Nonlinear sliding sector design for multi‐input systems with application to helicopter control

Abstract

Summary The ability of helicopters to hover and land vertically has spurred an interesting field of research on the development of autonomous flight for these rotatory wing aircrafts. Linear control theory with gain scheduling, which is based on linearizing the system at the equilibrium points, dominated the helicopter autopilot design. Unlike the linear cascaded autopilot structure used in the existing literature, this paper uses state‐dependent linear like structure, including rate‐limited actuator dynamics, with cascaded autopilot topology. This approach allows nonlinear control laws to be implemented throughout the entire flight envelope, providing satisfactory robustness and stability over the various parameter uncertainties and time delays. The cascaded autopilot topology with nonlinear dynamical equations contains a new sliding sector control (SSC) mechanism which is derived for multi‐input nonlinear dynamical systems. The proposed SSC structure for multi‐input nonlinear systems is used in the inner loop of the cascaded autopilot system where the fastest dynamics are required to be controlled for rapid changes in the helicopter dynamical characteristics which enables one to stabilize the helicopter over a wide range of flight conditions. The proposed cascaded autopilot topology with the new SSC mechanism is tested in simulations to assess its robustness and stability properties. To establish its feasibility, the proposed control method is replaced with a suboptimal control method, namely state‐dependent differential Riccati equation (SDDRE) method, for the inner loop and the results of the proposed control architecture are compared with those of SDDRE method.

Quantized‐feedback hands‐off control for nonlinear systems

“…With the design of an inner [, ] sector ℵ i (18) and an outer [, ] sector ℵ o (19) as a subset of [, ] sector ℵ, a switching function 𝜒(𝜚(𝜁), 𝜉(𝜁)) that depends on 𝜚(𝜁) and 𝜉(𝜁) is defined as…”

“…These estimated regions provide the existence of global asymptotic stability for the closed-loop system, as cited in [12][13][14]. Moreover, many other publications are available for defining a region of attraction for several systems in [16][17][18]. All these designs involve the solution of the Riccati equation to decide its boundaries.…”

Observer‐based robust optimal control for helicopter with uncertainties and disturbances

“…In order to achieve robustness and good convergence, various methods have been investigated to deal with the control problem of helicopters subjected to model uncer-tainty and external disturbance [4,5]. As we all known, optimal control theory is one of the most widely studied techniques for helicopter control problems, such as LQR [6], SDRE [7], pseudospectral method [8], and MPC [9]. The linear optimal control method cannot provide a good performance due to the significant nonlinearity of helicopter system, and a nonlinear optimal controller is computationally expensive because of solving the Hamilton-Jacobi-Bellman (HJB) equation online [10][11][12].…”

Nonlinear State Dependent Sliding Sector Control of Gimbal Systems

“…Disturbances and unmatched uncertainty cases are also considered [12]. The nonlinear sliding sector is used for a MIMO case with the help of multiple sliding sectors and results are demonstrated with an autopilot design of a specific helicopter application [13]. Another application area of sliding sector control is the control of civil structures.…”