
This study investigates the angle tracking control of the electric power steering system, which is underactuated and with (possibly fast) time-varying uncertainties. We design the control based on constraint-following, that is, formulating the tracking goal as servo constraints. To tackle the uncertainty, especially the mismatched uncertainty, a robust control is proposed with two-layer performance: deterministically guaranteed and fuzzily optimized. Particularly, the control design is implemented in three steps. First, without considering uncertainty, a nominal control is designed. Second, an uncertainty decomposition technique is presented to account for uncertainty, which creatively allocates the mismatched uncertainty for the robust control design that also builds on the nominal system control. The robust scheme is deterministic without using any “if–then” rules and guarantees uniform boundedness and uniform ultimate boundedness for the system, that is, the deterministically guaranteed performance. Third, by using fuzzy set theory to describe uncertainty, a fuzzy-based performance index, including system performance and control cost, is introduced. A control parameter optimal design problem is formulated and analytically solved, that is, the fuzzily optimized performance. The effectiveness of the proposed approach is illustrated by rigorous proof and the simulation results on the electric power steering system.
Oscillation suppression is essential for the stability design of electric power steering (EPS) systems. The stability controller module in EPS controller is the key to solve the stability control problem of EPS system. This paper proposes a new method of stability analysis and stability controller module design for EPS systems. Furthermore, the dynamic characteristics of the EPS system are analyzed, and two critical factors on the resulting EPS stability, that is, large assist and variable assist gain are investigated experimentally. The transfer function from steering torque to sensor torque is redefined. A new transfer function is proposed for measuring the effect of variable assist gain on system performance. Based on the above factors and transfer functions, constraints on the stability controller design are proposed. Then the optimal parameters in the controller are obtained by maximizing an objective function including phase margin, gain margin, and crossover frequency. It is concluded from simulations and bench tests that the proposed stability controller can significantly reduce the torque oscillation of the EPS system.
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