Title Control synthesis versus saturation compensation for systems with rate and amplitude constraints

A control synthesis theory was proposed by Horowitz [2] to design a ‘three degrees of freedom’ controller for rate and amplitude constrained systems. Following anti-reset windup techniques, a saturation compensation structure was proposed to design compensators for given linear controllers 131. It is shown here that the compensator can be reformulated in terms of the control synthesis theory. Conversely, the ‘three degrees of freedom’ controller is a special case of the compensator construction. From this analysis, shortcomings (of the control synthesis theory are exposed and improvements using the compensator structure are discussed and illustrated by an example. 1 Tntroduction Practical control systems often encounter both rate and amplitude constraints from the actuators, reflecting physical bounds on finite power and energy transfers. In the literature, there are a few discussions on systems subject to both rate and amplitude constraints [2,5,7], with rate and amplitude constraints taken into account at the beginning of the controller designs. Alternative approach is to extend general actuator saturation compensators [4] for single constraints to systems subject to both rate and amplitude constraints [3]. Some recent theories of general anti-reset windup (ARW) [6,8] considered multiple saturation nonlinearities in parallel only, instead of in series as in rate and amplitude constrained systems. A ‘three degrees of freedom’ controller structure was proposed by Horowitz to handle both rate and amplitude constraints 121. Quantitalive feedback theory (QFT) was then used to design the controller to cater for the constraints and plant uncertainties. The synthesis theory was later extended to unstable plants [7] by restricting the controller outputs to within bounds. To this purpose a supervisory loop was introduced to adjust a nonlinear gain, inserted between the nominal controller ancl the actuator. Frequency domain techniques were used to design the nominal controller. The work in [5] considered the structure of amplitude nonlinearity before the rate nonlinearity. It also introduced a supervisory loop to ,idjust a nonlinear gain, called the error governor, in the closed-loop system. The error governor was inserted before the controller and adjusts the system error according to predetermined bounds. These works are viewed as control synthesis techniques as they are for controller design or to predetermine the control bounds. A compensator for both rate and amplitude WRL: http://hkumea. hku. hk/-khui constraints was proposed in [3]. Conditions for stability of the compensated system were derived and some guidelines for designing the compensators discussed. ARW methods are a posteriori techniques in that the compensators are fabricated for given controllers, which were designed assuming absence of saturation. The relationship between these two approaches is not yet available. In this work, the compensator structure [3] is reviewed in 92. The ‘three degrees of freedom’ control synthesis [2] is presented and reformulated as compensator structure in 93. It turns out to be a special case of the compensator discussed in $2. Compensator design methods for these two approaches are discussed next in $4, revealing some shortcomings of the synthesis theory. An illustrative example is presented in $5. 2 A Compensator Structure Let G be the transfer function of a plant, and the linear controller be described by (2.1) where y is the system output, w is the reference input and v is the controller output. R, S, T are polynomials in Laplace transform variable s or backward shift operator z-’ . R is monic. The arguments are omitted for convenience. The amplitude and rate constraints for the actuator are v = ( T / R ) w ( S / R ) y %ax 9 v 2 U, u(t) = v , U,nin I v I U, (2.2)