Robust Guaranteed-Cost Control for Half-Vehicle Active Suspension Systems Subject to Markovian Controller Uncertainties

Figures & data

Figure 1: Half vehicle active suspension system components diagram

Table 1: Half-vehicle active suspension system variables and parameters

Definition of the variable	Symbol	Definition of the parameter	Symbol
Front body displacement	$z_{\mathrm{sf}}\left(t\right)$	Distance between the front axle and the center of mass	$l_1$
Rear body displacement	$z_{\mathrm{sr}}\left(t\right)$	Distance between the rear axle and the center of mass	$l_2$
Front unsprung mass displacement	$z_{\mathrm{uf}}\left(t\right)$	Car body mass	$m_s$
Rear unsprung mass displacement	$z_{\mathrm{ur}}\left(t\right)$	Unsprung mass on the front wheel	$m_{\mathrm{uf}}$
Front terrain height displacement	$z_{\mathrm{rf}}\left(t\right)$	Unsprung mass on the rear wheel	$m_{\mathrm{ur}}$
Rear terrain height displacement	$z_{\mathrm{rr}}\left(t\right)$	Pitch moment of inertia about the center of mass	$I_{\phi }$
Pitch angle	$\phi \left(t\right)$	Stiffness of the passive elements of the front wheel	$c_{\mathrm{sf}}$
Center of mass Displacement	$z_c\left(t\right)$	Stiffness of the passive elements of the rear wheel	$c_{\mathrm{sr}}$
Front actuator force input	$u_f\left(t\right)$	Front tire stiffness	$k_{\mathrm{sf}}$
Rear actuator force input	$u_r\left(t\right)$	Rear tire stiffness	$k_{\mathrm{sr}}$

Figure 2: Ground velocities disturbances for the front (dashed line) and rear (solid line) wheels

Figure 3: Changing between two modes of the controller

Figure 4: Controlled states of the system

Figure 5: Controlled output z₁(t) = [z₁₁(t), z₁₂(t)]

Figure 6: Controlled outputs z₂(t) = [z₂₁(t), z₂₂(t), z₂₃(t), z₂₄(t)]

Figure 7: Control signal u(t) =[u₁(t), u₂(t)] of the system

Table 2: Parameters of simulated the active suspension system

Parameter	Value	Parameter	Value
$l_1$	1.3 m	$c_{\mathrm{sr}}$	1000 Ns/m
$l_2$	1.5 m	$k_{\mathrm{sf}}$	18.000 N/m
$m_s$	690 kg	$k_{\mathrm{sr}}$	22.000 N/m
$m_{\mathrm{uf}}$	40 kg	$k_{\mathrm{tf}}$	200.000 N/m
$m_{\mathrm{ur}}$	45 kg	$k_{\mathrm{tr}}$	200.000 N/m
$I_{\phi }$	1222 kgm^2	$z_{maxr}$	0.08
$c_{\mathrm{sf}}$	1000 Ns/m	$z_{maxf}$	0.08